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  • Engineering  (1,353)
  • 1990-1994  (1,353)
  • 1980-1984
  • 1925-1929
  • 1992  (757)
  • 1991  (596)
  • 1929
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  • 1927
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  • 1990-1994  (1,353)
  • 1980-1984
  • 1925-1929
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  • 1
    Electronic Resource
    Electronic Resource
    Trust region methods for structural optimization using exact second order sensitivity (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 275-293 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The performance of multiplier algorithms for structural optimization has been significantly improved by using trust regions. The trust regions are constructed using analytical second order sensitivity, and within this region, the augmented Lagrangian φ is minimized subject to bounds. Evaluation of first and second derivatives of φ by the adjoint method does not require derivations of individual (implicit) constraint functions, which makes the method economical. Eight test problems are considered and a vast improvement over previously used multiplier algorithms has been noted. Also, the algorithm is robust with respect to scaling, input parameters and starting designs.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320204
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  • 2
    Electronic Resource
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    New predictor/corrector algorithms with improved energy balance for a recent formulation of dynamic vehicle/structure interaction (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 223-253 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new class of predictor/corrector algorithms is proposed to solve the complex system of differential equations that arises from a Galerkin spatial discretization of the equations of motion in a recent formulation of dynamic vehicle/structure interaction. The applicability of the concept of a building-block vehicle/structure interaction model developed in our previous work - where the vehicle nominal motion is not prescribed a priori, but is part of the unknown motion of the system - is demonstrated through the construction of a simple vehicle model. In the new algorithms, the presence of the accelerations of the vehicle component is eliminated in the predictor structural equations, making these equations different from the corrector structural equations. The special treatment of the predicted axial motion that provides an artificial damping to eliminate unstable oscillations in the numerical results as proposed in the old algorithms is avoided. Accurate results from numerical simulations using the new algorithms are obtained, and there are no unstable oscillations that were observed in some other predictor/corrector schemes. The system energy balance is also better preserved compared with the old algorithms.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320202
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  • 3
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    Direct evaluation of singular integrals in elastoplastic analysis by the boundary element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 295-311 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new method for the direct and accurate evaluation of strongly singular integrals in the sense of Cauchy principal values and weakly singular integrals over quadratic boundary elements in three-dimensional stress analysis and quadratic internal cells in two-dimensional elastoplastic analysis by the boundary element method. A quadratic triangle polar co-ordinate transformation technique is applied to reduce the order of singularity of the singular integrals. Next, a form of Stokes' theorem is introduced in order to remove the singularity in the Cauchy principal value integrals; therefore, the evaluation of these integrals can be carried out by standard Gaussian quadrature. Numerical examples of 2-D elastoplastic problems and a 3-D elastic problem show the effectiveness and efficiency of the method.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320205
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  • 4
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    Projection methods in flexible multibody dynamics. Part II: Dynamics and recursive projection methods (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1941-1966 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In Part I of this paper the kinematic relationships between the absolute, elastic and joint accelerations are developed. In this paper, these kinematic equations are used with the generalized Newton-Euler equations and the relationship between the actual and generalized reaction forces to develop a recursive projection algorithm for the dynamic analysis of open-loop mechanical systems consisting of a set of interconnected rigid and deformable bodies. Optimal matrix permutation, partitioning and projection methods are used to eliminate the elastic accelerations while maintaining the inertia coupling between the rigid body motion and the elastic deformation. Recursive projection methods are then applied in order to project the inertia of the leaf bodies onto their parent bodies. This leads to an optimal symbolic factorization which recursively yields the absolute and joint accelerations, and the joint reaction forces. The method presented in this paper avoids the use of Newton-Raphson algorithms in the numerical solution of the constrained dynamic equations of open-loop kinematic chains since the joint accelerations are readily available from the solution of the resulting reduced system of equations. Furthermore, the method requires only the inversion or decomposition of relatively small matrices and the numerical integration of a minimum number of co-ordinates. Open-loop multibody robotic manipulator systems are used to compare the results and efficiency of the recursive methods with that of the augmented formulations that employ Newton-Raphson algorithms.
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620351003
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  • 5
    Electronic Resource
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    Coupling finite elements and magnetic networks in magnetostatics (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1991-2002 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper a new method for computing non-linear magnetostatic fields is introduced, which allows the simultaneous coupling of a finite element structure with a magnetic network. Combining the advantages of both methods while avoiding their drawbacks, this coupling yields both an accurate and time-efficient computation.The traditional method of the unknown mesh fluxes is applied for the solution of the magnetic network. The finite element solution, on the other hand, is based on a classical first-order interpolation of the unknown vector potential. The coupling is established by a proper organization of the unknowns on the boundary common to the finite element and network regions. In this way, a single system of non-linear equations is obtained.Moreover, it is shown that the coupled system of equations is equivalent to a single finite element system if generalized base functions are allowed. Consequently, various results from finite element theory may be applied. For instance, the matrix governing the iteratively linearized system of equations can directly be shown symmetrical and positive definite.Finally, the field inside a permanent magnet motor is calculated with the coupled method. Although the number of unknowns is dramatically reduced compared to a full FE calculation, the same level of accuracy is achieved. Hereby, the benefit of the coupled method is clearly proved.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620351005
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  • 6
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    A consistent model for first-order moderate rotation plate theory (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2049-2066 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The first-order shear deformation plate theory can be used in the small strain and moderate rotation non-linear elasticity by defining correctly the displacement vector form. In this paper, the problem of the consistency between the displacement vector form and the finite strain tensor approximation is analysed. Then, a new moderate rotation theory is proposed. The variational form of the governing equations is derived for the beam and the plate problems in a consistent way. Then, an iterative numerical procedure based on the finite element method and the secant striffness matrix is developed in order to solve the non-linear differential equation problem. Computations are made for one- and two-dimensional structures, in order to assess the performance of the von Kármán, finite elasticity, classical and the proposed moderate rotation theories.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620351008
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  • 7
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    A numerical method for the solution of two-dimensional inverse heat conduction problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 363-383 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerical method for the solution of inverse heat conduction problems in two-dimensional rectangular domains is established and its performance is demonstrated by computational results. The present method extends Beck's8 method to two spatial dimensions and also utilizes future times in order to stabilize the ill-posedness of the underlying problems. The approach relies on a line approximation of the elliptic part of the parabolic differential equation leading to a system of one-dimensional problems which can be decoupled.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320209
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  • 8
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    Announcements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 439-439 
    Details
    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.1620320212
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  • 9
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    The adaptation of structured grids to numerical solutions for transonic flow (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 921-937 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Methods are described for adapting a structured grid in response to a numerical solution, so that grid nodes become clustered where ‘solution activity’ is high, the aim being to reduce solution truncation errors without increasing the number of grid nodes employed, or modifying their connectivity. After introducing the concept of ‘equidistribution’, and discussing options for the measurement of solution activity, the paper concentrates mainly on two alternative techniques for producing smooth, regular grids which apply constraints on this equidistribution. The first technique described is based on a spring analogy, and is demonstrated here with examples of two- and three-dimensional inviscid flows, and with two-dimensional viscous flows. The second technique employs a Poisson grid generator with adaptive terms included in the control functions, and is demonstrated with a two-dimensional inviscid flow. A third method is then introduced, termed the LPE method, which allows a compromise to be chosen between grids generated by solving Laplace equations, Poisson equations and equidistribution equations. Since this method is still being developed, results are currently limited and tentative.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320414
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  • 10
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    Bounds on eigenvalues of finite element systems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 957-967 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Bounds on eigenvalues of various finite element systems are analysed by using an element eigenvalue theorem together with the Global Eigenvalue Theorem. Both two dimensional continuum dynamics and heat conduction problems are considered. These bounds provide stable time steps for explict time integration schemes. A reduced eigenproblem at element quadrature point level, with all zero eigenvalues suppressed, is also presented in this paper. The simplified eigenproblem results in simple formulas for calculating the eigenvalues.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320503
