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  • 201
    Electronic Resource
    Electronic Resource
    Fourth order Runge-Kutta method in 2d for linear boundary value problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1229-1245 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The standard formulae of the fourth order Runge-Kutta method are transformed into a finite difference equation which allow us to solve linear boundary value problems. This equation is manipulated further and extended into 2D for solving second order linear partial differential equations. The various transformations result in four equations for the two first derivatives, mixed second derivative and the function value in the depicted point of the mesh. Each of these quantities is expressed by the linear combination of values of the function given in the eight nearest nodes around the depicted node. Explicit formulation of the equations for corner, boundary, symmetry and internal nodes is given. The results of the new computer code are compared with an analytical result and precise measurements, as well as a FEM calculation. It is concluded, for the specific example investigated, that the new method is about ten or more times precise than the FEM with the same number of elements. The major merit of the method lies in the fact that it can be implemented on personal computers.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320605
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  • 202
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    Buckling under combined loading of shear deformable laminated anisotropic plates using ‘infinite’ strips (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1319-1331 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient formulation is presented to predict the buckling under combined loading of relatively long shear deformable laminated anisotropic plates. The numerical formulation is based on a semi-analytical Reissner-Mindlin ‘infinite’ strip. The effect of shear locking is eliminated by the use of higher Lagrangian polynomials. The deterioration of Kirchhoff theory (classical plate theory (CPT)) in the case of moderately thick anisotropic plate is highlighted. A complete convergence study of the present theory was carried out and the accuracy of the method is demonstrated by comparison with the published results.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310707
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  • 203
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    Adaptive error analysis in seepage problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1333-1356 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Numerical experiments in adapting variations of a computationally simple error estimator (the Zienkiewicz-Zhu estimator) to an existing finite element code are shown. The error estimator used allows both overall and local errors to be estimated. From the local estimates of error, refinements of the mesh are calculated to reach a prescribed error tolerance. These calculated refinements are used by a mesh refiner to produce a modified mesh which lowers the overall error to the prescribed value while keeping the mesh as crude as possible. The physical example on which these numerical experiments are performed is that of free surface flow through an earth dam with a toe drain. It is also shown how the problem formulation affects the error analysis and how the choice of computational scheme affects the mesh adaptation.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310708
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  • 204
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    Self-adaptive space and time grids in device simulation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1357-1374 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: For the solution of the three basic semiconductor equations in two space dimensions fully self-adaptive grids are a powerful tool to optimize the ratio between the number of unknowns and the accuracy of the solution. For the method of finite differences hardly any mathematically founded criterion for automatic grid control can be given which can be implemented in a computer program with acceptable effort. Therefore most of the strategies for self-adaptive grid control are totally heuristic or derived from physical properties.In this paper we present criteria for the design of an initial space grid. We discuss some conventional strategies for the automatic control of space grids (e.g. equidistribution of the local discretization error) and present new criteria (e.g. degree of coupling of the equations, physical properties like net generation rate). For the time grid an automatic step length control algorithm is presented and the interaction between space and time grid is analysed. Throughout the paper the results are illustrated by realistic examples.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310709
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  • 205
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    Linearization of dynamic equations of flexible mechanisms - a finite element approach (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1375-1392 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A finite element based method is presented for evaluation of linearized dynamic equations of flexible mechanisms about a nominal trajectory. The coefficient matrices of the linearized equations of motion are evaluated as explicit analytical expressions involving mixed sets of generalized co-ordinates of the mechanism with rigid links and deformation mode co-ordinates that characterize deformation of flexible link elements. This task is accomplished by employing the general framework of the geometric transfer function formalism. The proposed method is general in nature and can be applied to spatial mechanisms and manipulators having revolute and prismatic joints. The method also permits investigation of the dynamics of flexible rotors and spinning shafts. Application of the theory is illustrated through a detailed model development of a four-bar mechanism and the analysis of bending vibrations of two single link mechanisms in which the link is considered as a rotating flexible arm or as an unsymmetrical rotating shaft, respectively. The algorithm for the calculation of the matrix coefficients is directly emenable to numerical computation and has been incorporated into the linearization module of the computer program SPACAR1.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310710
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  • 206
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    Thick shell and solid finite elements with independent rotation fields (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1393-1414 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Thick shell and solid elements presented in this work are derived from variational principles employing independent rotation fields. Both elements are built on a special hierarchical interpolation and both possess six degrees of freedom per node. Performance of the elements is evaluated on a set of problems in elastostatics. However, the formulation presented herein is also suitable for transient and non-linear problems.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310711
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  • 207
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    Algorithms for draping fabrics on doubly-curved surfaces (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1415-1426 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Three algorithms for draping biaxially woven fabrics on arbitrarily curved surfaces are presented and compared for numerical accuracy and computational expense. The first one minimizes the elastic energy in each fabric cell, while the two others are based on placing a net of interlocked and inextensible fibres on the surface along geodesic lines. A benchmark shows that the minimum energy technique performs the best and is also the most promising for further optimization in terms of numerical quadrature formulae.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310712
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  • 208
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    Computational mechanics of probabilistic and reliability analysis, edited by: Wing Kam Liu and Ted Belytschko, Northwestern University. Published by: Elmepress International, 1989 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1469-1470 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310716
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  • 209
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310101
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  • 210
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    An alternating digital tree (ADT) algorithm for 3D geometric searching and intersection problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1-17 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A searching algorithm is presented for determining which members of a set of n points in an N dimensional space lie inside a prescribed space subregion. The algorithm is then extended to handle finite size objects as well as points. In this form it is capable of solving problems such as that of finding the objects from a given set which intersect with a prescribed object. The suitability of the algorithm is demonstrated for the problem of three dimensional unstructured mesh generation using the advancing front method.
