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  • 1
    Electronic Resource
    Electronic Resource
    A combined octree/delaunay method for fully automatic 3-D mesh generation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 37-55 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Fully automatic three-dimensional mesh generation is a fundamental requirement for automating the numerical solution of partial differential equations. Two techniques in particular - the octree and Delaunay approaches - have been used towards this end. A method that combines both approaches to fully automatic mesh generation is presented here. The resulting algorithm provides the linear growth rate and divide-and-conquer approach of the octree method with the simplicity and optimal properties of the Delaunay triangulation.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290105
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  • 2
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    A hybrid/mixed model for non-linear shell analysis and its applications to large-rotation problemsThis work is supported by National Science Foundation, under Research Grant Number EET-8714628 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 407-446 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Adopting an updated Lagrange approach, the general framework for the fully non-linear analysis of curved shells is developed using a simple quadrilateral C0 model (HMSH5). The governing equations are derived based on a consistent linearization of an incremental mixed variational principle of the modified Hellinger/Reissner type with independent assumptions for displacement and strain fields. Emphasis is placed on devising effective solution procedures to deal with large rotations in space, finite stretches and generalized rate-type material models. In particular, a geometrically exact scheme for configuration update is developed by making use of the so-called exponential mapping algorithm, and the resulting element was shown to exhibit a quadratic rate of (asymptotic) convergence in solving practical shell problems with Newton-Raphson type iterative schemes. For the purpose of updating the spatial stress field of the element, an ‘objective’ generalized midpoint integration rule is utilized, which relies crucially on the concept of polar decomposition for the deformation gradient, and is in keeping with the underlying mixed method. Finally, the effectiveness and practical usefulness of the HMSH5 element are demonstrated through a number of test cases involving beams, plates and shells undergoing very large displacements and rotations.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290213
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  • 3
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    Formulation of implicit finite element methods for multiplicative finite deformation plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 483-514 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Some constitutive and computational aspects of finite deformation plasticity are discussed. Attention is restricted to multiplicative theories of plasticity, in which the deformation gradients are assumed to be decomposable into elastic and plastic terms. It is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non-symmetric even for associated plastic flow. Both explicit (i.e. no equilibrium iteration) and implicit finite element formulations are considered. An assumed strain formulation is used to accommodate the near-incompressibility associated with fully developed isochoric plastic flow. As an example of explicit integration, the rate tangent modulus method is reviewed in some detail. An implicit scheme is derived for which the consistent tangents, resulting in quadratic convergence of the equilibrium iterations, can be written out in closed form for arbitrary material models. All the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly. Examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290304
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  • 4
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    Model reduction for thermal diffusion: Application of the Eitelberg, Marshall and aggregation methods to a heat transmission tube model (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 599-617 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This study, dealing with model reduction for thermal diffusion, describes the numerical techniques used: the Eitelberg, Marshall and aggregation methods. The non-linear model of a heat transmission tube, to which these methods are applied, is then described, pointing out the necessary initial algebraic treatment for reduction. Finally the outputs of the complete model and of several reduced ones are compared for some characteristic variations of the inputs. For this problem, the Eitelberg and Marshall methods, which can be used with a high coefficient of reduction, are well adapted.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290309
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  • 5
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    Singular behaviour near an interface crack tip of power law hardening materials using The Finite Element Iterative Method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 699-717 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Finite Element Iterative Method (FEIM) is extended to the analysis of asymptotic fields of materials with non-linear behaviour. It is used in the investigation of the asymptotic field of an interfacial crack of power law hardening materials. The material is assumed to deform according to the total deformation theory of plasticity. The results of the analysis provide evidence to support the hypothesis that the asymptotic field can be cast in the form of the HRR-singularity multiplied by a function of the product form. This function can be written as a series of oscillatory functions, similar to those encountered in an elastic field, each of which is valid over a substantial range of the process zone. The real part of these terms depends on the loading mode, process zone size as well as material properties; it is, however, very small compared to the HRR-singularity. The imaginary part which gives the phase shift is much smaller than the elastic value and is a weak function of the hardening power and the size of the process zone of interest; it eventually vanished at extremely small distances.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290403
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  • 6
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    Consistent force resultant distributions in displacement elements with varying sectional properties (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 775-783 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Force fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a ‘consistent’ relationship to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu-Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles.It follows that the extremely general Hu-Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field-inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290407
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  • 7
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    Improved hybrid solid element with a traction-free cylindrical surface (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 801-809 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: New 8-node solid elements with two parallel faces and one traction-free cylindrical surface are derived using the assumed stress hybrid model. Six new expressions of stress components are developed by using four stress functions and cylindrical co-ordinates, so that the normal stress σz on the plane perpendicular to the two parallel faces varies as a parabola, and the assumed stress field satisfies the equilibrium equations as well as the traction-free conditions over the cylindrical boundary. The assumed stress field also satisfies the compatibility conditions when the new element is degenerated into the 2-dimensional case. Examples have clearly demonstrated that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress σz.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290409
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  • 8
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    Explicit integration for three-dimensional degenerated shell finite elements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 861-880 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Explicit integration across the thickness for three-dimensional degenerated shell finite elements is analysed. For this purpose a modifed formulation is proposed. The Jacobian matrix of the physical-parameter spaces transformation is decomposed into a product of ‘in-middle-surface’ and ‘out-of-middle-surface’ terms. This enables an expansion to be carried out of the strain-displacement matrix into power series of the thickness variable. Explicit integration is then performed and the corresponding formulae of the stiffness and mass matrices are given. The possibility of ‘locking’ for thin structures is explained. The analysis is applied to homogeneous and multilayered structures. Numerical applications for linear problems are given in the last part of the paper.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290413
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  • 9
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    A semi-analytical method for time-domain analyses of dam-reservoir interactions (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 913-933 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Non-linear responses of dam-reservoir systems are not well understood, because of the lack of an exact time-domain solution for the far field (extending to infinity) of the fluid. This paper presents a procedure for efficient time-domain analyses. It is based on a semi-analytical solution and is suitable for the determination of the interactive behaviour of dam-reservoir systems.In this formulation, the fluid domain is divided into a near (to the dam) field, which is finite, and a far field extending to infinity. Arbitrary shapes of the upstream face of the dam, and of the bottom of the reservoir floor in the near field, are presumed. Furthermore, the far field is assumed to have a constant depth. The irregular near field is modelled by using the finite element method. A time-domain semi-analytical solution is obtained for the far field. For a vertical dam subjected to earthquake and ramp loadings, numerical solutions obtained compared well with the piecewise exact form of the analytical solution.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290502
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  • 10
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    Advanced development of time-domain BEM for two-dimensional scalar wave propagation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1003-1020 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved formulation for solving 2D transient scalar wave propagation problems by the Boundary Element Method (BEM) is presented. The kernels presented are simpler and better behaved than those that have appeared in the published literature. An appropriate set of temporal shape functions for linear variation is used. For spatial variations isoparametric quadratic elements are used. All of these represent significant improvements over the present level of sophistication in the analysis of 2D transient scalar problems. The algorithm is implemented in a general purpose boundary element code known as GPBEST.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290507
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  • 11