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  • 11
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    Conference diary (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2103-2104 
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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.1620351012
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  • 12
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    Direct evaluation of singular boundary integrals in two-dimensional biharmonic analysis (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2067-2078 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Development of techniques to provide rapid and accurate evaluation of the integrations required in boundary element method (BEM) formulations are receiving more attention in the literature. In this work, a series of direct expressions for surface integrals, required for a boundary element solution of the non-homogeneous biharmonic over a general two-dimensional curvilinear surface, are presented. The concept of an isoparametric representation, usually applied to the variation of the field variables and the geometry, is extended to the parametric mapping of the curvilinear geometry. The result renders the typically complicated Jacobian function into a series of polynomial expressions based on the shape function set and several discrete Jacobian values. An application of the isoparametric approximation of the Jacobian for a quadratic element representation is developed. Implementation of this approximation significantly improves the accuracy of the boundary integral solution by eliminating error associated with numerical quadrature. Overall computational efficiency is improved by reducing the time necessary to calculate individual surface integrals and evaluate field variables at internal points. A numerical solution of the boundary integral equations of phenomena governed by the biharmonic equation is presented and compared with an exact analysis.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620351009
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  • 13
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    An infinite boundary element formulation for three-dimensional potential problems (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 2079-2100 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An infinite boundary element (IBE) is presented for the analysis of three-dimensional potential problems in an unbounded medium. The IBE formulations are done to allow their coupling with the finite element (FE) matrices for finite domains and to obtain the overall matrices without destroying the banded structure of the FE matrices. The infinite body is divided into a number of zones whose contributions are expressed in terms of the nodal quantities at FE nodes by employing suitable decay functions and performing mainly analytical integrations of the boundary element kernels. The continuity and compatibility conditions for the potential and the flux at the FE-IBE interface are developed. The relationships for the contributions of the IBE flux vectors to the FE load vectors are given. The final equations for the IBE are obtained in the usual FE stiffness-load vector form and are easily assembled with the FE matrices for the finite object. A series of numerical examples in heat transfer and electromagnetics were solved and compared with alternative solutions to demonstrate the validity of the present formulations.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620351010
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  • 14
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    Efficient and accurate four-node quadrilateral C0 plate bending element based on assumed strain fields (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1041-1055 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Based on the assumed element strain fields and the interrelated displacement-rotation interpolations, a four-node (12 dof) quadrilateral C0 finite element, designated as QCCP-2, for the analysis of thick/thin plates is developed in this paper. The four-node C0 plate element presented here possesses a linear bending strain field, and the element stiffness matrices are given explicitly. Therefore, the present four-node C0 plate element is more efficient and accurate than the existing four-node C0 plate elements where the constant strain stiffness matrices are obtained by numerical integration. By the use of the interrelated displacement-rotation interpolations, QCCP-2 is capable of automatically satisfying the Kirchhoff assumption for the case of thin plates. Consequently, QCCP-2 is not only free of shear locking, but also free from the numerical ill-conditioning. Furthermore, QCCP-2 passes the patch test of thin plates. The four-node quadrilateral C0 elements presented here can automatically reduce to the corresponding three-node triangular elements. Several numerical examples are given to demonstrate the efficiency and accuracy of the C0 plate bending element QCCP-2.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320508
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  • 15
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1249-1252 
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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.1620310614
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  • 16
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    Incompressibility without tears - HOW to avoid restrictions of mixed formulation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1189-1203 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The severe restrictions of the Babuška-Brezzi stability criteria permit only a limited number of interpolations for velocities (displacements) and pressure to be used for incompressible behaviour. These restrictions preclude the use of many useful elements. We show in this paper how such difficulties can be side-stepped by seeking the steady state solution through the use of various time marching schemes. This permits a simple iterative approach to incompressible (or nearly incompressible) problems of fluid mechanics or solid mechanics and provides a stimulus for the use of such procedures in metal forming flow, etc.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320603
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  • 17
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    Optimal placement of actuators and sensors in control-augmented structural optimization (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1165-1187 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A control-augmented structural synthesis methodology is presented in which actuator and sensor placement is treated in terms of (0, 1) variables. Structural member sizes and control variables are treated simultaneously as design variables. A multiobjective utopian approach is used to obtain a compromise solution for inherently conflicting objective functions such as structural mass, control effort and number of actuators. Constraints are imposed on natural frequencies, peak transient displacements and accelerations, peak actuator forces and dynamic stability as well as controllability and observability of the system. The combinatorial aspects of the mixed (0, 1)-continuous variable design optimization problem are made tractable by combining approximation concepts with branch and bound techniques. Some numerical results for example problems are presented to illustrate the efficacy of the design procedure set forth.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320602
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  • 18
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    Creep deformation structural analysis using an efficient numerical algorithm (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1427-1442 
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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 a fast numerical algorithm for the implementation of material models for creep into finite element codes. First, an overview of existing algorithms for transient and steady-state creep is given. Next, a new formulation is presented which reduces the constitutive integration to the solution of a scalar non-linear algebraic equation. A solution is shown to exist without the need for subincrementation. Details of the numerical algorithm are then discussed. The paper closes with several numerical examples which illustrate the speed, robustness and accuracy of the proposed procedure as implemented in the Lawrence Livermore National Laboratory finite element codes NIKE2D and NIKE3D.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620350704
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  • 19
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    How to recognize the order of infinitesimal mechanisms: A numerical approach (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1351-1395 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Structures presenting kinematical inderterminacy are usually called mechanisms. This paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load. Among them a first distinction is made between infinitesimal and finite ones, the former being characterized by one or several directions of lower (but not zero) stiffness, whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation. Moreover, there exists the possibility to make a further distinction among the infinitesimal mechanisms, according to which is the order of the stiffness along the direction considered above. The way of evaluating this order is to perform a local analysis of the strain energy of the assembly, once the displacement field is parametrized in terms of a suitable parameter. By means of a finite element technique, this analysis can be easily performed through the numerical approach presented in this report.
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    URL: http://dx.doi.org/10.1002/nme.1620350702
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  • 20
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    Solutions to shape and topology eigenvalue optimization problems using a homogenization method (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1487-1502 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A solution strategy to find the shape and topology of structures that maximize a natural frequency is presented. The methodology is based on a homogenization method and the representation of the shape of the structure as a material property. The problem is formulated as a reinforcement problem in which a given structure is reinforced using a prescribed amount of material. Two dimensional, plane elasticity problems are considered. Examples are presented for illustration.
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    URL: http://dx.doi.org/10.1002/nme.1620350707
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  • 21
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    Announcements (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992), S. 1541-1542 
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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.1620350710
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  • 22
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    Equivalent homogeneous finite element for composite materials via reissner principle. Part II: Finite element for shells (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1497-1509 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The lateral hulls of multi-shelled ships such as Catamarans or Trimarans can be considered as rigid solids, or compared to thin walled beams in multi-layered materials for the global statical or dynamical behaviour of the ship. Unfortunately this approximation no longer hold after a detailed study of the hulls.Working in these problems we proceed to a fine analysis of the stress field at the neighbourhood of the linkage shell-arm or of the holes for access input to the hull itself. Analysis with a beam model is inadequate and the shell theory must be more appropriate. Numerous papers have been devoted to shell elements, see References 1 to 8 to mention just a few. Some of them require a reduced or selective integration scheme.9-12 We choose to start from the Ahmad element, 13, 14 which is suitable for moderate thick shells.15.16 The final aim of this paper is to explain how to build up a multi-layered equivalent homogeneous shell element which is both economical and accurate. Some examples will be given and compared with those obtained with the Ahmad finite element.