    Additional Material: 14 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310102
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  • 211
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    Causal FFT treatment applicable to singularity functions (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 53-66 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The objective of this paper is to present a method of causal FFT treatment which is available to not only approximately time-limited and band-limited functions but also singularity functions appearing frequently in earthquake engineering problems such as time domain response analyses and seismic record processing. By means of the causal FFT treatment for a singularity function, it is possible to determine several causal functions. The properties of the obtained causal functions are discussed in detail. The 0 second and 0 Hz value problems of engineering importance concerning the determination of the discrete singularity values of non-time-limited or non-band-limited functions are presented. Finally, by presenting numerical examples, several problems existing in the FFT analyses of singularity functions and a method to solve the problems are explained in detail.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310104
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  • 212
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    Automatic conversion of triangular finite element meshes to quadrilateral elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 67-84 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for the fully automatic conversion of a general finite element mesh containing triangular elements into a mesh composed of exclusively quadrilateral elements. The initial mesh may be constructed of entirely triangular elements or may consist of a mixture of triangular and quadrilateral elements. The technique used employs heuristic procedures and criteria to selectively combine adjacent triangular elements into quadrilaterals based on preestablished criteria for element quality. Additional procedures are included to eliminate isolated triangles. The methods operates completely without user intervention once the nodal co-ordinates and element connectivity of the original mesh are supplied.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310105
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  • 213
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    Geometrically non-linear constant moment triangle which passes the von Kármán patch testResearch supported by the Procurement Executive of the Ministry of Defence, U.K. (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 241-263 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A geometrically non-linear constant moment triangular finite element is designed under Kirchhoff theory from a Hu-Washizu functional such that it passes the totality of von Kármán patch tests for constant strain and constant curvature. The non-linear triangle has the same connection properties as in the linear theory where the constant strain triangle is superposed upon the displacement version of the constant moment triangle.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310204
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  • 214
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    Modelling of superelements in mechanism analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1565-1593 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The paper deals with substructuring for dynamic analysis of flexible multibody systems. Three different techniques based on component synthesis are discussed, corresponding respectively to fully consistent mass discretization, lumped mass discretization and corotational approximation of inertia forces. To simplify the computer implementation, only the lumped mass and corotational approximations have been considered in detail and programmed. Both approaches are validated on simple examples of rotating beams for which a full elastic model is available using a fully non-linear beam element. The computational efficiency of the corotational inertia approach is also demonstrated on the deployment of a large flexible satellite antenna.
    Additional Material: 27 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320805
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  • 215
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    Contribution to symbolic analysis of deformable multi-body systems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1621-1635 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The aim of this paper is to present the equations of motion of deformable multi-body systems in a compact form which is suitable for symbolic generation. Particular attention is paid to obtaining the various equations corresponding to joint displacements and body deformations in a unified manner. A large number of common intermediate terms are identified and appropriately assembled in the final form of the equations; for the various applications, this simple consideration permits one to drastically save on the computational effort. This paper also presents the data which are necessary to completely formulate the problem when the body deformations are described by a linear elasticity model (obtained from a modal or finite element description).
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320807
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  • 216
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    Modelling and control of flexible robots (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1595-1619 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The object of this paper is to present a study on the modelling and control of flexible robots by using a knowledge based control design approach. We first develop an appropriate model of such a mechanical system in the case of open loop robot structures. We use a total Lagrangian formulation. After discretization, the degrees of freedom are the joint variables and the elastic degrees of freedom of each link. The elastic motions are referred to the rigid configuration of the considered link. The control law is obtained by using a non-linear decoupling technique which is applied to the joint variables. A second control loop performs an active damping of the elastic motions: it is based on the linearized model and uses the LQR method. This approach has been experimented with a two flexible links robot. The results demonstrate its feasibility. Further developments mainly concern theoretical aspects on the robustness of these control laws, the identification of the model parameters and the choice of other appropriate modelling techniques.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320806
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  • 217
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    Computer methods in flexible multibody dynamics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1657-1668 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320809
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  • 218
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    A method for selecting deformation modes in flexible multibody dynamics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1637-1655 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In multibody dynamics one may use a number of mode shapes for each body to capture flexibility effects. If a co-rotational and co-translational formulation is applied, rigid body motions are described using special generalized co-ordinates for reference frames and such motions cannot therefore be spanned by the chosen set of mode shapes.Constraint modes are attractive to use following the FEM direct stiffness appraoch and can give accurate solutions with a minimum number of mode shapes in static and low frequency excitation problems. A set of constraint modes often span rigid body motions.The objective of this paper is to show the usefulness of combining constraint modes with an orthogonalization and subsequent rigid body mode shape rejections. In this way the remaining deformation modes together with the reference frame generalized co-ordinates span the solution space of the original set of constraint modes.Two numerical examples are included. A simulation of a truck frame vehicle passing a bump was carried out. A rotating structure with positioning PID-control was studied.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320808
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  • 219
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    A time-dependent incompressible viscous BEM for moderate Reynolds numbers (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1627-1648 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The boundary element method is applied to transient viscous incompressible flow. The time-domain formulation allows a boundary-only solution for linear Stokes flow. For higher speed flows in which the non-linear convective effects cannot be ignored, a volume integral must be retained. However, the introduction of reference velocities often limits the non-linear region to the vicinity of obstacles or bounding surfaces. Additionally, the volume terms are rewritten to eliminate the need for the calculation of velocity gradients. A general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis. This implementation includes a Newton-Raphson algorithm, permitting accurate solutions up to the moderate Reynolds number range. Several numerical examples are provided to validate the present approach.
