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  • Articles  (322)
  • Engineering  (322)
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  • 1995-1999
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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.
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    URL: http://dx.doi.org/10.1002/nme.1620320204
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  • 2
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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 
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    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.
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    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 
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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 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.
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    URL: http://dx.doi.org/10.1002/nme.1620320205
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  • 4
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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 
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    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.
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    URL: http://dx.doi.org/10.1002/nme.1620320209
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  • 5
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    Announcements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 439-439 
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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.1620320212
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  • 6
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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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  • 7
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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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  • 8
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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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  • 9
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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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  • 10
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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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  • 11
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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.
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    URL: http://dx.doi.org/10.1002/nme.1620320602
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  • 12
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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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  • 13
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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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  • 14
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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.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310806
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  • 15
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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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    ISSN: 0029-5981
    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).
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310808
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  • 16
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310807
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  • 17
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620320309
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  • 18
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620320308
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  • 19
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620320310
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  • 20
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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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    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.1620320312
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  • 21
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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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    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.1620320313
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  • 22
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620320311
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  • 23
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310103
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  • 24
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310108
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  • 25
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310107
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    Exact block diagonalization of large eigenvalue problems for structures with symmetry (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 265-285 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310205
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310207
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310206
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310208
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310303
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    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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    URL: http://dx.doi.org/10.1002/nme.1620310304
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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
    Source: Wiley InterScience Backfile Collection 1832-2000
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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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    URL: http://dx.doi.org/10.1002/nme.1620310306
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    An Eulerian approach for die compaction processes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 509-524 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 525-545 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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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    URL: http://dx.doi.org/10.1002/nme.1620310308
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 611-614 
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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.1620310312
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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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)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 615-618 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    URL: http://dx.doi.org/10.1002/nme.1620310313
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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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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    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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    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.
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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
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    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.
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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
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    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.
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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
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    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.
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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
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    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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    Linear-non-linear dynamic substructures (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 967-985 
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    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.
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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
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    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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    A Computationally viable higher-order theory for laminated composite plates (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1069-1086 
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    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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    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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    Mesh relaxation: A new technique for improving triangulations (1991)
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    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
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    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
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    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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    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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    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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    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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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    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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    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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    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
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    URL: http://dx.doi.org/10.1002/nme.1620320819
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    An adjoint variable method for sensitivity analysis of non-linear elastic systems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1649-1667 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An adjoint variable method for design sensitivity analysis of non-linear elastic systems is presented. The method uses domain parameterization and a mutual form of the Hu-Washizu energy principle, and extends results reported in a recent work for linear elastic systems to non-linear elasticity. Non-linearities due to finite deformations and non-linear, hyperelastic constitutive models are considered. In contrast to other methods for non-linear sensitivity analysis, the present formulation can be applied with force, displacement or mixed approximate solution methods.The mutual energy expression used in the adjoint sensitivity derivation is developed from a non-linear extension of the Hu-Washizu energy functional and yields a linear governing equation for the adjoint system. This has important ramifications for the computational cost of a sensitivity analyses of non-linear systems: excluding the cost of determining the response of the system, the cost of a sensitivity analysis for a non-linear system is essentially the same as that for a linear system. Finite element implementation of the resulting sensitivity expressions is discussed, and two numerical examples are presented. The first example involves large deformations of a Mooney-Rivlin body, while the second involves design sensitivity analysis for mixed solution methods.
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    Lagrange constraints for transient finite element surface contact (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 103-128 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new approach to enforce surface contact conditions in transient non-linear finite element problems is developed in this paper. The method is based on the Lagrange multiplier concept and is compatible with explicit time integration operators. Compatibility with explicit operators is established by referencing Lagrange multipliers one time increment ahead of associated surface contact displacement constraints. However, the method is not purely explicit because a coupled system of equations must be solved to obtain the Lagrange multipliers. An important development herein is the formulation of a highly efficient method to solve the Lagrange multiplier equations. The equation solving strategy is a modified Gauss-Seidel method in which non-linear surface contact force conditions are enforced during iteration. The new surface contact method presented has two significant advantages over the widely accepted penalty function method: surface contact conditions are satisfied more precisely, and the method does not adversely affect the numerical stability of explicit integration. Transient finite element analysis results are presented for problems involving impact and sliding with friction. A brief review of the classical Lagrange multiplier method with implicit integration is also included.