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    URL: http://dx.doi.org/10.1002/nme.1620310805
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  • 23
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    Equivalent homogeneous finite element for composite materials via reissner principle. Part I: Finite element for plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1477-1495 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The stiffness matrix in the finite element method for multi-layered materials is generally computed by expressing the strain energy in each layer and adding them together. In order to lower the computing time, which may be prohibitive if the number of layers is high, and to get accurate information on the stresses, especially on transverse shear stresses, we present a new finite element using the Reissner principle. In the first part the case of plates will be detailed: extensions to shell problems will be presented in the second part. The efficiency of the method is tested on a special analytic solution, and some examples are given.
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    URL: http://dx.doi.org/10.1002/nme.1620310804
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  • 24
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    Iterative solution techniques in boundary element analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1511-1536 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Iterative techniques for the solution of the algebraic equations associated with the direct boundary element analysis (BEA) method are discussed. Continuum structural response analysis problems are considered, employing single- and multi-zone boundary element models with and without zone condensation. The impact on convergence rate and computer resource requirements associated with the sparse and blocked matrices, resulting in multi-zone BEA, is studied. Both conjugate gradient and generalized minimum residual preconditioned iterative solvers are applied for these problems and the performance of these algorithms is reported. Included is a quantification of the impact of the preconditioning utilized to render the boundary element matrices solvable by the respective iterative methods in a time competitive with direct methods. To characterize the potential of these iterative techniques, we discuss accuracy, storage and timing statistics in comparison with analogous information from direct, sparse blocked matrix factorization procedures. Matrix populations that experience block fill-in during the direct decomposition process are included. With different degrees of preconditioning, iterative equation solving is shown to be competitive with direct methods for the problems considered.
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    The solution of large displacement frictionless contact problems using a sequence of linear complementarity problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1553-1566 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A Newton method for solution of frictionless contact problems is presented. A finite element discretization is performed and the contact constraints are given as complementarity conditions. The resulting equations, which represent the equilibrium of the system, are formulated as a generalized equation. Generalized equations, from the discipline of Mathematical Programming, are a way of writing multi-valued relations, such as complementarity conditions, in a way that is similar to ordinary equations. Newton's method is then used, in a straightforward way, to solve the present non-linear generalized equation, resulting in a sequence of Linear Complementarity Problems (LCP's).
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    URL: http://dx.doi.org/10.1002/nme.1620310808
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    Shifted integration technique in one-dimensional plastic collapse analysis using linear and cubic finite elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1537-1552 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The present study is concerned with the physical explanations of the linear and the cubic finite elements for beams and axisymmetric shells through comparisons of their strain energy approximations with those of the Rigid Bodies-Spring Models which are discrete elements suitable for plastic collapse analysis using the concepts of plastic hinges and hinge lines. The established conditions for the equivalence between these two modellings, which are given as the relations between the locations of the numerical integration points and those of the occurrence of plastic hinges, can be conveniently used in the economical plastic collapse analysis of framed structures and axisymmetric shells where the locations of plastic hinge formations are controlled by the movement of numerical integration points. Some numerical results are shown in order to prove numerically the obtained relations and to verify the validity of the proposed shifting technique of numerical integration points, which is identified as ‘the shifted integration technique’ in the present paper.
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 35 (1992) 
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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.1620350901
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    A numerical approach for determining weight functions in fracture mechanics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 595-607 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The paper deals with the development of a numerical method for determining Weight Functions in two-dimensional problems. After a short review of some recent numerical techniques an original approach is presented. The method is based on Finite Element calculations with coarse meshes and on the knowledge of some values of the Stress Intensity Factor for one reference loading condition. The validity of the method is demonstrated for a theoretical case and its accuracy and suitability are discussed with reference to practical applications.
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    Forced harmonic vibration of rotating beam systems in space analysed by use of exact finite elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 571-594 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A general computational technique is developed for the accurate analysis of forced non-synchronous harmonic vibration of linear structures rotating with constant speed about a fixed axis in the inertial space. The structures studied are built up from piecewise uniform straight Rayleigh-Timoshenko beam members having coinciding cross-sectional centres of geometry, shear and mass, and vibrating in coupled tension, torsion, bending and shearing. Hysteretic and viscous dampings in the beam material and in a Winkler-type ambient medium are considered. Rigid bodies and modal bodies and also discrete masses, springs and dampers can be included in the structure. The six coupled scalar partial linear differential equations governing the motion of a loaded beam are established in a corotating local co-ordinate system. A transcendentally frequency-dependent non-symmetric complex-valued 12 × 12 stiffness matrix is derived, over a state-space analogy and an associated eigenproblem, for a harmonically vibrating beam member non-synchronously excited at its ends. This matrix is exact in the sense that no assumed shape functions and no lumped masses are used. The general computational technique is here applied to a simple beam rotating about (1) its longitudinal axis and (2) about a transverse axis. The study clarifies the influence of gyroscopic effects and of material and support dampings on the dynamical behaviour of the beam at different rotational speeds and forcing frequencies. Resonance frequencies are found. Frequency response functions and frequency maps are plotted.
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    Boundary elements with equilibrium satisfaction - A consistent formulation for potential and elastostatic problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 609-621 
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    Notes: A direct boundary element formulation which produces equilibrium satisfaction in the numerical solutions is presented. It consistently originates from the standard boundary integral equation with a simple modification in the fundamental solution and can be applied to general potential and elasticity problems. Since boundary equilibrium is guaranteed for any problem discretization, the procedure is also found useful to generate improved stiffness matrices, which permits combination with finite elements.Some elastostatic examples are included to demonstrate the applicability of the formulation.
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    Tangent constitutive matrices for inelastic finite element analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 645-646 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 647-649 
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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.1620320313
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    Static and dynamic contact/impact problems using fictitious forces (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 623-643 
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    Notes: A new finite element model for the contact/impact problem is presented, and both its static and dynamic implementations are described. In this geometrical non-linear formulation, contact (from node to surface) is simulated through fictitious equivalent pressure along the boundary. Contrary to most existing models, this formulation entails relatively few matrix decompositions and thus is computationally inexpensive. The model is first assessed through some classical contact problems, and is subsequently applied to the fracture mechanics based analysis of a cracked dam under seismic excitation.
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    Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentumResearch supported by AFOSR under contract nos. 2-DJA-544 and 2-DJA-771 with Stanford University (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 19-52 
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    Notes: We show that, for rigid body dynamics, the mid-point rule formulated in body co-ordinates exactly conserves energy and the norm of the angular momentum for incremental force-free motions, but fails to conserve the direction of the angular momentum vector. Further, we show that the mid-point rule formulated in the spatial representation is, in general, physically and geometrically meaningless. An alternative algorithm is developed which exactly preserves energy, and the total spatial angular momentum in incremental force-free motions. The implicit version of this algorithm is unconditionally stable and second order accurate. The explicit version conserves exactly angular momentum in incremental force-free motions. Numerical simulations are presented which illustrate the excellent performance of the proposed procedure, even for incremental rotations over 65 degrees. The procedure is directly applicable to transient dynamic calculations of geometrically exact rods and shells.
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    An investigation of a finite rotation four node assumed strain shell element (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 127-150 
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    Notes: The paper presents a shell formulation based on the ‘degenerated solid approach’. The theory employs covariant strains and performs explicit integration through the shell thickness. The rigid body motion is exactly represented. The consistent tangent stiffness matrix is evaluated for the four node quadrilateral. It is shown, in the final part, that this type of element, which distinguishes itself by a very simple and easily understandable theory, gives good answers for linear as well as non-linear applications.