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    Time-domain radiation boundary for analysis of plane Love-wave propagation problem (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1049-1063 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new method of modelling the radiation effect in a time-domain finite element analysis of semi-infinite solids is proposed. The domain to be analysed is divided into a finite, interior region and a semi-infinite, exterior region. The standard finite elements are used to model the interior region. An infinite element is used to model the semi-infinite region. The main feature of the proposed method is the selection of semi-infinite shape functions to develop the infinite element. A procedure is proposed whereby the necessary shape functions are derived directly from frequency-domain analytical mode shapes. The interior and exterior regions are coupled by enforcing displacement continuity at the interface. The validity of the method is demonstrated in this paper by analysing a two-dimensional, linear (damped), anti-plane, shear-wave (plane Love-wave) propagation problem. The results obtained by the proposed method are compared with those obtained by direct finite element analysis with a fixed boundary placed sufficiently far from the location of loading to avoid wave reflections.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290510
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  • 12
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    A new implementation of the Lanczos method in linear problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 141-159 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Lanczos algorithm has proved to be a powerful solution method not only for finding the eigenvalues but for solving linear systems of equations. In this work a new implementation of the algorithm is presented for solving linear systems of equations with a sequence of right-hand sides. The versions of the method proposed in the past treat the right-hand side vectors successively by keeping the tridiagonal matrix and the orthonormal basis in fast or secondary storage. The new technique handles all approximations to the solution vectors simultaneously without the necessity for keeping the tridiagonal matrix or the orthonormal basis in fast or secondary storage. Thus, when the first solution vector has converged to a required accuracy good approximations to the remaining solution vectors have simultaneously been obtained. It then takes fewer iterations to reach the final accuracy by working separately on each of the remaining vectors.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290110
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  • 13
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    A non-proportional loading finite element analysis of continuum damage mechanics for ductile fracture (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 197-209 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of a finite element analysis based on an anisotropic model of continuum damage mechanics theory proposed recently by the authors for ductile fracture under non-proportional loading. The condition of non-proportional loading is formulated by introducing a dynamic co-ordinate system of principal damage allowing the principal direction of damage during the loading to rotate accordingly.The finite element analysis developed under non-proportional loading is applied to predict the crack initiation load of a centre-cracked plate under uniform loading. The predicted load agrees satisfactorily with those determined experimentally with centre-cracked thin plates made of aluminium alloy 2024-T3. The analysis also reveals under non-proportional loading the hysteresis effect of the principal directions of damage and stress. In addition, the influence of varying anisotropic damage coefficients on the crack initiation load and the crack tip displacement profile is also examined. The larger the degree of the anisotropy, the higher the crack initiation load. The magnitude of the crack tip displacement profile is found to be proportional to the degree of material anisotropy.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620290113
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  • 14
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 449-452 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290215
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  • 15
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    Non-linear optimization technique for partial solution of generalized eigenvalue problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 473-482 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an alternative to the subspace iteration and Lanczos techniques, both of which are now used to solve partial eigenvalues and eigenvectors of large generalized linear first order symmetric matrix systems. It is based on non-linear optimization of a modified Rayleigh quotient. The elements of the eigenvector are the decision variables. Orthogonality constraints with respect to the two matrices are incorporated in the sequential unconstrained optimization scheme. By imposing normality with respect to one of the matrices, the Hessian matrix reduces to a much simpler form for which the Woodburry transformation may be used. This, in combination with the fact that the banded structure of the matrices is maintained, results in a number of operations of the same order as the two standard methods. Shifting is readily integrated. Numerical comparison with existing techniques demonstrate the practicality of this method.
    Additional Material: 7 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620290303
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  • 16
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    Importance and use of rigid body mode in boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 453-472 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The superposition of a rigid body mode on a body should result in a corresponding change in displacement values but should not affect the stresses. However, in the numerical solution by the boundary element method (BEM) large errors may be obtained for displacements and stresses if a rigid body mode is present in the input data. To eliminate the effects of the rigid body mode on the numerical accuracy of the solution, the fundamental solutions for displacements must be correctly interpreted and used. The rigid body mode may be unknowingly present in the boundary condition data. It may be present because the boundary data are not known accurately. Or it may be present if the displacement values at the support have been computed from a separate analysis. A rigid body mode may arise due to the collocation nature of satisfying the boundary conditions. The point values of the applied load at the collocation point may not satisfy equilibrium. Or the point values of the specified displacements may not satisfy the condition of zero translation and rotation. For bodies under pure traction, we know that the analytical solution can contain an arbitrary amount of rigid body mode. Numerically, however, some unknown value is assigned to this rigid body mode. It might be desirable (for example in limit analysis) to eliminate the rigid body mode from the displacements to obtain deformation of a point with respect to a point on the body. In addition, knowledge and elimination of the rigid body mode is necessary for the implementation of a scheme described by this author in an earlier work. The importance of the earlier work is that it reduced the sensitivity of the BEM to changes and errors in the input data. In this paper the causes, and the effects of the rigid body mode on the BEM, the correct interpretation of the fundamental solution for displacements and an algorithm for determining and accounting for the rigid body mode are discussed. A numerical example validates the ideas in this paper for the indirect version. The algorithm for the direct version is presented without a numerical example in the Appendices.
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    URL: http://dx.doi.org/10.1002/nme.1620290302
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  • 17
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    A panel method computation for oscillating aerofoil in compressible flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 559-578 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A panel method using source and doublet singularity has been proposed to solve for subcritical aerodynamics of a two dimensional steady and unsteady aerofoil. The source singularities are placed on the aerofoil surface. The doublet singularity is distributed by a function along the chordline of the aerofoil; this distribution is further projected downstream into infinity.The aerodynamics of an oscillating aerofoil is investigated. The governing unsteady linearized potential equation has a Hankel function as its fundamental solution, which is a source type function. A combination of source and doublet singularity is therefore used for solving the unsteady compressible problem by means of the panel method, this methodology being an extension of a steady aerofoil formulation. Incremental effects of profile change in aerofoil and wake geometry are accounted for. A surface boundary condition is applied on the stationary mean aerofoil surface with time dependent geometrical changes accounted for. An unsteady Kutta condition of equal pressure across the trailing edge is assumed. Results are presented on the aerodynamic influence of Mach number, oscillating frequency parameter, angle of incidence and change of pivoting point. Results are also compared with linear theory, a subsonic experimental result and a subcritical solution of a transonic model.
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    URL: http://dx.doi.org/10.1002/nme.1620290307
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  • 18
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    A new approach in non-linear mechanics: The large time increment method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 647-663 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non-linearities and is tested on some examples in elastoplasticity. The method considerably reduces the number of transfers between local and global levels, hence the numerical cost of calculation is also diminished.
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    URL: http://dx.doi.org/10.1002/nme.1620290312
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  • 19
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    Vibration analysis of fluid-solid systems using a finite element displacement formulationThis research was sponsored by the Lawrence Livermore National Laboratory under contract CERDA LLNL-1513603. This support and the interest of Dr G. L. Goudreau are gratefully acknowledged. (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 683-698 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This report presents a finite element solution for the vibration interaction between an inviscid fluid and a solid. The equation of motion governing the inviscid fluid is expressed in terms of the displacements. This ensures that compatibility and equilibrium will be satisfied automatically along the interface of the coupled systems. To suppress circulation modes with non-zero energy, reduced integration is used when computing the element stiffness matrix contributed by the fluid. In addition, a projection is used on the element mass matrix in order to remove the spurious modes which result from the use of reduced integration. Numerical examples for both fluid and coupled fluid-solid systems are performed and the results are shown.
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    URL: http://dx.doi.org/10.1002/nme.1620290402
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  • 20
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    A dynamic contact buckling analysis by the penalty finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 755-774 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper deals with the application of the finite element method to dynamic contact buckling problems. The penalty function method is applied to incorporate the contact conditions in the equation of motion and a trial-and-error method is employed to obtain the converged contact state. Numerical examples are analysed to show the effectiveness and the validity of the method, and it is applied to a dynamic buckling problem involving contact phenomena.