    Additional Material: 10 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310812
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  • 220
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320101
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  • 221
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    Numerical stability and constitution analysis of λ-type incompatible elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1669-1682 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The weak connection conditions and an independence principle for internal displacements which can guarantee the numerical stability of the incompatible element solution are presented in this paper. A number of problems such as the uncoupling of the two types of displacement functions in the λ-type element, zero energy modes, etc., have been investigated. Some simple and practical guidelines for establishing trial functions of non-compatible elements are given.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310814
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  • 222
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    A refined global-local finite element analysis method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 29-43 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A refined global-local method was proposed to improve the efficiency of finite element analysis. The proposed method was based on the regular finite element method in conjunction with three basic step, i.e. the global analysis, the local analysis and the refined global analysis. In the first two steps, a coarse finite element mesh was used to analyse the entire structure to obtain the nodal displacements which were subsequently used as displacement boundary conditions for local regions of interest. These local regions with the prescribed boundary conditions were then analysed with refined meshes to obtain more accurate stresses. In the third step, a new global displacement distribution based on the results of the previous two steps was assumed for the analysis, from which much improved solutions for both stresses and displacements were produced. Numerical examples showed that the proposed method yielded accurate solutions with significant savings in computing time compared with the regular finite element method. Further, this method is suitable for parallel computation.
    Additional Material: 13 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320103
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  • 223
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    Some computational issues in strain localization problems for rate independent solids (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 79-101 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Issues related to the constitutive modelling and computational treatment of strain localization are examined for the class of rate independent solids. The significance of the constitutive description in localization problems is emphasized and constitutive models currently employed are briefly reviewed. Difficulties faced in finite element analysis, fundamentally associated with the loss of ellipticity of the related boundary value problem, and present trends in the computational treatment are discussed and illustrated by numerical examples.
    Additional Material: 17 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320106
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  • 224
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    New hybrid Laplace transform/finite element method for three-dimensional transient heat conduction problem (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 45-61 
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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 results obtained by the implementation of a new hybrid Laplace transform/finite element method developed by the authors. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite element method. Previously reported hybrid Laplace transform/finite element methods1 have been confined to one nodal solution at a time. When applied to many nodes it takes an excessive amount of computer time. By using a similarity transform method on the matrix of the complex number coefficients this restriction is removed and the reported new method provides a more useful tool for the solution of linear transient problems. Test examples are used to show that the basic accuracy is comparable to that obtainable by analytical, finite difference and finite element methods.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320104
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  • 225
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    Solution of Helmholtz equation by Trefftz method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 63-78 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The application of the Trefftz method for calculating wave forces on offshore structures is presented. Indirect and direct formulations using complete and non-singular systems of Trefftz functions for the Helmholtz equation are posed in this paper. An effective technique using different interpolation functions for the velocity potential and wave force are suggested to improve the computational accuracy of the wave force. The numerical examples show that the present method is highly efficient and accurate.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320105
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  • 226
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    An efficient hybrid quadrilateral Kirchhoff plate bending element (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 149-169 
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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 the formulation of a hybrid stress quadrilateral Kirchhoff plate bending element based on an extended complementary energy functional first proposed by Tong. With the inclusion of a Lagrange multiplier in the functional to enforce a constraint on the assumed moment space, the construction of the C1 deflection profile inside the element is no longer necessary. The continuity requirement on the deflection across the element interfaces is fulfilled by interpolating the generalized nodal displacements over the element boundary in the usual way. Special attention is paid to the selection of assumed moment space such that the element stability, convergency, invariance and nodal point numbering insensitivity are secured while the implementational cost of the element is kept low. Quadratic serendipity interpolation of the transverse deflection is adopted to discretize the distributed transverse loading. Numerical examples are presented and the accuracy achieved is found to be satisfactory.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320109
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    Natural approach for geometric non-linear analysis of thin-walled frames (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 211-212 
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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.1620320113
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    Stress analysis by boundary element methods, by J. Balas, J. Sladek and V. Sladek, Studies in Applied Mechanics, 23 Elsevier Scientific Publications, Amsterdam. No. of pages: 682. Price: US $219.50, 1990 ISBN 0-444-98830-0 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 215-215 
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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.1620320115
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 219-222 
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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.1620320118
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320201
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    A two-node beam element including transverse shear and transverse normal deformations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1027-1039 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A variational higher-order theory for bending and stretching of linearly elastic orthotropic beams including the deformations due to transverse shearing and stretching of the transverse normal fibre is presented. The theory assumes a linear distribution for the longitudinal displacement and a parabolic variation of the transverse displacement across the thickness. Additionally, independent expansions are introduced for the through-thickness displacement gradients with the requirement of a least-square compatibility for the transverse strains and the satisfaction of exact stress boundary conditions at the top/bottom beam surfaces. The theory is shown to be well suited for finite element development requiring simple C0- and C-1- continuous displacement interpolation fields. To demonstrate the computational utility of the theory, a simple two-node stretching-bending finite element is formulated. The analytic and finite element results are obtained for a simple bending problem for which an exact elasticity solution is available. It is shown that the inclusion of the transverse normal deformation in the present theory enables improved displacement, strain and stress predictions, particularly, in the analysis of deep beams.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320507
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    Source field superposition analysis of two-dimensional potential problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1079-1091 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The source field superposition method for problems governed by Laplace's equation involves representing the potential field in a given solution domain as a superposition of fields generated by a number of sources. These sources are located outside the solution domain, and in the case of two-dimensional singly-connected finite domain problems can be uniformly distributed around the perimeter of a circle enclosing the physical domain. Some test problems are used to make detailed comparisons with the boundary element method. The results show that remarkable accuracy can be achieved, often to five or six significant figures, with very little computational effort relative to other numerical methods. In contrast to the boundary element method, however, geometric corners require no special treatment, and high aspect ratio of the solution domain is not a significant limitation.