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    A Treatment of wall boundaries for turbulent flows by the use of a transmission finite element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 113-126 
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    Notes: A method to connect momentum Navier-Stokes equations with the universal law of the wall using the finite element method is developed for turbulent wall flows. This method is based on a domain decomposition of the fluid into subdomains near a solid boundary where the law of the wall is valid. A transmission formulation is introduced to match these regions and a new class of boundary finite element is used. This finite element takes into account the near-wall profile of the velocity and the transmission conditions. Computational results are presented for Poiseuille flow and flow over a backward-facing step.
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    Exact block diagonalization of large eigenvalue problems for structures with symmetry (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 265-285 
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    Notes: We consider large eigenvalue problems for skeletal structures with symmetry. We present an algorithm, based upon a novel combination of group-theoretic ideas and substructuring techniques, that block-diagonalizes such systems exactly and efficiently. The procedure requires only the structural matrices of a repeating substructure, together with the symmetry modes, which are obtained from symmetry considerations alone. We first present a simple paradigmatic example and then follow with several non-trivial applications involving large lattice structures.
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    Vectorial and parallel processing in stress analysis with the boundary element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 307-317 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    On the strain Assumption in a finite element model for plates and shellsModified version of a paper presented at the 30th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Mobile, AL, U.S.A., April 3-5, 1989 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 287-305 
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    Notes: Two different methods of assuming independent strain fields are examined for the nine node degenerate solid shell element. In the first case, the assumed strain field is chosen for the local orthogonal co-ordinate systems defined at the Gaussian integration points. In the second case, the independent strain is assumed for a local orthogonal co-ordinate system defined at the origin of the parent co-ordinates. The results of numerical tests involving simple example problems demonstrate that the second method is capable of exactly representing constant stress or moment states even when element geometries are distorted. In addition, both methods lead to a finite element model which is free of locking.
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    Non-linear analysis of stiffened plates using super elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 319-343 
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    Keywords: Engineering ; Engineering General
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    Notes: A new numerical technique for large deflection elasto-plastic analysis of stiffened plates is presented. The method uses super finite elements which are macro elements having analytical as well as the usual finite element shape functions, specially designed so that only one plate element per bay and one beam element per span are needed. The large deflection theory by von Karman and the von Mises yield criterion and associated flow rule are employed. The governing equations are derived using the principle of virtual work, integrated numerically using Gauss quadrature and solved by Newton-Raphson iteration. Numerical solutions are presented for simple beams and plates, and plates stiffened in one or two mutually perpendicular directions. Good approximations are obtained with only one-element representations of each plate bay or beam span with significant savings in computing time, costs and storage requirements as compared with using regular finite elements.
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    Frictional contact problems of kinked cracks modelled by a boundary integral method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 427-446 
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    Keywords: Engineering ; Engineering General
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    Notes: A numerical method is presented for the solution of two dimensional crack problems including the effects of crack kinks and frictional contact between crack faces. The metod is based on an integral equation for the resultant forces along a crack. Coulomb friction between contacting crack surfaces is taken into account. The numerical implementation is demonstrated by considerations of surface and sub-surface piece-wise straight line cracks in a half-plane. Numerical results are presented to illustrate the efficiency and the reliability of the presented method.
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    Infinite boundary elements for dynamic problems of 3-D half space (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 447-462 
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    Keywords: Engineering ; Engineering General
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    Notes: In this paper, a new procedure for solving 3-D dynamic problems of unbounded foundations in the frequency domain by using BEM is studied. For simulations of wave propagations due to far field effects, a type of infinite boundary element (IBEM) is presented for modelling a 3-D regular or irregular half space. The wave type considered could be compressional, shear or a combination of the two. Through the analysis of the asymptotic behaviour of 3-D fundamental solutions for elasto dynamics, a rather feasible technique for obtaining singular integral coefficients for dynamic problems has been developed. Through the analysis of the dynamic response for a 3-D square foundation under a uniform load distribution, excellent accuracy has been achieved in agreement with previous numerical solutions. Another example-analysis of the dynamic compliance of a rigid square plate on a half space-has also shown very good results. The development of this infinite boundary element provides a powerful tool for dealing with 3-D structure foundation interaction or wave propagation problems for irregular foundations such as arch dam canyons.
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    A perturbation analysis and finite element approximate model for free surface flow over curved beds (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 493-507 
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    Keywords: Engineering ; Engineering General
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    Notes: A perturbation analysis is developed for 1-D shallow water flow over a curved bed for applications such as spillways. The perturbation approach leads to a new formulation of the problem with associated weak integral statement and approximation using finite elements. The flow may exhibit a hydraulic jump in the downstream regime. An artificial dissipation technique is introduced to stabilize the non-linear problem and suppress numerical oscillations. Numerical results demonstrate the performance of the model and compare it with the steep-slope shallow water formulation corresponding to the model with zero curvature.
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    An Eulerian approach for die compaction processes (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 509-524 
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    Notes: For the analysis of deformation processes the Eulerian approach is usually formulated in material velocities. To describe the die compaction of compressible media, this paper presents an Eulerian simulation method, basically expressed in displacements. The material behaviour is modelled by the theory of elastoplasticity. Frictional interaction with the surroundings is included. As a spatially fixed finite element mesh is applied, rezoning is governed by the process specification and not, as in the Lagrangian approach, by the mesh distortion. The solution scheme, using a Newton-Raphson algorithm, is considered in detail. A consistent iteration procedure is derived. Examples demonstrate the merits of the method developed.
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    A combined surface integral and finite element solution for a three-dimensional contact problem (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 525-545 
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    Notes: A method is described to determine contact stresses and deformation using a combination of the finite element method and a surface integral form of the Bousinesq solution. Numerical examples of contacting hypoid gears are presented.
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    Contact-impact by the pinball algorithm with penalty and Lagrangian methods (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 547-572 
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    Keywords: Engineering ; Engineering General
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    Notes: Contact-impact algorithms, which are sometimes called slideline algorithms, are a computationally time-consuming part of many explicit simulations of non-linear problems because they involve many branches, so they are not amenable to vectorization, which is essential for speed on supercomputers. The pinball algorithm is a simplified slideline algorithm which is readily vectorized. Its major idea is to embed pinballs in surface elements and to enforce the impenetrability condition only to pinballs. It can be implemented in either a Lagrange multiplier or penalty method. It is shown that, in any Lagrange multiplier method, no iterations are needed to define the contact surface. Examples of solutions and running times are given.
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    Announcements (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 611-614 
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    Keywords: Engineering ; Engineering General
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    Solid elements with rotational degrees of freedom: Part 1 - hexahedron elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 573-592 
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    Keywords: Engineering ; Engineering General
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    Notes: This is the first of a two part paper on three-dimensional finite elements with rotational degrees of freedom (DOF). Part I introduces an 8-node solid hexahedron element having three translational and three rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 20-node hexahedron element. The new element produces a much smaller effective band width of the global system equations than does the 20-node hexahedron element having midside nodes.A small penalty stiffness is introduced to augment the usual element stiffness so that no spurious zero energy modes are present. The new element passes the patch test and demonstrates greatly improved performance over elements of identical shape but having only translational DOF at the corner nodes.
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    Conference diary (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 615-618 
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    Solid elements with rotational degrees of freedom: Part II - tetrahedron elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 593-610 
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    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This is the second part of a two part paper on three-dimensional finite elements with rotational degrees of freedom (DOF). Part II introduces a solid tetrahedron element having 3 translational and 3 rotational DOF per node. The corner rotations are introduced by transformation of the midside translational DOF of a 10-node tetrahedron element. To further enhance the element performance a least squares strain extraction technique is also implemented to develop the stiffness matrix with a desired field. The strain smoothing improves performance without causing a loss in generality.As with the hexahedron in Part I, the element stiffness is augmented with a small penalty stiffness to eliminate any possible spurious zero energy modes. The new tetrahedron element passes the patch test and demonstrates much improved performance over the 4-node translational DOF only (constant strain) tetrahedron element.