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    URL: http://dx.doi.org/10.1002/nme.1620290406
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  • 21
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    The dynamic response of compliant materials to an impulsive pressure field (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 811-831 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic interaction between a compliant material and an impulsive pressure field, periodic in space and instantaneous in time, was examined as a first step at modelling the interaction between organized structures in a turbulent boundary layer and a compliant surface. The interaction, modelled two-dimensionally, was treated dynamically by matching the pressure forces to the surface stresses in the compliant material at each instant of time. A new boundary element method was formulated to model the compliant material which was treated as a linear isotropic material, elastic in dilatation and viscoelastic (Standard) in shear. The inertial forces and viscoelastic creep stresses have been included in this formulation as transient body forces. The elastic interaction was characterized by a non-dimensional threshold velocity, above which the elastic instabilities grew temporally and spatially in the downstream direction to produce a non-linear breakdown of the interaction. Freestream velocities as high as 9CT (shear wave speed) were found to produce stable elastic interactions. Thinner materials produced smaller amplitude waves of higher frequencies that grew more rapidly than those in thicker materials. The stability characteristics were independent of the location of the compliant material with respect to the spatial distribution of the pressure pulse. For viscoelastic interactions, the stability curve, which serves as a bound on the types of materials capable of producing drag reduction, shows distinct regions of elastic types of interactions (Class B) and damping dominated interactions (Class A) as a function of the constants of the rheological model describing the compliant material. Class A disturbances in these interactions show slower growth or decay than Class B disturbances.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 909-912 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620290415
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    A finite element formulation for the coupled thermoviscoelastic response of solid-fluid systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 953-968 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The coupled thermoviscoelastic response of a solid-fluid system is computed by a finite element formulation which involves only temperature and displacement fields. The Laplace transform with respect to time is applied to the coupled equations. This results in a global matrix in the transform domain that is symmetric and banded and the time response is obtained by numerical inversion of the transformed solution. Also, this formulation permits the use of fractional derivatives to model viscoelastic material behaviour.
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    A subspace forward iteration method for solving the quadratic eigenproblem associated with the FDE formulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 935-951 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents the development of an efficient and numerically stable algorithm for accurately computing the eigensolutions of the quadratic real symmetric eigenproblem arising in the finite dynamic element (FDE) formulation. Closely related to the subspace forward iteration method, the proposed scheme is well suited to extracting the lowest natural frequencies and associated mode shapes of large practical eigenproblems, takes full advantage of the banded configuration of the stiffness, inertia and dynamic correction matrices involved in the eigenproblem and ensures a monotonic convergence from above to the required eigenpairs. A shifting technique for convergence acceleration and an eigenpair verification scheme are also presented. Numerical examples are shown demonstrating the excellent performance of the solution procedure.
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    URL: http://dx.doi.org/10.1002/nme.1620290503
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    Application of the boundary element method to non-linear diffusion with reaction problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1021-1031 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral solution method based on the concept of the direct boundary element technique has been applied to develop a solution procedure for problems of diffusion with a non-linear reaction in one dimension. The non-linearity is handled by a process of quasi-linearization over subintervals or elements in the main domain of integration. The weighting functions are defined for each subinterval such that the discretization is exact for the corresponding linear problem. This leads to a new powerful and simple method for the solution of this class of problems. A banded global matrix is obtained with both the concentration and its gradient as the unknown variables, and the problem is solved in an iterative manner. Illustrative results are presented for a test problem of diffusion with a second order reaction in an infinite slab, an infinite cylinder and spherical geometries. The accuracy of the method for situations with a sharp concentration gradient is demonstrated. The technique can also be used to numerically compute the solution in the boundary layer for fast reactions.
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    Flow through fissured porous media with deformable matrix (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1079-1094 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An approach, which is based on the double porosity concept and takes into account pore deformation, has been presented to derive a set of coupled differential equations governing the behaviour of fissured porous media. This approach has resulted in a set of non-linear (variable coefficient) differential equations. Various coefficients involved in the formulation have been explicitly defined in terms of measurable physical parameters. The finite element technique has been employed as the numerical tool for the solution of these equations. The results based on the proposed non-linear formulation have been compared with those of previously presented linear (constant coefficient) formulations. It is found that, in relatively rigid formations, the linearity assumption is quite reasonable and can successfully model the behaviour of fissured porous media. However, in very deformable formations, the linearity assumption could lead to a significant level of error in the numerical solutions.
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    Validation of structural computation codes in elastoviscoplasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1109-1130 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses various procedures for the implementation of viscoplastic constitutive equations in Finite Element Codes. The set of constitutive equations that has been used is described. Several kinds of implementation, using various numerical techniques, are proposed. Validations of these implementations and comparisons between them are investigated by means of a set of simple but comprehensive examples.
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    A finite element methodology to predictage-related mechanical property and structural performance changes in high performance polymers (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1159-1175 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The treatment of ageing processes in polymers by the finite element (FE) method is described. The development of this analytical method is motivated by the need to assess the effects of ageing on the structural performance of polymers and polymeric composites, particularly when the structures are large and expensive to replace. Also, there is a need to assess the effectiveness of corrective action options when ageing problems do occur, which can be treated by this method. The method describes the treatment of multiple, reactive chemical species in multi-layered polymeric materials by the finite element method. Example problems featuring the simultaneous diffusion and chemical reaction are illustrated: a simple problem of binary diffusion and reaction with comparison of numerical to exact results, and the staged ageing/structural analysis of a solid rocket motor.
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    Application of the zienkiewicz-zhu error estimator for plate and shell analysis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1281-1298 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An effective and efficient error estimation scheme for finite element plate and shell analysis is presented. The error estimate method proposed is applicable to all the plate and shell elements developed using either classical plate and shell or continuum mechanics theories. The global error in energy norm is computed by summing all the elemental errors. The method is well suited for adaptive mesh refinement as the error contribution for each element is known. Demonstration examples using uniform and adaptive refinement schemes for both the plate and shell analysis show the effectiveness of the method proposed.
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    An approach to the generation of triangular grids possessing few obtuse triangles (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1299-1321 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A triangular mesh generator is presented which makes extensive use of side swapping and mesh smoothing to create a grid with few obtuse triangles. To perform the above task a data structure is presented which holds full adjacency information both for nodes and elements. It is shown how this data structure is employed in the process mesh generation, and how the methods of computational geometry such as region decomposition are used not only to decompose a complex region, but also to reflect the boundary grading into the interior the region. Algorithms are provided to show the mechanism of these processes and practical examples are given to support the approach.
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    Least-squares characteristics and finite elements for advection-dispersion simulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1343-1358 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The method of characteristics is combined with the method of least-squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split-operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection-dispersion simulation.