    Additional Material: 7 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320510
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    Applications of a self-adaptive algorithm to non-linear finite element analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1057-1077 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A self-adaptive algorithm has been developed and implemented for the implicit time integration of non-linear finite element analysis. In this algorithm, a proper time increment for the next time step is estimated based on the deformation pattern at the preceding step. The iteration process for the equalibrium employs expeditious methods such as quasi-Newton updates and line searches as well as an adaptive stiffness matrix update strategy for efficiency. Convergence difficulties induced from inadequate prediction of step size or the change in non-linearities are tackled by the bisection method. These procedures were also successfully applied to static problems by ignoring the damping and the inertia forces. The objective of this paper is to demonstrate the applicability and the effectiveness of the adaptive algorithm in a wide spectrum of non-linear problems. Six example problems are illustrated, some of which are rather novel. As demonstrated in this paper, the self-adaptive algorithm implemented in MSC/NASTRAN is proving to be versatile, accurate and efficient.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320509
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    A comparison of preconditioned iterative techniques using rapid operator application against direct solution methods (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1137-1144 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The p-version of the finite element method which uses high order hierarchic basis functions within an element allows for ease of adaptive computation, and high accuracy with relatively few degrees of freedom. However, the solution time and storage requirements for large 3-D problems can be very high when direct methods are used to factor global matrices. Iterative techniques with rapid operator application have minimal storage requirements because neither element nor global matrices are formed, but may not converge rapidly enough. We study an approach that attempts to combine the two methods by using direct factorization of the matrix corresponding to low level polynomials as a preconditioner to an iterative method at a higher polynomial level. This resulting solution scheme converges more rapidly than an unpreconditioned scheme but has much lower storage requirements than direct methods. We illustrate the effectiveness of this scheme on some large three-dimensional problems in structural analysis.
    Additional Material: 4 Tab.
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    URL: http://dx.doi.org/10.1002/nme.1620320513
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1161-1162 
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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.1620320515
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1163-1163 
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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.1620320516
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320601
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    Transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1203-1230 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several new formulations for structural design sensitivity analysis (DSA) of elastic solids are presented that consistently account for steady and transient thermal loading, along with centrifugal and gravity loading. The approach employs implicit differentiation of the discretized boundary integral equations and facilitates the production of accurate and efficient computational procedures that obviate the need for matrix factorizations in the DSA step. For centrifugal, gravity and general thermal loading, a new DSA concept employing a particular integral technique is developed. For centrifugal, gravity and steady thermal effects, a surface integration approach is also presented, and the two methods compared. Alternative strategies for modelling the behaviour of temperature distributions of evolving shapes undergoing shape optimization and the ramifications of these strategies in the DSA process are also discussed. It is shown that, for certain classes of thermoelastic problems, shape optimization can be performed without the need to incorporate thermal analysis or DSA into the overall process. A thermoelastic surface stress sensitivity analysis formulation is presented that does not require additional numerical integration. A new thermoelastic sharp corner traction component consistent sensitivity analysis formulation is also presented. This technique is shown to work for any initial stress distribution. Numerical sensitivity results are presented for many problems with analytical solutions.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310612
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310701
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    Application of the boundary element method to transient heat conduction (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1231-1247 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM., Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310613
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. ii 
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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.1620310702
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    Non-linear bending analysis of plates and shells by using a mixed spline boundary element and finite element method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1283-1294 
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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 mixed spline boundary element and finite element method is suggested to analyse non-linear bending of plates and shells. Only the fundamental solutions for plates are required in order to establish the boundary integral equations. A quadratic rectangular spline element is adopted to deal with the membrane effects of plates and shells. Numerical examples show that the approach developed in this paper is very effective and especially promising for the non-linear analysis of plates and shells.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310705
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    On the formulation of the acoustic boundary element eigenvalue problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1271-1282 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Acoustic algebraic eigenvalue analysis by the Boundary Element Method (BEM) can be formulated by the Dual Reciprocity Method (DRM) of Nardini and Brebbia or by the Complementary Function-Particular Integral Method (PIM) proposed by Ahmad and Banerjee. But both DRM and PIM require inversion of a matrix of size at least as large as the system matrices before the equations can be cast in the form of generalized eigensystem. This makes these methods inefficient for large problems of practical interest. In this paper, a rather simple technique is proposed which eliminates the need to invert any matrix in the process of setting up the algebraic eigenvalue problem, especially for the most important case where all the boundary walls are acoustically hard (∂P/∂n = 0). A few example problems having known analytical and experimental results are solved in order to demonstrate the validity of the new technique. It is also demonstrated that, unlike in elasticity, here the boundary element domain must be adequately zoned or an adequate number of internal points must be incorporated in order to solve truly 2-D or 3-D problems.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310704