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    An adaptive procedure for stabilizing convergence quality in frequency-constrained design optimization of bar structures supporting non-structural massThis work was presented in part at the Second NASA/Air Force Symposium on Multidisciplinary Analysis and Optimization in Hampton, Virginia on September 28-30, 1988 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1-27 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents an improved optimality criteria (OC) method for minimum-weight design of bar structures supporting non-structural mass and subjected to multiple natural frequency constraints and minimum gauge restrictions. The convergence quality of the OC method hinges on both the number of active constraints retained and the choice of a proper step size. This being the case, a criterion, which uses previous scaled designs to ‘adaptively’ tune the step size, is established with the purpose of dissolving the (sometimes violent) oscillations of scaled design weights in the iteration history. As the step size is tuned, the convergence rate is descreased. Hence, a modified Aitken's accelerator, which extrapolates from previous scaled designs to obtain an improved one, is used. Its effect is to both increase the overall rate and reduce the net cost of convergence by reducing the number of repeat finite element analyses. The method presented here is used to qualitatively survey the convergence of several OC recursive schemes compositely used to resize and to evaluate the Lagrange multipliers. Design examples are presented to demonstrat the method. The method is adaptable, as it eliminates the need for adjustments of internal parameters during the redesign stage.
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    Generalized numerical integration of moments (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 129-147 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Sampling points and weighting coefficients of the Gaussian type are presented for integrands typically encountered in axisymmetric finite elements. The proposed method is a generalization of Gaussian Integration of Moments for non-zero limits of integration. The method achieves one extra order of accuracy in the integration of polynomials as compared with the Gauss-Legendre method with the same number of sampling points. Although the locations of sampling points require the solution of non-linear equations, analytical solutions are presented for the cases of one and two sampling points. Special cases of these general expressions are shown to include both Gauss-Legendre integration corresponding to an integration range at a considerable distance from the axis of symmetry, and Fishman integration corresponding to an integration range whose lower limit lies on the axis of symmetry.
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    A numerical study of the deviation of the crack ending at the interface in a multilayer (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 171-181 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The study of the deviation of a crack reaching the interface separating two materials in a multilayer in a 4-point deflection is considered. This study is based on the use of special isoparametric finite elements.1 (The elements surrounding the crack tip have nodes placed at a distance α from the crack tip, and in this way we impose a singularity of the stresses in the neighbourhood of the crack.)The Erdogan2 criterion that estimates the deviation angle shows that this angle is a function of the initial angle of the crack, and the properties of each component of the multilayer.
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    Petrov-Galerkin finite element model for compressible flows (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 255-274 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A Petrov-Galerkin method for the solution of the compressible Euler and Navier-Stokes equations is presented. It is based on the introduction of an anisotropic blancing diffusion in the direction of the local direction of propagation of the scalar variables. The local direction in which the anisotropic diffusion is introduced is uniquely determined, and the magnitude of the balancing diffusion is automatically calculated locally using a criterion that is optimal for one-dimensional transport equations.The algorithm has been implemented using four-noded bilinear elements with forward Euler and second-order Runge-Kutta methods of integration in time. Several applications are presented and show the stability and approximation properties of the method.