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    A robust self-starting explicit computational methodology for structural dynamic applications: Architecture and representations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1441-1454 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Conventional approaches for computational structural dynamics (CSD) relevant to time-integration methods involve first employing the classical Galerkin formulations for the spatial discretization to yield a set of ordinary differential equations in time and then employing finite difference approximations for deriving the appropriate step-by-step algorithms. And, almost all of the widely advocated (existing) step-by-step schemes for structural dynamics require an initial acceleration vector to be specified (evaluated) in addition to displacement and velocity vectors for starting the schemes. Unlike the above, in this paper we introduce new representations and architecture towards providing not only direct self-starting features with the elimination of acceleration computations but also for enhancing the computational architecture itself via several other inherent distinguishing characteristics. Thereby, a robust and effective methodology of computation is presented which is an extension of our previous efforts (see Tamma and Namburu3). In particular, to illustrate the basic concepts, in this paper we focus attention on the development of explicit time-integration formulations. The methodology involves expressing the governing dynamic equations of motion in conservation form, and firstly temporal discretization is accomplished in the spirit of Lax-Wendroff-type formulations. Therein, discretization in space is accomplished by introducing stress-based representations and employing the classical Galerkin scheme, and, quite naturally, we advocate employing finite elements as the principal computational tool because of its several inherent advantages. The stability and accuracy of the proposed formulations and the several added distinguishing features are briefly highlighted. Considerations on the effects of damping are additionally included and the introduction of general boundary conditions in a natural setting permits an effective generalized architecture for general applications. Numerical test models are presented to validate the overall developments for computational structural dynamics.
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    Two-dimensional mesh generation, adaptive remeshing and refinement (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1501-1526 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses the generation of unstructured triangular meshes by the advancing front technique. We also employ the technique to discretize surfaces. A simple and effective algorithm for the specification of element sizes is described. A similar idea is then applied to adaptive remeshing where a completely new mesh is created on the basis of the isolines of a certain important variable. The isolines are obtained from the FE-calculation based on the previous mesh. In this paper, attention is focused on the Poisson's equation. The optimal a priori error estimate for the problem is used to estimate the number of isolines needed for the remeshing. When the estimated error exceeds the tolerance in only a small part of the domain, the adaptive procedure is switched automatically to an adaptive refinement.
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    Development of an automatic, two-dimensional finite element mesh generator using quadrilateral elements and Bezier curve boundary definition (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1551-1567 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes the development of an automatic, two-dimensional, quadrilateral element mesh generator. The methodology is based on the looping algorithm developed in part by Dr M. L. C. Sluiter. Bezier curves are used to define the boundaries of the parts to be meshed. The required interaction by the user is reduced to specifying the boundary geometry, the preferred element size and the refinement coefficient. Transition elements are automatically generated between regions of varying element sizes. The ability to offset specified boundary curves insures well-conditioned elements along the boundary. Meshes for several sample geometries are presented to illustrate the versatility of the mesh generator.
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    A class of mixed assumed strain methods and the method of incompatible modesResearch supported by AFOSR under contract nos. 2-DJA-544 and 2-DJA-771 with Stanford University (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1595-1638 
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    Keywords: Engineering ; Engineering General
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    Notes: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.
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    Solution of radiative problems using variational based finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1701-1714 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The calculation of temperature distributions for systems exchanging radiation heat requires as a first step the determination of the heat fluxes caused by radiation at its surfaces. The functional of the variational principle is the starting point of a numerical solution method.By using finite element procedures a system of linear equations is derived, which supplies an approximation of the radiosity. Having the radiosity, the heat flux at the surfaces, which governs the boundary condition for the temperature distribution in the structure, can be calculated. A method of determining the view-factors using the concept of the finite element method is also given.
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    Dynamics of multibody systems, A. A. Shabana, Wiley, New York, 1989. No. of pages: 480. ISBN 0-471-61494-7. price £39.30/$63.20 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1797-1797 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620290812
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    A use of linear programming for the analysis of plane strain rigid-plastic flow (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1-12 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an application of linear programming for the analysis of plane strain rigid-plastic flow. First, linear programming and the theory of a rigid-plastic material are briefly revised. The implementation of linear programming for rigid-plastic flow is then described. The method is to subdivide the material into rigid triangular blocks which may slide upon each other, dissipating energy at a rate proportional to the rate of sliding. Many different modes of deformation are possible; linear programming is used to select the mode that gives the least rate of total energy dissipation. The indentation of a strip by blunt-nosed indenters is used as an example. Results of the linear programming method are compared with the exact slip line field solutions.
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    A new approach to boundary modelling for finite difference applications in solid mechanics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 99-113 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Procedures for extending the useful scope of the finite difference method in solid mechanics applications are presented. The improvements centre around the introduction of the physical nature of the deformations into the equations used to formulate the approximate solution. This is accomplished by evaluating the coefficients of Taylor series expansions for the displacement approximations in terms of rigid body motions, strains and derivatives of strains. This procedure is demonstrated with plane stress applications. The ability to interpret the derivative approximations physically allows the fictitious nodes typical of the finite difference method to be rationally incorporated into the model as a means of enforcing traction boundary conditions. An example problem is solved using both regular and irregular meshes. The displacements and stresses compare well with finite element solutions.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 201-205 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    A finite element simulation of metal flow in moulds (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 821-831 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical tools for simulating the casting process are employed in an increasing manner by foundry engineers in order to understand and improve casting techniques. The correct simulation of metal flow and temperature profiles during filling is an important part of an overall numerical simulation kit which includes solidification and residual stress evaluations.In this study, we develop a two-dimensional finite element model for studying metal flow and temperature fields during filling of mould cavities. A proper choice of turbulent/laminar model, correct tracking of metal free surface and evaluation of temperature to include metal-air-sand interaction are some of the essential features of the model.
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    A layered composite shell element for elastic and thermoelastic stress and stability analysis at large deformations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 833-858 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite shell element for layered fibre reinforced composite shells has been developed. The degeneration principle is used in combination with specific kinematic assumptions. The thermo-elastic material is either described by the behaviour of the local components, i.e. fibre and matrix material laws and geometrical configuration in each layer, or by the overall orthotropic layer material laws.Thickness integration for obtaining the different contributions to the shell element's stiffness matrix is performed analytically and prior to the numerical in-plane integration. This leads to a considerable saving in computer time during the incremental-iterative analysis.Geometrical non-linearities in terms of large deformations and material non-linearities in terms of layer craccking are taken into account. Accompanying eigenvalue analyses allow the determination of the - sometimes rather complicated - buckling behaviour with non-linear prebuckling deformations.
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    Fixed grid techniques for phase change problems: A review (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 875-898 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim of this paper is to categorize the major fixed grid formulations and solution methods for conduction controlled phase change problems. Using a two phase model of a solid/liquid phase change, the basic enthalpy equation is derived. Starting from this equation, a number of alternative formulations are obtained. All the formulations are reduced to a standard form. From this standard form, finite element and finite volume discretizations are developed. These discretizations are used as the basis for a number of fixed grid numerical solution techniques for solidification phase change systems. In particular, various apparent capacity and source based enthalpy methods are explored.
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    A numerical study of three-dimensional natural convection during freezing of water (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 899-914 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical study of three-dimensional natural convection with phase change in a rectangular parallelepiped is described. The fluid has temperature-dependent variable properties. The governing equations are approximated by finite differences, second order in space and first order in time. A boundary-fitted co-ordinate system is implemented to predict the shape and the movement of the solid-liquid interface. Preliminary results have been obtained for freezing of water in a cube for Rayleigh numbers in the range of about 105-106.
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    Conference diary (1990)
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    International Journal for Numerical Methods in Engineering 30 (1990), S. 391-395 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Finite element modelling of crack tip behaviour in viscoelastic materials. Part I: Linear behaviour (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 371-387 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A finite element algorithm which can be used to model either linear or non-linear viscoelastic material behaviour is described. The algorithm is verified for the linear case by comparing numerical and analytical solutions for (a) a uniaxial tensile specimen, and (b) an infinite plate with a hole subjected to a remote uniaxial stress. The algorithm is then used to determine the stress and strain fields near the tip of a moving crack in a linear viscoelastic medium. Numerical solutions for both growing and healing cracks are compared with results expected based upon the extended correspondence principle. Excellent agreement between theoretical and numerical solutions is obtained in all cases. Sources of numerical error in the FE solution procedure are identified and documented. The algorithm has not been verified for the non-linear case, since (except for very simple geometries and loading configurations) no closed-form solutions involving non-linear viscoelastic material behaviour are available. A comparison between the measured and predicted response of a non-linear viscoelastic material behaviour will be presented in a following paper.