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    A new method for finite element transitional mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1253-1270 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the preparation of finite element meshes, inclusion of transitional blocks is important in order to construct optimal meshes. In this paper, a new method is proposed which is capable of generating quaddominated arbitrary transitional meshes. These meshes are well graded and do not require any mesh smoothening algorithm. The inverse isoparametric mapping combined with an elimination procedure is used to construct transition zones. This new algorithm is described in detail and its efficiency is illustrated with appropriate examples.Different methods available for inverse isoparametric mapping are discussed with their merits and limitations. Many of the existing techniques for inverse isoparametric mapping require the calculation of some special coefficients which may vary with the element type. These techniques lose their clarity and efficiency in the case of three dimensional and higher order two dimensional elements. In this paper, a generalized iterative procedure is proposed to carry out the inverse isoparametric mapping. The computations in this approach are already part of every finite element program based on the isoparametric formulation. Hence implementation of the new algorithm is very simple and straightforward.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310703
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    A monomial-based method for solving systems of non-linear algebraic equations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1295-1318 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A monomial-based method for solving systems of algebraic non-linear equations is presented. The method uses the arithmetic-geometric mean inequality to construct a system of monomial equations that approximates the system of non-linear equations. A change of variables transforms the monomial system into a system of linear equations, which is readily solved. Special properties of the monomial method are identified and their significance is discussed. Invariance properties of the monomial method produce a built-in, self-adjusting scaling of the variables and equilibration of the equations of the linear system. Other special properties can lead to useful bounds on, and invariances of, the conditioning of the linear system. An invariance to uniform scaling is responsible for extremely rapid convergence to the equation surfaces in the initial iterations. An invariance to multiplication of the algebraic equations by a certain class of functions leads to a useful insensitivity to form of the algebraic system. Insensitivity of the monomial method to solutions with negative components avoids meaningless solutiuons of the algebraic system that appear as undesirable by-products of the formulation. A practical engineering design problem is solved to demonstrate the special properties of the monomial method.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310706
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    Flow modelling in industrial processes, edited by Alan W. Bush, Barry A. Lewis and Michael D. Warren, Ellis-Horwood, Chichester, U.K., 1989. ISBN: 0-7458-0477-2 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1469-1469 
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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.1620310715
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    Stabilization by non-conforming modes: 9-node membrane element with drilling freedom (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1453-1468 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A simple technique of stabilizing spurious zero energy modes by non-conforming modes is presented. The non-conforming modes are derived by removing one or a number of nodes from the original element, and hence the associated stiffnesses are used to stabilize a uniform reduced integrated 9-node element. Three models were pursued to control the communicable spurious modes. The proposed model has been on the basis of including drilling freedoms and retaining much of the excellent performance of the original 9-node element with uniform reduced integration.The drilling freedoms are incorporated by constraining the true continuum mechanics definition of rotation at the reduced integration points by the penalty function method.A patch test was applied and a considerable number of problems were tested to investigate the performance of the new element.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310714
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    Group theory and G- vector spaces in structural analysis, By G.M. Zloković (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1470-1470 
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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.1620310717
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    Constrained minimization of vibrational magnitudes using a modal reduction method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1585-1604 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A numerically effective method is suggested and applied for evaluating objective and constraint functions when so-called vibrational magnitudes of a mechanical structure are minimized. General damped linear structures under external harmonic loading are considered. The magnitude functions studied can relate to displacements, velocities and accelerations and also to sectional and reactive forces. Both magnitudes at a specific frequency and peak magnitudes and averaged magnitudes over a frequency range are investigated. An arbitrary set of magnitude functions can be used in the constraints. Design variables are masses, dampings and stiffnesses of discrete and discretized continuous elements contained in the structure. The objective and constraint functions are expressed by use of the modal parameters (generally complex-valued) of the structural system. A reduced modal model is established and updated during the optimization process. Approximate derivatives (sensitivities) of the objective and constraint functions with respect to changes in design variables are calculated employing perturbed modal parameters. The optimization problem is solved by use of a primal method. Numerical examples demonstrate applications to the classical damped vibration absorber with two design variables and to a beam system used in a light-weight machine foundation with 14 design variables.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310810
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    Characteristics of subspace in reduced basis technique (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1567-1583 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the reduced basis technique the coefficients of global shape functions are taken as generalized degrees of freedom. The non-linear system is solved iteratively in a reduced subspace using considerably less unknowns. This paper investigates the characteristics of the reduced system, the relationship between the reduced system and the main system, the criterion to judge the critical point with reduced quantities and the criterion of convergence in the reduced subspace.