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    URL: http://dx.doi.org/10.1002/nme.1620310311
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    A design optimization procedure to minimize fillet bending stresses in an epicyclic gear system (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 859-878 
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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 design algorithm for epicyclic gear systems. The criterion on which the design performance is assessed is the maximum tensile stress induced in the fillets of the sun, planet and annulus gears. From an initial set of prescribed real and integer design parameters the finite element method is used to determine the maximum tensile fillet stresses in each gear. An objective function is formulated to represent the total stress in the system by combining the maximum fillet stresses in each component. A sequential procedure is then used to minimize the objective function subject to equality, inequality and integer function constraints.The finite element method is used to evaluate the stresses in the gear teeth and iterative application of the analysis and optimization stages converges to produce a design vector such that the maximum stress produced in all components of the system is minimized.Since the effectiveness of each design is assessed using the finite element method, the factorized stiffness matrix is reused to calculate the design derivatives. This makes the processes very efficient in its use of computer resources.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310504
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    Application of B-spline approximation to symmetric buckling problems of truncated shallow spherical shells subjected to line loads (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 895-907 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: By using cubic B-spline approximations, reasonably accurate solutions are obtained for line-loaded shallow spherical shells with a centre hole within a wide range of values of the geometrical parameter K (0 ≤ K ≤ 400, \documentclass{article}\pagestyle{empty}\begin{document}$ K = \sqrt {12(1 - v^2)} 2f/h $\end{document}, f = shell rise, h = shell thickness). It was found that the buckling loads Pc as well as the buckling threshold of the geometrical parameter Kc increase monotonically as the radius of the centre hole β increases if the hole edge is reinforced with a rigid ring and the outer edge of the shell is simply supported. However, the effect of the centre hole on Pc decreases rapidly as K increases and becomes negligible for K ≥ 45 and β ≤ 0.4.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310506
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    Consideration of constraints within the finite element method by means of matrix operators (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 909-926 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The following paper describes the incorporation of different constraints into a finite element system by means of matrix operators in conjunction with consecutive corresponding transformations. Instead of increasing the number of equations-as e.g. the Lagrange Multiplier Method10, 14 does-the Matrix Operator Method yields a set of reduced magnitude which can be solved more efficiently. The method will be developed for two classes of constraints: (i) stiff coupling of previously known subdomains and (ii) contact problem between two bodies. The assembly rules to obtain the system matrices are deduced. An application is given by a three-dimensional example of structural analysis in mechanical engineering.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310507
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    A frequency dependent rectangular plate finite dynamic element for high precision transverse vibration analysis of simply supported plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 927-947 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The need for adding to the many existing rectangular plate elements is justified and the inclusion of the twist parameter, in the degrees of freedom selected, is shown to be essential. Using a rational choice of parameters to form the deflection functions for a simply supported plate element, a constant term, sixteen degrees of freedom rectangular element is developed which is shown to predict exactly the first mode frequency and mode shape when used in whole plate modelling. The properties of this ‘dynamic’ element are combined with the properties of an existing ‘static’ element to obtain the frequency dependent properties of a ‘blended’ element. It is demonstrated that in order to obtain high accuracy in eigenvalue determination it is necessary to use three separate modellings of the plate using a square element and two rectangular elements which are oriented orthogonally. From 3 × 3 and 2 × 5 modelling, it is shown that the frequencies of the first 20 modes of a simply supported square plate, resulting from matrix eigenvalue determinations are obtainable within one per cent of the exact values. Modes 11 and 18 are determined exactly. Mode shape distortions associated with frequency errors are examined and shown to be minimal for the first 20 modes.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310508
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    A critical analysis of quadratic beam finite elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 949-966 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new methodology of evaluation of C0 beam elements is presented. It is shown that, knowing the stiffness matrix of an arbitrary type of element, it is possible to create equivalent equilibrium conditions expressed in the form of one difference equation for a regular beam discretized by these elements. The study of the convergence of one difference equation gives an interpretation of the source of troubles occurring in low-order bending elements which is more convincing than the usually applied consideration of the conditioning of element stiffness matrices. A careful examination of quadratic Mindlin elements provides a very clear explanation of the shear locking essence in the Timoshenko beam. The presented method enables one to identify errors that appear also in the reduced integrated or constrained elements. For each type of analysed quadratic element an adequate difference equation is derived and compared with the exact one. Based on this comparison a simple method of corrections is proposed that completely eliminates the errors associated with the application of C0 bending elements.
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    URL: http://dx.doi.org/10.1002/nme.1620310509
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    Linear-non-linear dynamic substructures (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 967-985 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The dynamic substructure method is extended to linear and non-linear coupling systems. Only those master co-ordinates with non-linear nature (non-linear co-ordinates) are retained. Other slave co-ordinates relating to the linear part (linear co-ordinates) are eliminated by the dynamic substructure method. The dynamic flexibility matrix associated with the linear co-ordinates is first expanded in terms of the fixed interface natural modes. The condensed dynamic stiffness-matrix associated with the non-linear co-ordinates is formed subsequently. The convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and Taylor series expansion. To find the steady state solutions, the non-linear responses are expanded into a Fourier series. Responses of the linear co-ordinates are related to the non-linear co-ordinates analytically. To solve for the unknown Fourier coefficients, the harmonic balance method gives a set of non-linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients. A Newtonian algorithm is adopted to solve for the unknown Fourier coefficients iteratively. The computational cost of a non-linear analysis depends heavily on the number of degrees of freedom encountered. In the method, the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310510
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    Accurate integration of singular kernels in boundary integral formulations for Helmholtz equation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1055-1068 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Boundary integral formulations for the 2D Helmholtz equation involve kernels in the form of modified Bessel functions. Accurate schemes for evaluating integrals of the kernels and their derivatives are presented. Special attention is paid to integrals involving singular and near singular kernels. Both boundary and domain integrals are considered. It is shown that, with the use of series expansion functions for the modified Bessel functions, the boundary integrals can be evaluated analytically in the neighbourhood of the singularity. For domain integrals, the behaviour of the kernels in the vicinity of the singularity is used to construct accurate numerical quadrature schemes. A transient heat conduction problem is formulated as a Helmholtz equation, solved, and compared against analytic solution to demonstrate the effectiveness of these schemes in relation to traditional methods. References are made to previous work to advocate the utility of the boundary integral method for non-linear and time-transient problems.
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    URL: http://dx.doi.org/10.1002/nme.1620310603
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    A Computationally viable higher-order theory for laminated composite plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1069-1086 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational higher-order theory involving all transverse strain and stress components is proposed for the analysis of laminated composite plates. Derived from three-dimensional elasticity with emphasis on developing a viable computational methodology, the theory is well suited for finite element approximations as it incorporates both C0 and C-1 continuous kinematic fields and Poisson boundary conditions. From the theory, a simple three-node stretching-bending finite element is developed and applied to the problem of cylindrical bending of a symmetric carbon/epoxy laminate for which an exact solution is available. Both the analytic and finite element results were found to be in excellent agreement with the exact solution for a wide range of the length-to-thickness ratio. The proposed higher-order theory has the same computational advantages as first-order shear-deformable theories. The present methodology, however, provides greater predictive capabilities, especially, for thick-section composites.
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    URL: http://dx.doi.org/10.1002/nme.1620310604
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    A Petrov-Galerkin formulation for the incompressible Navier-Stokes equations using equal order interpolation for velocity and pressure (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1135-1149 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new Petrov-Galerkin method for the incompressible Navier-Stokes equations is presented. The use of the so-called ‘optimal upwind’ parameter in multidimensions is justified by a time-scale analysis of the relevant physical processes. The resulting procedure circumvents the Babuška-Brezzi condition and allows equal order interpolation for velocity and pressure to be used.