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    Multiple scale finite element methods (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 969-990 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: New temporal and spatial discretization methods are developed for multiple scale structural dynamic problems. The concept of fast and slow time scales is introduced for the temporal discretization. The required time step is shown to be dependent only on the slow time scale, and therefore, large time steps can be used for high frequency problems. To satisfy the spatial counterpart of the requirement on time step constraint, finite-spectral elements and finite wave elements are developed. Finite-spectral element methods combine the usual finite elements with the fast convergent spectral functions to obtain a faster convergence rate; whereas, finite wave elements are developed in parallel to the temporal shifting technique. Therefore, the spatial resolution is increased substantially. These methods are especially applicable to structural acoustics and linear space structures. Numerical examples are presented to illustrate the effectiveness of these methods.
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    Multi-domain two- and three-dimensional thermoelasticity by BEM (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 991-1008 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A computationally advantageous multi-domain boundary element formulation is presented for uncoupled thermoelastic analysis of two- and three-dimensional isotropic media. Particular integrals capable of representing exactly a quadratic temperature distribution in both two and three dimensions are employed. These particular integrals are derived using an orderly approach. When temperature data are provided at discrete points, the best fit quadratic distribution is generated in the least square error sense which, together with a multi-domain approach, makes it possible to represent an arbitrary temperature distribution within acceptable bounds. Numerical examples are given to show the efficiency and effectiveness of the present formulation, which is now incorporated in a general purpose boundary element code named GPBEST.
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    The Lanczos algorithm applied to unsymmetric generalized eigenvalue problem (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1009-1026 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: Application of the two-sided Lanczos recursion to the unsymmetric generalized eigenvalue problem is presented. The system matrices are real and unsymmetric. Therefore, the recursions are performed in real arithmetic and complex arithmetic is employed in the QR algorithm used to extract the eigenvalues of the transformed tridiagonal matrix. The biorthonormal transformation of the unsymmetric generalized eigenvalue problem is considered in detail with appropriate proofs presented in Appendices. Issues relating to the computer implementation of the unsymmetric generalized eigenvalue problem are discussed. The example problems solved demonstrate the working of the algorithm in extracting the complex and/or real eignevalues of an unsymmetric system of matrices. Also, the algorithm is applied to extract a few of the eigenvalues of a large fluid-structure interaction problem, and the results are compared with the eigenfrequencies extracted by an unsymmetric subspace iteration procedure presented in the literature.
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    A method of finite element tearing and interconnecting and its parallel solution algorithm (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1205-1227 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.
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    Parallel/vector improvements of the frontal method (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1267-1281 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: We present, discuss, and report on the performance of two combined parallel/vector frontal algorithms which have been incorporated in a production finite element code. Two parallelization strategies are described. The first approach is algebra driven and is recommended for the solution of problems with a large bandwidth on a coarse grain configuration. The second strategy is targeted for finer grain systems; it blends the first one with a substructuring technique that is based on a careful partitioning of the finite element mesh into a series of subdomains. Using only 4 IBM 3090/VF processors, the proposed algorithms are shown to deliver speed-ups as high as 17 with respect to a serial non-vectorized frontal solver.
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    Stochastic design sensitivity in structural dynamics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1247-1265 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method to analyse stochastic design sensitivity for problems of structural dynamics is presented. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element context. An alternative form of the constraint functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations exicited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition technique: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient; they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. A number of numerical results for the deterministic and stochastic sensitivity analysis of beams and shells illustrates the paper.
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    Adaptive analysis of thin shells using facet elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1283-1301 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: An adaptive mesh refinement (AMR) procedure is used in static thin shell analysis using triangular facet shell elements. The procedure described herein uses the h-version of adaptive refinement based on an error estimate determined by using the best guess values of bending moments and membrane forces obtained from a previous solution. It includes the use of a relaxation factor to achieve better convergence. Some examples are presented to illustrate this method. The results obtained are compared with those of uniform mesh refinement (UMR).
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    An algorithm for three-dimensional convection and diffusion with very different horizontal and vertical length scales (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1303-1319 
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    Keywords: Engineering ; Engineering General
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    Notes: An algorithm is developed and tested for the numerical solution of the three-dimensional convection - diffusion equation appropriate for the marine environment, in which the horizontal and vertical scales differ by one or two orders of magnitude. The algorithm splits the horizontal and vertical parts of the process, treating the horizontal convection and diffusion explicitly and the vertical convection and diffusion by an implicit finite element method that is unconditionally stable. The overall stability conditions on the algorithm are discussed and its accuracy is verified through a number of test problems whose exact solutions are known.