    Additional Material: 11 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310809
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    A boundary element method for steady incompressible thermoviscous flow (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1605-1626 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A boundary element formulation is presented for moderate Reynolds number, steady, incompressible, thermoviscous flows. The governing integral equations are written exclusively in terms of velocities and temperatures, thus eliminating the need for the computation of any gradients. Furthermore, with the introduction of reference velocities and temperatures, volume modelling can often be confined to only a small portion of the problem domain, typically near obstacles or walls. The numerical implementation includes higher order elements, adaptive integration and multiregion capability. Both the integral formulation and implementation are discussed in detail. Several examples illustrate the high level of accuracy that is obtainable with the current method.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310811
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    A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 385-418 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new scheme to integrate a system of stiff differential equations for both the elasto-plastic-creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code, through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.
    Additional Material: 15 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320210
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 441-443 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320213
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    On the numerical integration of a class of pressure-dependent plasticity models with mixed hardening (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 419-438 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Radial return algorithms, for both three-dimensional and plane stress situations, are developed for a class of pressure-dependent plasticity models (formulated in state variables) with mixed hardening. The consistent tangent matrix has been developed which, among other advantages, does not require numerical inversion. The algorithms, for Gurson's mixed hardening model, are incorporated in a finite element program to solve several simple uniaxial tension problems. When compared with numerically integrated solutions, the results from the finite element analysis show excellent agreement. Finally, results of the axisymmetric necking problem, using Gurson's mixed hardening model, are presented as an example of application.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320211
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320301
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  • 256
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    Optimal use of a numerical method for solving differential equations based on Taylor series expansions (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 471-499 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Efficiency in solving differential equations is improved by increasing the order of a Taylor series approximation. Computing time can be reduced up to a factor of 40 and an amount of memory storage can be saved, up to a factor of 70.The truncation error can be estimated not only by order but also by magnitude.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320303
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  • 257
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    A hierarchical approach to automatic finite element mesh generation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 501-525 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A point-based two-stage hierarchical method for automatic finite element mesh generation from a solid model is presented.Given the solid model of a component and the required nodal density distribution, nodes are generated according to the hierarchy - vertex, edge, face and solid. At the vertices, nodes are established naturally. Nodes on the edges, faces and inside the solid model are generated by recursive subdivision. The nodes are then connected to form a valid and well-conditioned finite element mesh of tetrahedron elements using modified Delaunay Triangulation. Checks are conducted to ensure the compatibility of geometry and topology between the solid model and the mesh.
    Additional Material: 21 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320304
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    Efficient boundary element analysis of sharp notched plates (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 445-470 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The present paper further develops the boundary element singularity subtraction technique, to provide an efficient and accurate method of analysing the general mixed-mode deformation of two-dimensional linear elastic structures containing sharp notches. The elastic field around sharp notches is singular. Because of the convergence difficulties that arise in numerical modelling of elastostatic problems with singular fields, these singularities are subtracted out of the original elastic field, using the first term of the Williams series expansion. This regularization procedure introduces the stress intensity factors as additional unknowns in the problem; hence extra conditions are required to obtain a solution. Extra conditions are defined such that the local solution in the neighbourhood of the notch tip is identical to the Williams solution; the procedure can take into account any number of terms of the series expansion. The standard boundary element method is modified to handle additional unknowns and extra boundary conditions. Analysis of plates with symmetry boundary conditions is shown to be straightforward, with the modified boundary element method. In the case of non-symmetrical plates, the singular tip-tractions are not primary boundary element unknowns. The boundary element method must be further modified to introduce the boundary integral stress equations of an internal point, approaching the notch-tip, as primary unknowns in the formulation. The accuracy and efficiency of the method is demonstrated with some benchmark tests of mixed-mode problems. New results are presented for the mixed-mode analysis of a non-symmetrical configuration of a single edge notched plate.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320302
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  • 259
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    A comparative study of the behaviour of a direct solver and a preconditioned iterative solver for the equations arising from the discretization by Chebyshev collocation of a second-order partial differential equation on a square (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 527-539 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The behaviour is compared of two solvers for the discrete equations arising from the discretization using Chebyshev collocation of a second-order linear partial differential equation on a square. The alternative solvers considered are a direct solver and an iterative solver based on preconditioning with the matrix arising from finite-difference discretization of the governing equation. The total error of the collocation derivatives and the separate contributions from round-off and discretization error are examined. The efficiency of the two solvers is compared. The iterative solver is more efficient than the direct solver on fine grids for equations similar to the Poisson equation, provided that there are Dirichlet boundary conditions on at least three of the sides of the square.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320305
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    The moment redistribution effect of the C0 structural elements formulation (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 541-557 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A new formulation was proposed recently for the removal of the shear and membrane locking mechanisms from the C0 structural elements. The performance of the new formulation was shown to be excellent in many cases of beam, plate and shell element applications, completely eliminating all locking problems. However, this formulation has its own problems. The potential introduction of softening effects (yielding softer models) and a rotational zero energy mode describe the problematic behaviour of the new formulation in cases of C0 plate and shell element applications. Analysis of this behaviour reveals some interesting aspects of the classical finite element formulation and allows for a better insight into the overall behaviour of the C0 structural elements. As a result of the present analysis, a modification of new formulation, remedying its problematic behaviour, will appear soon.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320306
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    A physical interpretation of conventional finite element formulations of conduction-type problems (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 559-569 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An essentially physical approach is utilized to derive a finite element formulation of conduction-type problems. The same systems of algebraic equations, which are usually yielded by Galerkin or variational methods, are obtained here on the basis of energy balances which lead to conservative numerical models, both at element and at node levels. As a result, it is shown that, in conventional implementations of the finite element method for conduction-type problems, there is no artificial creation or destruction of a conserved variable. Therefore, for such formulations, inaccuracies that arise with finite sizes of elements do not depend on non-conservation but are due solely to approximation erros. In the paper, a clear physical interpretation is also given for all the matrices and vectors which are commonly defined in most finite element formulations of conduction-type problems.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320307