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    A robust quadrilateral membrane finite element with drilling degrees of freedom (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 445-457 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A quadrilateral membrane finite element with drilling degrees of freedom is derived from variational principles employing an independent rotation field. Both displacement based and mixed approaches are investigated. The element exhibits excellent accuracy characteristics. When combined with a plate bending element, the element provides an efficient tool for linear analysis of shells.
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    Towards adaptive mesh refinement: Application of new rectangular hybrid finite elements in 2D elasticity problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 473-489 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A modified global approach to choosing stress terms for hybrid finite elements in plane stress problems is based on the known requirement of minimum number of stress parameters. Let nβ be the number of independent β-stress parameters, nq the number of nodal displacements and nR the number of rigid body degrees of freedom, then the satisfaction of the criterion nβ ≥ nq - nR of the assembled structure instead of the individual element enables the reduction of nβ. New rectangular hybrid transition elements applied in adaptive mesh refinement and a new eight node rectangular invariant element including only 12 β parameters, based on the modified criterion, are presented here.The new elements, which are used in order to analyse the stress singularity of two bonded elastic plates of different materials, yield reliable results compared with results based on classical hybrid elements, displacement elements and the analytic solution.
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    Specifications of boundary conditions for Reissner/Mindlin plate bending finite elements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 981-1011 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Plate bending finite elements based on the Reissner/Mindlin theory offer improved possibilities to pursue reliable finite element analyses. The physical behaviour near the boundary can be modelled in a realistic manner and inherent limitations in the Kirchhoff plate bending elements when modelling curved boundaries can easily be avoided. However, the boundary conditions used are crucial for the quality of the solution. We identify the part of the Reissner/Mindlin solution that controls the boundary layer and examine the behaviour near smooth edges and corners. The presence of boundary layers of different strengths for different sets of boundary conditions is noted. For a corner with soft simply supported edges the boundary layer removes the singular behaviour of Kirchhoff type from the stress resultants. We demonstrate the theoretical results by some numerical studies on simple plate structures which are discretized by an accurate, higher-order plate element. The results provide guidance in choosing efficient meshes and appropriate boundary conditions in finite element analyses.
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    Errata (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. ii 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620300702
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    Effect of the coupling between stretching and bending in the large displacement analysis of plates (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1233-1262 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The effect of the rotary inertia on the non-linear dynamics of plates that undergo a large reference displacement is examined in this paper. An assumed displacement field that accounts for the coupling between the stretching and bending of the plate as the result of considering the effect of the rotary inertia is used to identify the configuration of the plate. Furthermore, the coupling between the stretching and bending of the plate as the result of finite rotation is also considered in this investigation. Based on the assumed displacement field that accounts for the effect of the rotary inertia, a non-linear finite element formulation is developed for the large displacement analysis of plates. The element equations of motion are expressed in terms of a set of element invariants that depend on the assumed displacement field as well as the rotary inertia. The use of the formulation presented in this paper is demonstrated using numerical examples.
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    Curved Mindlin beam and axi-symmetric shell elements - A new approach (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1263-1274 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Two sets of strain definitions for analysis of curved Mindlin beams and axi-symmetric shells are examined. Their conventional finite element implementations are shown to be unsuitable. The parameter used as a nodal degree of freedom in the first conventional method to describe the cross section rotation is in general a discontinuous function and has no clear physical meaning. The second conventional method has relied on an incorrect differentiation for its successful use in finite element analysis. A new approach which overcomes these problems is presented. Examples are given to illustrate the incorrect results that can be obtained from the two conventional methods and to show that the new approach provides accurate solutions to general curved beam and axi-symmetric shell problems.
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    Announcements (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1360-1362 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Numerical analysis, algorithms and computation, by J. Murphy, D. Ridout and Brigid McShane. Publisher: Ellis Horwood, Chichester; No. of pages: 150; ISBN 0-85312-751-4 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1357-1357 
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    Keywords: Engineering ; Engineering General
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    URL: http://dx.doi.org/10.1002/nme.1620300711
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    Books received (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1358-1359 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1363-1366 
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620300801
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    Preface (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1367-1367 
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    Keywords: Engineering ; Engineering General
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    Finite element analysis of mixing phenomena in tangential twin-screw extruders for non-Newtonian fluids (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1369-1383 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A flow analysis of non-Newtonian fluids inside co-rotating tangential twin-screw extruders is presented with the emphasis on mixing phenomena. A new simplified approach was proposed in modelling the flow, i.e. the flow in twin-screw extruders was considered as a sequence of flows in two regions: (i) the translation region (T-region), similar to a single-screw extruder; and (ii) the mixing region (M-region), representing the central part of twin-screw extruders. The flow has been assumed to be isothermal, steady-state and creeping. Furthermore, it was assumed that the velocity field does not change significantly in one co-ordinate (i.e. the down-channel direction in the case of the T-region and the axial direction in the case of the M-region) as compared with the other co-ordinate directions. Accordingly, a quasi-three-dimensional finite element method has been developed to analyse the flows in both regions. The mixing mechanisms inside the T - and M-regions were analysed and the inter-channel mixing in the M-region was quantified. The residence time distribution and performance characteristic of a single screw with a self-wiping profile were also calculated.
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    Finite element procedures for strain estimations of sheet metal forming parts (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1385-1401 
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    Keywords: Engineering ; Engineering General
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    Notes: A finite element algorithm is developed to predict the strain distribution of sheet forming parts and to evaluate their formability at the design stage. The algorithm is simply called the inverse approach since we know the positions of the material points on the final product and we determine the positions of the corresponding material points in the initial blank. This is also a direct algorithm which avoids the path dependent incremental procedure of plasticity and contact. This paper presents some theoretical aspects related to the large logarithmic strains with membrane triangular elements, the deformation theory of plasticity, the isotropic and anisotropic material properties of metal sheets and the non-linear solution techniques. Some particular problems are also studied, such as the influence of friction forces under the punch and blankholders, the ‘optimization’ of the initial blank's contour and the deep drawing in several steps. The results are compared with those obtained by experiments and by the more classical incremental approach.
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    Bulge predictions in steady state bar rolling processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1403-1413 
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    Keywords: Engineering ; Engineering General
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    Notes: A new algorithm for free surface corrections in Eulerian finite element computations is presented and applied to a steady state bar rolling process to predict lateral spread. A variety of rolling geometries are examined, including differing height to width ratios and reductions. The bulge profiles, as well as the maximum and mean bulge amounts, are compared in detail with experiments.
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    Application of the finite element method to the simulation of sheet forming processes: Comparison of calculations and experiments (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1415-1430 
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    Notes: Elastic-plastic finite element calculations have been carried out to analyse sheet forming processes such as hydrostatic bulging of circular and rectangular blanks and the axisymmetric stretching of sheets (with different punch radii). The results, partly obtained by different finite element models, are compared with experimental data. It could be shown that, regarding the examples considered, experiments and calculations fit well and that a more sophisticated modelling of the contact boundary conditions improves the accuracy of the results. As a first attempt to handle more complex sheet forming operations, the deep drawing of a rectangular cup has been analysed. A summary of the theoretical background as well as some comments on the solution method and the implementation are given.