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1365-1368 
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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.1620320613
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    Delamination buckling of laminated plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1321-1337 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The subject of this paper is the buckling of laminated plates, with a pre-existing delamination, subjected to in-plane loading. Each laminate is modelled as an orthotropic Mindlin plate. The analysis is carried out by a combination of the finite element and asymptotic expansion methods. By applying the finite element method, plates with general delamination regions can be studied. The asymptotic expansion method reduces the number of unknown variables of the eigenvalue equation to that of the equation for a single Kirchhoff plate. Numerical results for the critical buckling load are presented for several examples. The effects of the shape, size and position of the delamination on the buckling load are studied through these examples.
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    Modelling of structures by finite elements Volume 1: Elastic solids; Volume 2: Beams and plates. In French: Modelisation des structures par elements finis Volume 1 : Solides elastiques [Price: 150 FR.]; Volume 2 : Poutres et plaques [Price 200 FR.] by Jean-Louis Batoz and Gouri Dhatt, Editions Hermes, Paris, France, 1990 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1363-1363 
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    Keywords: Engineering ; Engineering General
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    An alternating technique for evaluating weight functions for 3-D surface flaws in finite solid bodies (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1339-1361 
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    Notes: An efficient method, based on the Schwarz-Neumann alternating technique, is presented for computing weight functions of a general solid (3-D as well as 2-D), with embedded or surface-flaw configurations. The total rate of change of the crack-opening displacements, due to simple perturbations of crack-dimension characteristics, is conveniently decomposed into the infinite-domain and boundary-correction parts. The former is determined from available analytical solutions of ideal-shaped cracks, whereas the latter is computed numerically by imposing nil boundary-traction requirements for the displacement field corresponding to the weight functions. Numerical examples, with solutions for 3-D weighted-average and local stress intensity factors, indicate that the proposed method is very accurate and efficient.
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    Conference diary (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 1369-1370 
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    Three-dimensional full Navier-Stokes solvers for incompressible flows past arbitrary geometries (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1427-1451 
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    Notes: The computation of the three-dimensional viscous flow past several geometries is investigated. An iterative technique resting on the fully elliptic mode is applied to the Reynolds-Averaged Navier-Stokes Equations written in a non-orthogonal curvilinear body-fitted co-ordinate system. Results of the computation are compared with available experiments.
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    Masthead (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991) 
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    Keywords: Engineering ; Engineering General
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    Conference diary (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1471-1474 
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    Keywords: Engineering ; Engineering General
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    In memoriam: Lothar Collatz (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1475-1476 
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    Announcement (1991)
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    International Journal for Numerical Methods in Engineering 31 (1991), S. 1476-1476 
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    Preface (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 651-651 
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    Keywords: Engineering ; Engineering General
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    Masthead (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991) 
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    Shape reconstruction and volume meshing for complex solids (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 665-675 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The reconstruction of a solid surface from a series of cross-sections and the generation of a volume mesh that conforms with a prescribed surface are issues that arise in numerous applications. We describe an approach to both these problems that is based on the generation of a tetrahedral mesh which automatically captures a triangulation of the surface points. A simple algorithm for introducing a set of interior points permits a simple partition of the volume mesh into two disjoint sets of tetrahedra such that one set determines the interior of the solid while the second determines the exterior.