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    A general methodological analysis for optimum design (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 85-111 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Generalized applications of modern numerical analysis methods - while digital computers experienced a fast development - produced a first revolution in design techniques, allowing one to perform computations considered unapproachable until that time. Introduction of Computer Aided Design (CAD) techniques - while high-performance graphic peripherals experience a fast development - is actually producing a second revolution, by making easy and fast most routine design tasks. However, the introduction of Computer Aided OPTIMUM Design techniques has not yet produced the expected third revolution, in spite of the big amount of research and the interest of its potential applications. The authors think that this fact is due mainly to the dispersion of the optimum design research, and to the lack of a well established doctrine.In this paper we approach the design process from a general methodological perspective, suitable to be applied to a wide range of problems. The design process is organized in several related levels. This approach leads naturally to the concept of optimum design and to the statement of a general mathematical programming problem. The practical application of this methodology to any particular problem takes an efficient and modular form. First and second order sensitivity analysis techniques are introduced from the general formulation, and alternative techniques (adjoint state) of the direct differentiation method are discussed.DAO2, a powerful and versatile computer aided optimum design system by the Finite Element Method, has been developed by the authors1 according to this general methodology. The system can solve efficiently 2D and 3D structural fixed-geometry and shape optimization problems. The power and viability of this methodology is illustrated by the solution to a structural optimization problem. The shape of the central section of an arch dam is optimized. A linear elastic structural FEM analysis is simultaneously performed for plane stress and for radial symmetry - while constraints are imposed for several load cases - taking into account the construction and loading stages. It should be emphasized that the same optimum design is reached in a small number of iterations starting from two significantly different initial designs.
    Additional Material: 10 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310106
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    Non-linear B-stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticityResearch supported by IBM under Contract No. 2-DJS-986, and NSF under Grant 2-DJA-491 with Stanford University (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 151-176 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward-Euler return maps as a particular case. More importantly, it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary Helmholz free energy function (B-stability). Since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm, the requirement of B-stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity. The analysis that follows depends critically on the assumption of convexity. In particular, the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation. The proposed algorithms obey the discrete counterpart of this classical principle.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310109
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    Sparse matrices: Numerical aspects with applications for scientists and engineers, by U. Schendel, Ellis Horwood, Chichester, 1989. Price: £21.95, £42.95. ISBN 074580635X. No. pages: 115 pages (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 193-193 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310111
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    Sparse matrices: Numerical aspects with applications for scientists and engineers, by U. Schendel, Ellis Horwood, Chichester, 1989. Price: £21.95 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 193-194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310112
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  • 266
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    Sparse matrices: Numerical aspects with applications for scientists and engineers, by U. Schendel, Ellis Horwood, Chichester, 1989. Price: £21.95 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 193-194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310113
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    Convergence of the Newton-Raphson algorithm in elastic-plastic incremental analysis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 177-191 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method. This assumption permits the incremental problem to be formulated as a convex non-linear programming problem. The classical Newton-Raphson algorithm can be adopted to provide an iterative solution of the non-linear programming problem. It is shown that if an elastic or secant predictor modulus is used, the algorithm converges monotonically. However, if a tangent predictor is used, a line search algorithm must be included to ensure convergence.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310110
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    Numerical models in geomechanics, proceed-ings of the 3rd international symposium on nu-merical models in geomechanics, Niagara Falls, 8-11 May, 1989. Edited by S. Pietruszcazk and G. N. Pande. Elsevier Applied Science, 1989. Price: £85.00 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 194-195 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310114
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    Practical time-stepping schemes, by W. L. Wood, Oxford Applied Mathematics and Com-puting Science Series, Clarendon Press, Oxford, 1990. Price: E17.50. ISBN: 8596774. No. pages: 373 pp (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 195-195 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310115
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    Computational mechanics of probabilistic and reliability analysis. Wing Kam LiU and Ted Belytschko (eds.), Elmepress International, Lausanne, Switzerland 1989. 622 pages (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 195-195 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310116
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    Books received (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 197-198 
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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.1620310117
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    Announcement (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 199-201 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310118
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 203-206 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310119
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310201
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    A mixed finite element for the analysis of large inelastic strains (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 229-239 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A 4-node element with 1 integration point is developed for the analysis of elastoplastic large strains. It is based on the Hu-Washizu principle and uses a co-rotational formulation. Special care is taken to avoid spurious zero-energy modes and incompressibility locking.This element successfully passes the large strain patch test. It proves to be accurate and computationally very cheap.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310203
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    On special points on load-displacement paths in the prebuckling domain of thin shells (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 207-228 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Points on load-displacement paths of thin shells subjected to proportional loading, at which the second and/or the third derivative of the displacement components with respect to the load parameter vanishes, are termed ‘special points’. Such points represent global characteristics of the state of deformation of the shell in the sense that for the respective values of the load parameter the mentioned rate(s) of all displacement components at all points of the shell must vanish. It will be shown that special points on load-displacement paths correspond to special points of one order lower on the Det KT-λ diagram, where Det KT is the determinant of the tangent stiffness matrix within the framework of the finite element method and λ is a dimensionless load parameter. Points of inflection on load-displacement diagrams, for example, correspond to extreme values on the Det KT-λ diagram. The main reason for the occupation with special points on load-displacement paths is that points of inflection and flat points on these paths correspond to special points on eigenvalue curves in the context of accompanying linear stability analyses of geometrically non-linear prebuckling analyses of thin shells by the finite element method, investigated in a companion paper.