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    URL: http://dx.doi.org/10.1002/nme.1620310608
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    Mesh relaxation: A new technique for improving triangulations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1121-1133 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Given a list of points defining a domain boundary, a three-stage process is often used to triangulate a domain. First, an appropriate distribution of interior points is generated. Next the points are connected to form triangles. And, finally, the connectivity data are used to reposition the interior points using the Laplacian smoothing technique, thereby usually improving the shapes of the shapes of the triangles. This paper describes a new techniques for mesh improvement - adjusting the connection structure during the second stage of this process. The new scheme, which we call mesh relaxation, consists of a procedure for iteratively making the mesh topology more regular by edge swapping. For each interior edge, a relaxation index is computed that depends on the degrees of its end points and adjacent points. Any edge for which this index exceed a prescribed threshold will be swapped, i.e. replaced by a new edge connecting the adjacent points of the original edge. After all edge swaps are completed, Laplacian smoothing is applied to the mesh. Example show that, when the mesh point density varies smoothly and due care is taken in the vicinity of the boundary, mesh relaxation can dramatically increase the regularity of the mesh and produce improve triangle shapes.
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    URL: http://dx.doi.org/10.1002/nme.1620310607
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
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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.1620320701
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    A boundary integral equation method for an inverse problem related to crack detection (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1371-1387 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper discusses an application of a boundary integral equation method (BIEM) to an inverse problem of determining the shape and the location of cracks by boundary measurements. Suppose that a given body contains an interior crack, the shape and the location of which are unknown. On the exterior boundary of this body one carries out measurements which are interpreted mathematically as prescribing Dirichlet data and measuring the corresponding Neumann data, or vice versa, for a field governed by Laplace's equation. The inverse problem considered here attempts to determine the geometry of the crack from these experimental data. We propose to solve this problem by minimizing the error of a certain boundary integral equation (BIE). The process of this minimization, however, is shown to require solutions of certain are proposed. Several 2D and 3D numerical examples are given in order to test the performance of the present method.
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    URL: http://dx.doi.org/10.1002/nme.1620320702
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    Stress analysis of flat plates with shear using explicit stiffness matrix (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1389-1409 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An explicit expression for the stiffness matrix is worked out for a triangular plate bending element considering the effect of transverse shear deformation. The element has twelve nodes on the sides and four nodes internal to it. The formulation is displacement type and the use of area co-ordinates makes it possible to obtain the shape functions explicitly. Separate polynomials are assumed for transverse displacement and rotations. To obtain the element stiffness matrix no matrix inversion or numerical integration need be carried out and only a few matrix multiplications of low order are necessary. The element, which is initially of thirty five degrees of freedom, can be reduced to a thirty degrees of freedom one by condensation of the internal nodes. An interesting feature of the element developed is that the values of nodal moments computed at a node point, considering different elements surrounding the node, do not vary significantly. Thus the nodal moments can be obtained directly at node points. Also, the element does not give rise to any inconvenience like locking, even for very thin plates. The straightforward approach in formation of the element stiffness will cut down the storage space considerably and will also call for less CPU time, thus making the use of the element well suited to low capacity computers. A number of plate bending problems have been worked out using the present element for different thickness to side ratios and a comparison has been made with the available results. Good accuracy has been observed in all cases, even for a small number of elements.
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    A penalty finite element analysis for nonlinear mechanics of biphasic hydrated soft tissue under large deformation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1411-1439 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The non-linear response of soft hydrated tissues under physiologically relevant levels of mechanical loading can be represented by a two-phase continuum model based on the theory of mixtures. The governing equations for a biphasic soft tissue, consisting of an incompressible solid and an incompressible, inviscid fluid, under finite deformation are presented and a finite element formulation of this highly non-linear problem is developed. The solid phase is assumed to be hyperelastic, and the stress-strain relations for the solid phase are defined in terms of the free energy function. A finite element model is formulated via the Galerkin weighted residual method coupled with a penalty treatment of the continuity equation for the mixture. Using a total Lagrangian formulation, the non-linear weighted residual statement, expressed with respect to the reference configuration, leads to a coupled non-linear system of first order differential equations. The non-linear constitutive equation for the solid phase elasticity is incrementally linearized in terms of the second Piola-Kirchhoff stress and the corresponding Lagrangian strain. A tangent stiffness matrix is defined in terms of the free energy function; this matrix definition can be applied to any free energy function, and will yield a symmetric matrix when the free energy function is convex. An unconditionally stable implicit predictor-corrector algorithm is used to obtain the temporal response histories. The confined compression mechanical test of soft tissue in stress relaxation is used as an example problem. Results are presented for moderate and rapid rates of loading, as well as small and large applied strains. Comparison of the finite element solution with an independent finite difference solution demonstrates the accuracy of the formulation.
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    Numerical simulation of mechanical systems using methods for differential-algebraic equations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1531-1542 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple approach to the numerical simulation of mechanical systems consisting of rigid and flexible bodies is presented. The mechanical system may consist of rigid bodies, different types of flexible bodies, joints and actuators and may have arbitrary topological structure with kinematical loops. The equations of motion are formulated as a large sparse system of equations in absolute co-ordinates as well as relative co-ordinates. These equations are numerically integrated as a system of differential-algebraic equations using modern numerical methods.
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    Dynamics of flexible multibody systems using cartesian co-ordinates and large displacement theory (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1543-1563 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A formulation for the dynamic analysis of flexible systems, composed of slender bodies that can be accurately modelled by beams is presented in this paper. A new set of state variables, composed of Cartesian co-ordinates of points and unit vectors, is introduced to define the beam with respect to an inertial frame. A non-linear Timoshenko beam finite element capable of handling finite displacements with small linear elastic strains is developed. This allows relative displacements between material points of a single beam to be arbitrarily large. Since deformations are not explicit variables, there is no need to define a moving reference frame attached to each flexible body. Instead, deformations are obtained through a displacement-deformation relation based on finite-displacement beam theory. The differential equations of motion are obtained using the Lagrange equations. A symmetric, constant and sparse mass matrix is obtained in the inertial frame. Constraints are introduced with a penalty formulation and the resulting set of ordinary differential equations is integrated with Newmark's family of methods. The whole formulation is extremely simple and the results demonstrate the capabilities and efficiency of the proposed method for dynamic simulation, even when relative displacements are finite in a single beam or coupling effects are significant.
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    A decoupled flexible-relative co-ordinate recursive approach for flexible multibody dynamics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1669-1689 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An extended kinematic graph concept and a variational-vector calculus approach are employed to develop a new recursive formulation for the dynamic analysis of flexible multibody systems. The extended graph concept introduced defines frames and transformations between frames as nodes and edges, respectively, rather than the more traditional body and joint convention. Kinematic relationships between adjacent flexible bodies are derived, using joint relative co-ordinates and a state vector notation that represents both translational and rotational components of velocity. Deformation kinematics are formulated in terms of modal co-ordinates, under small deformation assumptions. Joint relative co-ordinates are decoupled from deformation modal co-ordinates in both kinematic relations and in the recursive dynamics algorithm, leading to a significant reduction in the dimension of matrices that must be inverted. Dynamic analysis of a flexible closed-loop spatial robot is performed to illustrate the efficiency of the algorithm.
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    Dynamic analysis of spatial flexible multibody systems using joint co-ordinates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1799-1812 
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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 a systematic method for deriving the minimum number of equations of motion for spatial flexible multibody systems. Relative kinematics are developed using relative joint co-ordinates and relative joint velocities to formulate a minimum number of equations of motion. The present method takes advantage of the simplicity of the absolute co-ordinate formulation and computational efficiency of the relative joint co-ordinate formulation. The system equations of motion are first formulated in terms of a coupled set of absolute reference co-ordinates and elastic modal co-ordinates. These equations are transformed to the joint co-ordinate space by use of a velocity transformation matrix including the elastic modal velocities. A computer algorithm is proposed and extended to closed loop mechanisms. One example of a flexible vehicle is presented and the results are discussed to illustrate the computational efficiency of the method.