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    A comparison of adaptive-grid redistribution and embedding for steady transonic flows (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 653-663 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: In recent years, numerical analysts have increasingly turned to adaptive-grid techniques to efficiently obtain highly-accurate solutions to partial-differential equations. This paper presents a comparison of two distinct grid-adaptation approaches, grid-point redistribution and grid-embedding, applied to two-dimensional, steady, inviscid, shocked flows. Grid redistribution is accomplished through a control function approach applied to the elliptic-grid generator while the embedding approach consists of a fixed global grid and an automatically chosen number of irregularly shaped, embedded regions. For both techniques, the Euler flow equations are integrated to steady state using Ni's Lax-Wendroff-type integrator to predict the flow fields about a variety of isolated airfoil configurations. The application of a common integration scheme as well as a common adaptive control function leads to a direct comparison of the effectiveness of the two adaptation approaches for the types of problems tested.
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    Adaptive finite element methods for hyperbolic systems with application to transient acoustics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 677-707 
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    Keywords: Engineering ; Engineering General
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    Notes: The solution of the hyperbolic systems of equations governing transient acoustics by adaptive finite elements and various finite difference time discretization schemes is addressed. Emphasis is placed on the use of a class of implicit Runge-Kutta methods for temporal approximations.
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    Automatic three-dimensional mesh generation by the finite octree technique (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 709-749 
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    Keywords: Engineering ; Engineering General
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    Notes: An octree-based fully automatic three-dimensional mesh generator is presented. The mesh generator is capable of meshing non-manifold models of arbitrary geometric complexity through the explicit tracking and enforcement of geometric compatibility and geometric similarity at each step of the meshing process. The resulting procedure demonstrates a linear growth rate with respect to the number of elements and can be easily integrated with any geometric modeller through a set of geometric operators.
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    An adaptive finite element method for transient compressible flows with moving boundaries (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 751-765 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A description is given of an adaptive finite element method for the simulation of two dimensional compressible flows with moving boundaries. The method is implemented on an unstructured triangular grid and the mesh adaptation is achieved by local grid regeneration, using an error estimation procedure coupled to an automatic triangular mesh generator. Two numerical examples are included to illustrate the numerical performance of the method.
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    Finite element analysis of heat transfer and flow problems using adaptive remeshing including application to solidification problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 767-781 
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    Keywords: Engineering ; Engineering General
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    Notes: An error estimation technique for adaptive finite element analysis of heat conduction problems is described. The performance of this technique is demonstrated using a two-dimensional steady-state linear benchmark problem with a known analytical solution. A transient non-linear heat conduction problem involving solidification is then solved as a typical practical application. Some preliminary investigations for error indicators in flow problems are presented.
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    Paving: A new approach to automated quadrilateral mesh generation (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 811-847 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper presents a new mesh generation technique, paving, which meshes arbitrary 2-D geometries with an all-quadrilateral mesh. Paving allows varying element size distributions on the boundary as well as the interior of a region. The generated mesh is well formed (i.e. nearly square elements, elements perpendicular to boundaries, etc.) and geometrically pleasing (i.e. mesh contours tend to follow geometric contours of the boundary). In this paper we describe the theory behind this algorithmic/heuristic technique, evaluate the performance of the approach and present examples of automatically generated meshes.
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    Adaptivity and mesh generation (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 783-810 
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    Keywords: Engineering ; Engineering General
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    Notes: The objective of achieving economically finite element solutions of specified accuracy is now within reach. The importance of this objective is finally recognized by commercial code originators and efforts directed at automating the process are meeting with success.Three essential ingredients are here necessary. These are: (i) economical and efficient a posteriori error estimating processes; (ii) close prediction of the refinement necessary for a specific accuracy to be achieved so that numerous trial and error solutions can be avoided; (iii) implementation of the predicted refinement.With h and h-p adaptive processes Step (iii) requires powerful mesh generator facilities capable of achieving meshes of specified density.The paper considers all three aspects, introducing some novel concepts in error estimation and discussing in some detail the problem of mesh generation. As such, it introduces the other papers of this special issue, which discuss various aspects in more detail.