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    Compatible description of tool surfaces and FEM meshes for analysing sheet forming operations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1471-1502 
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    Keywords: Engineering ; Engineering General
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    Notes: Implementation of the 3-D finite element method (FEM) of sheet forming operations has proceeded slowly. In particular, describing the arbitrary tool surfaces in an accurate and smooth manner, with well behaved first and second derivatives, has been a major obstacle. A new geometric method, suitable for representing any rigid tool surface, has been developed and shown to be superior to the usual schemes. The new method relies on the described tool surface for position data only. The spatial derivatives are obtained by considering only the sheet mesh nodal positions. This new scheme has been implemented with a rigid-viscoplastic FEM program using general surface descriptions based on B-splines and linear inter-polation. Analytic representations of a hemispherical and rounded square punch were also compared. the comparisons show that the proposed method offers several advantages over other general formulations.1. The new representation is the proper one for formulating the equilibrium condition. Alternate forms can produce spurious results.2. The proposed method introduces inherently smooth surface derivatives that improve numerical stability, even with crude surface resolution. Suitable test problems show covergence with the new method far past the divergence points of the simulations using the standard general surface description.3. The method is reasonably efficient, with a time penalty of approximately 30-50 per cent (unoptimized) with respect to analytic surface descriptions.
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    Numerical analysis of polymer injection moulding process using finite element method with marker particles (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1569-1576 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical method for analysing an axisymmetric injection moulding process is presented. A consistent approximation to pressure is applied for a penalty function formulation of Galerkin's finite element method. To analyse the moving free surface and visualize the transient flow pattern, marker particles are introduced. An axisymmetric abrupt cavity, which is filled with a generalized Newtonian fluid, is solved to verify the scheme. As a practical example problem, the transient flow through moulds of a memory disc is analysed.
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    A flow formulation for rate equilibrium equations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 1619-1632 
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    Notes: A succinct derivation of a rate equilibrium equation is presented. An Eulerian finite element flow formulation is then developed for the direct solution of the steady state velocity field and Cauchy stress field within an elasto-plastic material. The formulation is used for the analysis of strip drawing.
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    An alternative numerical procedure for simulating the dynamical response of non-linear elastic rods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 123-139 
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    Keywords: Engineering ; Engineering General
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    Notes: In this paper there is presented an alternative numerical procedure for obtaining approximations to non-linear conservation laws like those that describe the dynamical behaviour of elastic rods (composed of materials whose stress-strain relation is non-linear). The above-mentioned procedure consists of approximating the solution of the Riemann problem (associated with the considered conservation law) by a piecewise constant function (satisfying the jump conditions) and using Glimm's scheme for advancing in time, step by step. The proposed numerical approach eliminates the necessity of solving (in a complete way) the associated Riemann problem, easing and cheapening its computational implementation. This procedure is employed for simulating the dynamical response of an elastic-non-linear rod, fixed at its edges, that is left in a non-equilibrium state. There is presented a comparison between results obtained through a classical procedure and through the procedure proposed in this work.
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    Effects of material non-linearity on the residual stresses in a dendritic silicon crystal ribbonThis paper presents results of research performed for the FSA project, Jet Propulsion Laboratory, California Institute of Technology sponsored by the U.S. Department of Energy through an interagency agreement with NASA (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 181-195 
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    Keywords: Engineering ; Engineering General
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    Notes: Thermal stresses developed in a dendritic silicon crystal ribbon have been shown to cause plastic deformation and residual stresses in the ribbon. This paper presents an implementation of a numerical model proposed for thermo-elasto-plastic behaviour of a material. The model has been used to study the effects of plasticity of silicon on the residual stresses. The material properties required to implement this model are all assumed, and the response of the material to the variations in these assumed parameters of the constitutive law and in the finite element mesh is investigated. The steady state growth process is observed to be periodic with non-zero residual stresses. Numerical difficulties are also encountered in the computer solution process, resulting in sharp jumps and large oscillations in the stress responses.
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620290201
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    Higher derivative explicit one step methods for non-linear dynamic problems. Part I: Design and theory (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 275-290 
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    Notes: A new higher order explicit one step scheme is presented for use in the solution of a certain class of non-linear problems in structural dynamics. The generalized scheme covers some recently developed multistep algorithms as well as some new one step methods with improved numerical properties. A weighted residual approach is used which contains new aspects for design of single step algorithms. Accuracy and stability are investigated for linear and non-linear systems. Algorithms with higher accurary than the central difference method are developed and optimized to minimize the reduction in the stability limit.
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    Studies in anisotropic plasticity with reference to the Hill criterion (1990)
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 315-336 
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    Notes: Algorithms based upon the notion of return mapping have been developed for the Hill yield function of anisotropic plasticity. The relative accuracy of two algorithms is assessed by means of iso-error maps. The choice of the algorithm turns out to be much more critical for the orthotropic Hill criterion than for the underlying isotropic von Mises plasticity model. A tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator. The model has been applied to three shell/plate structures.
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    Inelastic transient dynamic analysis of three-dimensional problems by BEM (1990)
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    International Journal for Numerical Methods in Engineering 29 (1990), S. 371-390 
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    Notes: A direct Boundary Element formulation and its numerical implementation for inelastic transient dynamic analysis of three-dimensional solids is presented. The formulation is based on an initial stress approach and is the first ever of its kind in the field of the Boundary Element Method. This formulation employs the Navier-Cauchy equation of motion, Graffi's dynamic reciprocal theorem, Stokes' fundamental solution and the Divergence theorem, together with Kinematical and Constitutive equations to obtain the pertinent integral equations of the problem in the time domain within the context of small displacement theory of elastoplasticity. The boundary integral equations are cast in an incremental form, in which elastoplastic relations of the incremental type are used for the material description. These equations are then solved using a time-stepping algorithm in conjunction with an iterative solution scheme to satisfy the constitutive relations. Higher order shape functions are used to approximate the field quantities in space as well as in time. Finally, the applicability of this methodology is demonstrated by presenting a few example problems.
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    Two-level domain decomposition preconditioning for the p-version finite element method in three dimensionsThis research was partially sponsored by the National Science Foundation under grant DMS-8704169. This paper was presented at the Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, U.S.A., April 9-14, 1989 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1095-1108 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p-version finite element method for three-dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds.
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    An embedding method for the numerical solution of the cathode design problem in electrochemical machining (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1177-1192 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An embedding method is considered for the numerical determination of the cathode shape for a given anode shape in a two-dimensional electrolytic cell. Reference is made to an analytic solution to illustrate the difficulties which have to be overcome by any numerical method applied to this ill-posed problem. The embedding method searches amongst the direct solutions (i.e. anodes for given cathodes) since these, resulting from a well-posed problem, are less troublesome to compute. For anodes of the form βG(x), x the transverse direction, the embedding method gives good results for β less than 30-60 percent of the β for which the cathode first contains cusps or becomes triple-valued. It is shown that the embedding method performs better than some other numerical methods in overcoming the error growth difficulties associated with the illposedness of the problem.
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    Advanced time-domain formulation of BEM for two-dimensional transient elastodynamics (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1421-1440 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, a new formulation for two-dimensional time-domain transient elastodynamic analysis by the Boundary Element Method (BEM) is presented. The traction kernel is derived by using the causality of the waves and the resulting kernel is explicit and much simpler than the ones that have appeared in the recent literature. An appropriate set of linear time interpolation functions together with quadratic spatial variations are incorporated. Moreover, the algorithm has a capability of handling problems with multiply connected regions. All of these advanced features have resulted in an efficient formulation capable of producing very accurate results and represent significant improvements over the present level of sophistication in this area. This above algorithm is now a part of the general purpose BEM code known as GPBEST.