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    Constrained motion of deformable bodies (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1813-1831 
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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, issues related to the dynamic modelling of constrained deformable bodies that undergo large rigid body displacements are discussed. Particular attention is focused on finite element formulations. It is shown that the use of nodal co-ordinates and shape functions to describe the finite rotation of some of the commonly used finite elements leads to a linearization of the kinematics and dynamic relationships. The structure of the non-linear dynamic equations that govern the motion of deformable bodies that undergo large displacements is examined. Comments on the finite element formulation of the invariants of motion, the definition of the generalized forces and moments in flexible body dynamics and the computational strategy used for the automatic generation of the equations of motion are made. The computer formulation of the joint constraints between deformable bodies as well as the numerical algorithms currently used in many of the general purpose computer programs that are based on the augmented formulation are discussed. A decoupled joint-elastic acceleration recursive formulation is also presented. This formulation leads to a small system of acceleration equations whose dimensions are independent of the number of the elastic degrees of freedom of the system. In this paper, the coupling between the displacements of the deformable bodies is classified as kinematic, inertia and elastic. In view of this classification, comments on the validity of using the updated finite element Lagrangian formulation and the 4 × 4 transformation matrix in the dynamic analysis of flexible multibody systems are made. The coupling between the finite rotation and the wave motion in constrained deformable bodies is also discussed.
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1851-1852 
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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.1620320819
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992) 
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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.1620330101
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    Numerical solution of integral equations with a logarithmic kernel by the method of arbitrary collocation points (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 143-148 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An integral equation whose kernel presents logarithmic singularity is numerically solved by the method of arbitrary collocation points (ACP). As a first step a Gaussian quadrature of order n (hence of polynomial accuracy 2n- 1) is employed for the numerical approximation of the integral. Until now the collocation, which follows, was performed on special points x̄k, determined as roots of appropriate transcedental functions, in order to retain the 2n - 1 degree of polynomial accuracy of the Gaussian quadrature. In this paper an appropriate interpolatory technique is proposed, so that xk may be arbitrary and yet the high (2n - 1) accuracy of the Gaussian quadrature is retained.
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    Stabilized rapidly convergent 18-degrees-of-freedom flat shell triangular element (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 149-162 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A rank-sufficient flat triangular shell element with drilling degrees-of-freedom is described. A variational basis for this element has been provided by a three-field variational principle with relaxed interelement compatibility and traction continuity conditions. A generalized spurious mode control procedure has been developed in order to stabilize zero energy kinematical modes. Excellent performance has been found in an obstacle course and buckling problems.
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    Some comments on: Benchmark problems and testing of a finite element code for solidification in investment castings (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 213-215 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Additional Material: 2 Ill.
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    Computational structural mechanics and optimal control - the simulation of substructural chain theory to linear quadratic optimal control problemsJoint project of the Natural Science Foundation of China and the Royal society. (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 197-211 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The theory of optimal control and the theory of a substructural chain in static structural analysis are mutually simulated issues. From the minimum potential energy variational principle of the substructural chain, the generalized variational principle with two kinds of variables is derived first. By comparing that generalized variational principle with the variational principle in LQ control theory, the simulation relation is established. Based on that relation, the potential energy and mixed energy formulation of the algebraic Riccati equations are derived, then iterative algorithms are proposed which give the upper and lower bounds to the solution matrix. By using the solutions of the positive and negative co-ordinate algebraic Riccati equations, the canonical transformation matrices for the eigenproblems of the substructural chain and LQ control are constructed respectively, which reduce the eigenproblem to half-size. The properties of the solutions are analysed, which establishes the basis for expansion solutions.
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    Computer-aided analysis and design of electromagnetic devices, by S. Rantajeevan H. Hoole, Elsevier Science Publishing company, New York. 1989. ISBN 0-444-01327-x (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 217-219 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Reliability in computational mechanics, edited by J. T. Oden, Elsevier Science Publications, NY, 1990. No. of pages: 388. Price: $192.25. ISBN 0-444-88560-9 (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 220-220 
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    Keywords: Engineering ; Engineering General
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    Conference diary (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 221-222 
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    Keywords: Engineering ; Engineering General
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    Masthead (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992) 
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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.1620330201
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    Free vibration of axisymmetric and beam-like cylindrical shells, partially filled with liquid (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 235-268 
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    Keywords: Engineering ; Engineering General
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    Notes: A theory is presented for the determination of the free vibration characteristics of anisotropic thin cylindrical shells, partially or completely filled with liquid, for two circumferential wave numbers, n = 0, axisymmetric and n = 1, beam-like. The method used was a combination of finite element analysis and classical shell theory. The shell was subdivided into cylindrical finite elements and the displacement functions were obtained using the shell equations. Expressions for the mass and stiffness matrices for a finite element and for the whole structure were obtained. A finite element was developed for the liquid in cases of potential flow. The natural frequencies of the shell, both empty and partially filled, were obtained and compared with existing experiments and other theories.
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    Effective modelling of spatial buckling of beam assemblages, accounting for warping constraints and rotation-dependency of moments (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 469-502 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A simple, two-noded, finite element model for the three-dimensional buckling analysis of beam assemblages is developed. The underlying generalized-beam theory employed accounts for all coupled significant modes of deformations, including stretching, bending, shear and torsion, as well as warping. Its mixed formulation is of the two-field type, utilizing linear and constant interpolants for displacements and strain fields. Due considerations are given to the effect off inite rotations in space on the non-linear kinematic descriptions as well as the configuration-dependent behaviour of externally applied moment vectors of the conservative and non-conservative types. The performance of the model, and particularly the accuracy of its geometric and load-correction stiffnesses, is assessed in a fairly complete set of numerical simulations.
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    Finite element calculation of energy release rate for 2-D rubbery material problems with non-conservative crack surface tractions (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 907-927 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The energy release rate G for 2-D rubbery material problems with non-conservative crack surface tractions is calculated by a modified version of virtual crack extension method with finite element solutions. The formulation is demonstrated to be ‘patch-independent’ and therefore a complicated finite element model around the crack tip is not required.
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    A numerical technique for the analysis of cracks subjected to normal compressive stresses (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 929-942 
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    Keywords: Engineering ; Engineering General
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    Notes: The purpose of the present paper is the development of a numerical method for the evaluation of the Stress Intensity Factor in mode II at the tips of closed cracks subjected to compressive normal stresses and monotonically increasing shear stresses. A hybrid Boundary Element Technique, originally developed for the analysis of open cracks, has been suitably modified. The Stress Intensity Factor is evaluated directly on the basis of the displacement discontinuities computed at the crack tip element, by taking into account the development of frictional resistance on the crack surfaces. A limited number (10-15) of displacement discontinuity elements is found to be sufficient for an accurate evaluation of the Stress Intensity Factor. Some basic aspects of the mechanical behaviour of closed cracks are also investigated on the basis of the proposed method.
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    A thick-thin triangular plate element (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 963-973 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple and efficient triangular finite element is introduced for plate bending applications. The element is a three-node triangular one with three basic degrees of freedom per node and two internal rotation degrees of freedom, using selective reduced integration. Numerical examples indicate that, despite its simplicity, the element is not only competitively accurate, but also useful as a thick-thin triangular plate bending element. It is also pointed out that this element using selective reduced integration is in fact a mixed element.