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    Automated adaptive two-dimensional system for the hp-version of the finite element method (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 867-893 
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    Keywords: Engineering ; Engineering General
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    Notes: This paper presents an automated, adaptive finite element modelling system based on the hp-version of the finite element method. Error estimation and correction indication procedures with an automatic mesh generator and a p-version analysis code are combined to provide a computationally efficient modelling environment. Error prediction techniques are employed to find the best combination of finite element discretization, h-, and overall polynomial order, p-, needed to achieve the prescribed level of accuracy. The automated adaptive modelling results demonstrate the capability of the modelling system of predicting discretizations to perform a p-version finite element analysis to achieve prescribed levels of accuracy in the most efficient manner.
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    A new approach to the development of automatic quadrilateral mesh generation (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 849-866 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: A methodology for the automatic mesh generation of quadrilateral elements is proposed. The methodology is based on the facts that (i) a region can always be subdivided entirely into quadrilaterals if the polygon which forms the boundary of the region has an even number of sides, (ii) a quadrilateral can be formed by two triangles which share a common side. By taking advantage of the techniques developed in an existing automatic triangular mesh generator, quadrilateral meshes can be generated according to the distribution of user specified element size over the domain of interest. In particular, an automatic quadrilateral mesh generator based on the advancing front technique for triangular mesh generation1 is described. Techniques to improve the quality of the generated quadrilateral meshes are introduced. The robustness and versatility of the mesh generator are demonstrated by a variety of examples.
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    Conference diary (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 939-941 
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    Keywords: Engineering ; Engineering General
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    Masthead (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991) 
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    Keywords: Engineering ; Engineering General
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    Adaptivity for compressible flow computations using point embedding on 2-D structured multiblock meshes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 895-919 
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    Keywords: Engineering ; Engineering General
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    Notes: Structured meshes which consist of a single curvilinear network of lines and points have limited flexibility when applied to geometrically complicated domains. To alleviate this constraint the idea of multiblock structured meshes has been proposed. This approach subdivides the domain of interest into regions, each of which can be mapped into a transformed space equivalent to a rectangle. The connections between these regions define the mesh topology. By a suitable subdivision of the domain, multiblock grids, which are globally unstructured between blocks, but provide a structured grid within blocks, can be used to discretize highly complex geometrical domains. This technique has been used to great effect, both in two and three dimensions. However, structured meshes are not naturally amenable to adaptivity techniques based upon local point addition. This paper describes a method, based upon the quadtree data structure, which allows for local point refinement on multiblock meshes for use with flow algorithms for the simulation of compressible flow around aerospace geometries. The basic concepts of multiblock meshes, the use of the quadtree data structure, together with the treatment within the flow algorithm of locally embedded meshes, will be discussed.
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    A modified Euler method for dynamic analyses (1991)
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    International Journal for Numerical Methods in Engineering 32 (1991), S. 943-955 
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    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A modified version of the well known Euler method for numerical integration is presented, and its application in analyses of the dynamic response of structures is discussed. This modified method was first introduced in 1981, and it has been reported that it was discovered by accident. When first introduced, however, valuable information related to the accuracy, stability and merits of the method were not provided. It is shown that the modified Euler method has features that make it an attractive approach for applications in dynamic analyses of structures. Accuracy and stability analyses are made for the method by considering free-vibrational responses of linear, undamped, single-degree-of-freedom systems. The method is explicit and extremely easy to use. However, it is conditionally stable. Applications of the method are also made which illustrate its usefulness and inherent simplicity. Furthermore, comparisons of the modified Euler method and the Newmark beta method are reported which elucidate the relative merits of these methods.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320502
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    Elastic stress analysis of three-dimensional solids with small holes by BEM (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 369-384 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced level development of the boundary element method is presented for the elastic stress analysis of a three-dimensional solid containing a large number of small diameter, tubular shaped holes. The formulation has been developed such that these holes can be modelled by a system of curvilinear line elements, resulting in substantial savings in both data preparation and computing costs. This is accomplished by assuming a variation in the displacement field along the circumference defined in terms of trigonometric functions together with a linear or quadratic variation of displacements along the longitudinal direction.
    Additional Material: 15 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310210
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