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    URL: http://dx.doi.org/10.1002/nme.1620290704
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    A finite element model for non-linear shells of revolution with finite rotations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1455-1471 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The axisymmetric behaviour of geometrically non-linear elastic shells of revolution with finite rotations is discussed. In contrast to the approach of Reissner and to standard classical shell theories a new straightforward strategy is derived for the formulation of fully non-linear strain measures in the axisymmetric case. Within this approach the computation of the deformed director vector d is a main assumption which is essential to describe the fully non-linear bending behaviour. A Total Lagrangian Description is chosen to represent the large displacements. As an illustrative example the finite element formulation for a simple two-node conical element is given. A consistent linearization of the weak form leads to a quadratically convergence behaviour. The discussed shell examples under proportional loading show the good performance of the derived finite element formulation.
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    The numerical simulation of electron transmission through a two-dimensional quantum device by the finite element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1527-1537 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper we present a method for numerically solving the Schrödinger equation for the problem of electron transmission through a quantum device defined on a two-dimensional domain. An important aspect of our formulation is the treatment of the boundary conditions at the contact-device interfaces, allowing the problem to be discretized on the device domain only. With the FEM aproach that we employ, the nature of the potential field does not effect the computational expense (for smoothly varying fields). We examine a sample problem of a symmetric cavity in a wave-guide structure.
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290801
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    Natural approach for thin-walled beam-columns with elastic-plasticity (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1653-1679 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In a realistic analysis of thin-walled steel frames the warping of beam-columns of open cross-section must be considered. To model the behaviour of these structures up to collapse load, the plasticity of the material also has to be included in the analysis. This work presents the derivation of a new finite element for three-dimensional non-linear analysis of steel frames with bi-symmetrical cross-sections that models warping and elastic-plasticity. The displacement field is described by the Principle of Sectorial Areas and is modelled with Hermitian functions. For the material non-linearity the Incremental Plasticity Theory in a concentrated plasticity model has been used. The yield surfaces based on the natural stress resultants which include torsion and bimoment are used in the formulation of the element. The matrices of the proposed element are derived explicitly and implemented in a computer program which uses the Natural Approach. The implemented stress recovery process is insensitive to rigid-body motions. The accuracy of the finite element and the efficiency of the implementation are illustrated through examples.
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    Element by element a posteriori error estimation and improvement of stress solutions for two-dimensional elastic problems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 223-244 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A quantitative method of a posteriori error estimation based on finite element solutions is developed. The proposed method can estimate the error of solutions obtained by the finite element method for two-dimensional elastic problems with 4-node elements. Since the error is estimated element by element, the proposed method does not require a large memory or long computing time. Not only rectangular elements but also arbitrarily shaped 4-node elements can be used in this method for estimating the error in the finite element computation with high accuracy. The finite element solutions are improved by adding the estimated errors onto the original solutions. The proposed method can be utilized for any type of linear problem if an isoparametric finite element method is used.
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    Higher derivative explicit one step methods for non-linear dynamic problems. Part II: Practical calculations and comparisons with other higher order methods (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 291-301 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A generalized explicit one step alogorithm developed in Part I of this paper is presented in the form of a predictor-corrector scheme suitable for arbitrary non-linear analyses of structural dynamics problems. Convergence results are checked through practical calculations on linear and non-linear systems. The generalized algorithm proposed is compared with other recently developed higher order one step algorithms. The slight amount of additional computational effort compared to second order methods pays off in linear and weakly non-linear systems. The behaviour of the methods is also tested on extreme stiffening and softening systems to investigate reliability and robustness of the algorithm.
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    Non-linear vibration of frames by the incremental dynamic stiffness method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 337-356 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic stiffness method is extended to large amplitude free and forced vibrations of frames. When the steady state vibration is concerned, the time variable is replaced by the frequency parameter in the Fourier series sense and the governing partial differential equations are replaced by a set of ordinary differential equations in the spatial variables alone. The frequency-dependent shape functons are generated approximately for the spatial discretization. These shape functions are the exact solutions of a beam element subjected to mono-frequency excitation and constant axial force to minimize the spatial discretization errors. The system of ordinary differential equations is replaced by a system of non-linear algebraic equations with the Fourier coefficients of the nodal displacements as unknowns. The Fourier nodal coefficients are solved by the Newtonian algorithm in an incremental manner. When an approximate solution is available, an improved solution is obtained by solving a system of linear equations with the Fourier nodal increments as unknowns. The method is very suitable for parametric studies. When the excitation frequency is taken as a parameter, the free vibration response of various resonances can be obtained without actually computing the linear natural modes. For regular points along the response curves, the accuracy of the gradient matrix (Jacobian or tangential stiffness matrix) is secondary (cf. the modified Newtonian method). However, at the critical positions such as the turning points at resonances and the branching points at bifurcations, the gradient matrix becomes important. The minimum number of harmonic terms required is governed by the conditions of completeness and balanceability for predicting physically realistic response curves. The evaluations of the newly introduced mixed geometric matrices and their derivatives are given explicitly for the computation of the gradient matrix.
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    Biharmonic analysis of rectilinear plates by the boundary element method (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 517-539 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An improved boundary element formulation (BEM) for two-dimensional non-homogeneous biharmonic analysis of rectilinear plates is presented. A boundary element formulation is developed from a coupled set of Poisson-type boundary integral equations derived from the governing non-homogeneous biharmonic equation. Emphasis is given to the development of exact expressions for the piecewise rectilinear boundary integration of the fundamental solution and its derivatives over several types of isoparametric elements. Incorporation of the explicit form of the integrations into the boundary element formulation improves the computational accuracy of the solution by substantially eliminating the error introduced by numerical quadrature, particularly those errors encountered near singularities. In addition, the single iterative nature of the exact calculations reduces the time necessary to compile the boundary system matrices and also provides a more rapid evaluation of internal point values than do formulations using regular numerical quadrature techniques. The evaluation of the domain integrations associated with biharmonic forms of the non-homogeneous terms of the governing equation are transformed to an equivalent set of boundary integrals. Transformations of this type are introduced to avoid the difficulties of domain integration. The resulting set of boundary integrals describing the domain contribution is generally evaluated numerically; however, some exact expressions for several commonly encountered non-homogeneous terms are used. Several numerical solutions of the deflection of rectilinear plates using the boundary element method (BEM) are presented and compared to existing numerical or exact solutions.
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990) 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620300401
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    Thermo-mechanical finite element model of casting systems (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 579-599 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A coupled finite element model is developed to simulate the metal casting process. We present a new method for capturing the solidification zone and obtaining the corresponding rate of phase change. The latent energy release is predicted by the heat conduction rate and introduced by following the enthalpy-temperature curve. The influence of mould-metal contact is considered in calculating the heat flux through the mould-metal interface. A viscoplastic model is employed to predict the gap opening and evolution of plastification.Four examples are presented to demonstrate certain numerical aspects and the capability of the model for industrial applications.
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    Letter to the editor (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 211-215 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 219-222 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620290116
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    Computer simulation of turbulent swirling flows (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 533-557 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Simulation of turbulent swirling flows has been carried out to provide insight on streamline curvature effects. Numerical calculations were based on the control-volume method. Turbulence effects were represented by two-equation turbulence models. The analysis of steady flow between two concentric rotating cylinders showed that the most promising model which incorporates curvature effects is that based on mixing energy developed by Wilcox and Chambers, as opposed to the ad hoc modification to the standard k-∊ model. This model has also been used to simulate the decay of turbulent swirling flow in a short cylinder. A comparison between calculations and experimental results for such flow fields has been presented.