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    An integration scheme for Prandtl-Reuss elastoplastic constitutive equations (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 943-961 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We investigate the Generalized Midpoint Rule for the time integration of elastoplastic constitutive equations for pressure-independent yield criteria. The incremental equations are divided into one scalar hydrostatic pressure/dilation rate equation, and a stress deviator/strain rate deviator tensorial equation, the solution of which reduces to one single scalar equation in the plastic multiplier. The existence and uniqueness of an incremental solution is discussed. The pressure/deviator decomposition is the basis for reduced integration of the pressure term in the Principle of Virtual Work, in order to avoid locking and spurious pressure oscillations. It is also shown that an optimal choice of the parameter of the Midpoint Rule can be computed by reference to the analytical solution of the equations assuming no work hardening. A benchmark test shows that this choice allows increased time steps. This formulation is applied to two classical problems: bulging of a tube under internal pressure and tension test on a notched specimen, and a comparison with the analytical solution is performed. Finally, the hypothesis which sustains these formulations of elastoplasticity (constant strain rate during an increment) is discussed with reference to elastic unloading and residual stress computation.
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    Delaunay's mesh of a convex polyhedron in dimension d. application to arbitrary polyhedra (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 975-995 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: This paper presents a method for creating a Delaunay triangulation connected to a set of specified points. The theoretical aspect is recalled for an arbitrary dimension and the method is discussed in order to derive a practical approach, valid for dimensions 2 and 3, which is simple, robust and well adapted to computation. Convex polyhedral and arbitrary polyhedral situations are introduced.
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    Theoretical development and numerical verification of a geometrically non-linear, 3-D based finite element for composite materials (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1119-1138 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A geometrically non-linear thin shell element made from classical laminated materials is developed from three dimensional continuum concepts that admits arbitrarily large displacements and rotations. The development shows how explicit integration through the thickness of the element can be accomplished without sacrificing significant accuracy of the element.Computations obtained via the present formulation are compared with four test problems for which numerical data are available. All computations were carried out using the Crisfield-Riks arc length continuation algorithm with a full Newton-Raphson iterative scheme. Excellent agreement is observed for each test problem.
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    A new explicit variable time-integration self-starting methodology for computational structural dynamics (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1165-1180 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new explicit variable time-integration methodology and architecture which possesses self-starting attributes, eliminates the need to involve acceleration computations, and which has improved accuracy characteristics in comparison to the traditional central-difference-type formulations customarily advocated is described for applicability to computational structural dynamics. To sharpen the focus of the present study, an explicit variable time-integration architecture which is relatively simple, yet effective, is described. Unlike variable explicit time-integration formulations adopted in the past, the present self-starting variable time-integration architecture and implementation aspects facilitate a simplified representation and a straightforward and effective approach for combining finite element meshes requiring different time steps in a single analysis. Numerical test cases are provided which demonstrate the applicability of the proposed formulations.
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    An optimal method for the solution of the constrained eigenvalue/response problem for large structures comprising rigidly-connected substructures (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1139-1163 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Dynamic substructuring or modal synthesis is established as a powerful means by which the computational effort required to perform dynamic analyses of large structures comprising many degrees of freedom can be reduced. For the case where the substructures are rigidly connected a method of synthesis is proposed which gives very substantial improvements in efficiency over existing methods both in terms of the number of floating-point operations which must take place and the on-board computer memory required. The proposed method makes use of a stable co-ordinate transformation which reduces the mass matrix for the constrained composite-system to the identity matrix and makes the stiffness matrix banded. The bandwidth is exactly equal to twice the total number of constraints plus 1. This is usually very small in comparison with the total number of degrees of freedom in the constrained composite-system. The proposed method is ideal for combining a number of substructures into a single new substructure in an efficient way without necessarily disposing of any degrees of freedom. Approximate formulae are presented which give the ratios of the number of operations required for established methods compared with the number needed for the proposed method. These formulae determine when it is appropriate to use the method proposed here.
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    Non-singular boundary integral representation of potential field gradients (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1181-1195 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In this paper we derive the non-singular boundary integral representation of the field gradients for two-dimensional problems of classical potential field theory. Numerical implementation of this representation is developed too. The proposed method eliminates the most inaccurate influence coefficients which arise when singular integral representations are used and the internal point approaches the boundary. Since the integrands in this new method are finite at any internal point, accurate numerical results are achieved even in that portion of a solid which is very close to a discretized boundary. Two test problems are analysed in which the numerical results computed by strongly singular, weakly singular and non-singular integral representations are compared mutually and with exact solutions.
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    Computing alternative optimal collapse mechanisms (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1197-1216 
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    Keywords: Engineering ; Engineering General
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    Notes: Optimal plastic designs for structural frames can be obtained via static or kinematic considerations, each leading to a mathematical model requiring solution by linear programming. In both cases a mechanism can be found which satisfies the Foulkes optimality condition. However, this mechanism generally has many degrees of freedom and is most unlikely to be the actual collapse mode of the frame. A simple algorithm based on the method of redundant forces is presented for the automatic generation of the alternative optimal collapse mechanisms, any of which may be the actual collapse mode.
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    ALE finite element formulation for ring rolling analysis (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1217-1236 
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    Keywords: Engineering ; Engineering General
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    Notes: In this paper, a ring rolling process is analysed by the Arbitrary Lagrangian Eulerian (ALE) finite element method. Phenomena associated with the process, such as large deformations, elastoplastic material behaviour and the friction on the interface, are included in the analysis. Special modelling on driven, idle and guide rolls is given. Results which include the overall shape of the formed ring, the time histories of roll separating force and driving torque, the distribution of the normal pressure on the ring-roll interface as well as the distribution of effective stresses in the formed ring, are also presented.
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    On the development of explicit robust schemes for implementation of a class of hyperelastic models in large-strain analysis of rubbers (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1237-1249 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The issue of developing effective and robust schemes to implement a class of the Ogden-type hypereiastic constitutive models, for large-strain analysis of rubber-like materials, is addressed. To this end, explicit forms for the corresponding material tangent-stiffness tensors are developed, and these are valid for the entire deformation range; i.e. with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.
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    Tetrahedral elements for fluid flow (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1251-1267 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Several old and new tetrahedral elements are tested and compared to some classical hexahedral elements for the solution of three-dimensional incompressible fluid flow problems. The proposed elements are created by adding velocity degrees of freedom to the basic trilinear velocity, constant pressure tetrahedron so as to satisfy the Brezzi condition. Numerical tests carried out for an artificial divergence-free flow problem and the lid-driven cubic cavity up to a Reynolds number of 400 are used to compare the proposed elements and assess their accuracy.
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    The dual boundary element method: Effective implementation for crack problems (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1269-1287 
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    Keywords: Engineering ; Engineering General
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    Notes: The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.
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    A study of boundary layers in plates using Mindlin-Reissner and 3-D elements (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1305-1320 
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    Keywords: Engineering ; Engineering General
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    Notes: Finite elements based on Mindlin-Reissner theory and three-dimensional theory are used to study the distribution of shear forces and twisting moments in plates with various simple support conditions. Differences between the results obtained using these two theories are highlighted. A crude adaptive mesh refinement procedure is applied to improve the accuracy of the finite-element analysis.
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    Addendum - J. C. Simo and K.K. Wong, unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum, Int. J. Numer. Methods eng., 31, 19-52 (1991) (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1321-1323 
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    Keywords: Engineering ; Engineering General
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    Letters to the editor (1992)
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    International Journal for Numerical Methods in Engineering 33 (1992), S. 1325-1325 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Electronic Resource
    Announcements (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1329-1329 
    Details
    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.1620330617
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    Paper (German National Licenses)
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  • 100
    Electronic Resource
    Electronic Resource
    Conference diary (1992)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 33 (1992), S. 1327-1328 
    Details
    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.1620330616
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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