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    Parallel multisplitting, block Jacobi type solutions of linear systems of equations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 619-632 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three parallel iterative schemes to solve banded systems of equations are presented in this study. The techniques are special implementations of the theory of matrix multisplitting. The resulting algorithms are implemented on a Multiple Instruction Multiple Data (MIMD) grid architecture using 16 Transputer processors. Parametric analyses are performed to develop convergence criteria and examine the speed-up of solution. It is concluded that the algorithms make very efficient use of the parallel computer architecture, especially if this consists of a large number of nodes.
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    A finite-element model of two-layer ocean circulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 665-678 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A mixed finite-element formulation is applied to solve the quasi-geostrophic equations in a two-layer ocean domain enclosed by solid boundaries. A combination of leap-frog and θ-schemes is used to integrate the equations in time. Wood's formula of the wall vorticity is derived in our formulation for the case of square elements adjacent to the boundaries. Long-term computations with and without lumping have been carried out.
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    Natural approach for geometric non-linear analysis of thin-walled frames (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 30 (1990), S. 207-231 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new stiffness matrix for geometrically non-linear analysis of three-dimensional beam-columns with bisymmetrical, thin-walled, I-type cross-sections is presented. The displacement field is described in terms of natural and rigid-body displacements and both Cartesian and natural matrices are derived. A novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation. A companion paper1 that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross-section of the 3D beam-column element. The current development uses the updated Lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation. It is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid-body displacements.
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    A truncated Newton-Lanczos method for overcoming limit and bifurcation points (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1065-1077 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this study procedures for overcoming limit and bifurcation points in large-scale structural analysis problems are described and evaluated. The methods are based on Newton's method for the outer iterations, while for the linearized problem in each iteration the preconditioned truncated Lanczos method is employed. Special care is placed upon line search routines for accelerating the convergence properties and enhancing the stability of the outer method. The proposed methodology retains all characteristics of an iterative method by avoiding the factorization of the current stiffness matrix. The necessary eigenvalue information is retained in the tridiagonal matrix of the Lanczos approach.
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    Masthead (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990) 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
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    URL: http://dx.doi.org/10.1002/nme.1620290601
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    Hypersingular integrals in boundary element fracture analysis (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1135-1158 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new general purpose boundary element method for domains with cracks has been recently developed. This technique avoids the use of a multi-domain decomposition by including an additional integral equation expressing the boundary condition on the crack. The principal requirement of this technique is the analytic determination of certain hypersingular integrals of the Green's function which arise from this equation. In order to establish the applicability of this method for fracture, these integrals are evaluated herein for the Kelvin solution of the three-dimensional Navier equations of linear elasticity. Numerical results for fracture problems using the single-domain boundary element analysis are also presented.
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    Effects of spatial discretization on dispersion and spurious oscillations in elastic wave propagation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1205-1218 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dispersive and spurious oscillation properties of one-dimensional uniform finite element meshes are investigated using the information provided by the frequency response functions of the finite element meshes. The modal superposition method, in which the effects of temporal discretization are eliminated, is employed to integrate the discretized equations of motion. Compared with the commonly used complex variable method, this approach reveals more clearly the physical essence of the dispersion and spurious oscillation phenomena. A series of interesting results is obtained.
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    A hybrid differential-algebraic method for three-dimensional grid generation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1271-1279 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An effective method is presented for generating three-dimensional boundary-fitted grids. The technique is based on a two-step procedure involving the solution of differential equations and algebraic interpolations. A coarse grid with an arbitrarily given point distribution at all the boundaries is first generated by solving the Poisson equations, with the forcing functions being automatically adjusted during the grid generation to achieve orthogonality at the boundaries. A fine grid with a desired concentration of grid lines is then obtained by fitting tricubic spline functions on the coarse grid. A primary feature of the method is that the mesh spacing can be quickly and explicitly changed while retaining the smoothness over the entire field and the boundary orthogonality. Applications to a variety of geometries demonstrate the performance of the method.
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    Conference diary (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1359-1363 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620290616
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    A study of incremental-iterative strategies for non-linear analyses (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1365-1391 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper describes a study of incremental-iterative solution techniques for geometrically non-linear analyses. The solution methods documented are based on a modified Newton-Raphson approach, meaning that the tangent stiffness matrix is computed at the commencement of each load step but is then held constant throughout the equilibrium iterations. A consistent mathematical notation is employed in the description of the iterative and load incrementation strategies, enabling the simple inclusion of several solution options in a computer program. The iterative strategies investigated are iteration at constant load, iteration at constant displacement, iteration at constant ‘arc-length’, iteration at constant external work, iteration at minimum unbalanced displacement norm, iteration at minimum unbalanced force norm and iteration at constant ‘weighted response’. The load incrementation schemes investigated include strategies based on the number of iterations required to achieve convergence in the previous load step, strategies based on the ‘current stiffness parameter’ and a strategy based on a parabolic approximation to the load-deflection response. Criteria for detecting when the applied external load increment should reverse sign are described.A challenging example of a circular arch exhibiting snap-through (load limit point) behaviour and snap-back (displacement limit point) behaviour is solved using several different iterative and load incrementation strategies. The performance of the solution schemes is evaluated and conclusions are drawn.
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    Prediction of thermal stress and deformations due to phase change in solidifying objects via flux/stress based finite element representations (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1473-1485 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper presents numerical simulations for the prediction of thermal-stress and deformation fields resulting from phase change in solidifying bodies employing new finite element representations. The formulations developed in this paper provide different perspectives and physical interpretation for the modelling/analysis of thermo-mechanical problems and possess several inherent advantages. In comparison to traditional approaches for solving similar problems, the paper employs new computational architectures in conjunction with flux/stress based representations to enhance the overall effectiveness. Comparative numerical applications validate applicability of the formulations for predicting the temperature induced deformations and stresses resulting from effects due to phase change.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290707
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  • 99
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    A numerical integration scheme for finite element method based on symbolic manipulation (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1539-1549 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper is concerned with the improvement of the efficiency and accuracy of the usual numerical integration procedures for the finite element method. A modified numerical integration scheme based on both the symbolic manipulation system and the numerical integration formula is proposed. Its efficiency for the integration of complicated rational or irrational expressions is demonstrated through several numerical examples. To verify its effectiveness in the calculation of the finite element stiffness matrix, a simple numerical example is also presented.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290711
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  • 100
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    Inverse finite element techniques for the analysis of solidification processes (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1569-1587 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper provides a finite element methodology (FEM) for the solution of several one-dimensional inverse solidification problems. In particular two design related problems will be addressed. The first one uses an inverse technique to calculate the boundary heat flux history that will achieve a specified velocity and flux at the freezing front. This front velocity and flux history can be appropriately selected so that the cast structure is controlled. The second problem is the calculation of the boundary heat flux and freezing front position, given appropriate estimates of the temperature field in a specified number of sensor locations (thermocouples) inside a solidifying body.Front fixing and front tracking FEM techniques are used for the solution of the first problem, while a fixed domain finite element formulation (enthalpy method) is used for the solution of the second one. The ‘future information technique’ is employed in both problems. A detailed analysis of the effect on the solution of the error in the data, amount of future information used, time step, number of sensors and their location and of other parameters in the solution will be examined via several numerical tests. Finally, further applications of such inverse methodologies on the control of casting processes will be mentioned.
    Additional Material: 16 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290713
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