    Additional Material: 4 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310202
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    Announcements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 407-408 
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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.1620310212
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    An incompatible element for axisymmetric structure and its modification by hybrid method (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 385-405 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper introduces three four-node quadrilateral axisymmetric elements. The first one is an incompatible element while the second one is a modification of the first element by an extended Hellinger-Reissner principle. The second element is then simplified by incorporating the conceptual idea of free formulation and thus forms the third element. All of the three elements are found to be invariant, insensitive to nodal point numbering, free of locking for nearly incompressible material, able to pass the patch test and do not exhibit the false shear phenomenon. Numerical examples are given and satisfactory predictions are achieved.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310211
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 409-412 
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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.1620310213
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310301
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    Graded tetrahedral finite element meshes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 413-425 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Vertices in the body centred cubic (bcc) lattice are used to create a tetrahedral spatial decomposition. With this spatial decomposition an octree approach is combined with Delaunay triangulations to decompose solids into tetrahedral finite element meshes. Solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes. Local densities of interior tetrahedra are controlled by the densities of surface triangles. Accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems.
    Additional Material: 14 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310302
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310401
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    Application of discrete Fourier series to the finite element stress analysis of axi-symmetric solids (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 619-647 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper describes an efficient formulation, based on a discrete Fourier series expansion, for the analysis of axi-symmetric solids subjected to non-symmetric loading. In contrast to the commonly adopted continuous Fourier series approach, the discrete Fourier series representation has largely overcome problems such as the presence of Gibb's phenomenon and the lack of conformity of elements. The computational advantage over a fully three-dimensional formulation is illustrated. Finally, the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto-plastic soils.
    Additional Material: 17 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310402
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    Automatic mesh generation and adaptation by using contours (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 689-707 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A general and efficient remeshing algorithm is presented for the discretization of arbitrary planar domains into triangular elements in consistency with the given node spacing function.The contour lines of the node spacing function at suitable calculated levels provide the natural lines of division of the problem domain into subregions, where finite element meshes of different element sizes are generated using the available general-purpose mesh generators.1, 2Examples of remeshing for various node spacing functions are given to illustrate that high-quality gradation meshes can be generated automatically without any user's intervention by this simple contour line method.
    Additional Material: 20 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310405
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    Potential of earthing grid in heterogeneous soil (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 677-688 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Calculation of the scalar electric potential of an earthing grid in heterogeneous soil is obtained by the finite element technique combining differential and integral formulations of the problem. Such a combined formulation made it possible to generate easily the mesh of finite elements and to divide the problem domain into a sufficiently small number of large finite elements. The unbounded domain of calculation is solved by using mapped infinite elements. The contribution of singular sources is represented by the analytical expression, and included in the approximation function of the potential. A sufficiently satisfactory approximation is realized with a small number of singular source images, obtained by local imaging of sources within a finite element on its boundary surfaces. The calculation accuracy is tested on examples solvable by an average potential method which is based on an integral formulation of the problem.
    Additional Material: 5 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310404
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    p-version hierarchical three dimensional curved shell element for elastostatics (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 649-676 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a hierarchical three dimensional curved shell finite element formulation based on the p-approximation concept. The element displacement approximation can be of arbitrary and different polynomial orders in the plane of the shell (ξ, η) and the transverse direction (ξ). The curved shell element approximation functions and the corresponding nodal variables are derived by first constructing the approximation functions of orders pξ, pη and pξ and the corresponding nodal variable operators for each of the three directions ξ, η and ξ and then taking their products (sometimes also known as tensor product). This procedure gives the approximation functions and the corresponding nodal variables corresponding to the polynomial orders pξ, pη and pξ. Both the element displacement functions and the nodal variables are hierarchical; therefore, the resulting element matrices and the equivalent nodal load vectors are hierarchical also, i.e. the element properties corresponding to the polynomial orders pξ, pη and pξ are a subset of those corresponding to the orders (pξ + 1), (pη +1) and (pξ +1). The formulation guarantees C° continuity or smoothness of the displacement field across the interelement boundaries.The geometry of the element is described by the co-ordinates of the nodes on its middle surface (ξ = 0) and the nodal vectors describing its bottom (ξ = -1) and top (ξ = +1) surfaces. The element properties are derived using the principle of virtual work and the hierarchical element approximation. The formulation is equally effective for very thin as well as very thick plates and curved shells. In fact, in many three dimensional applications the element can be used to replace the hierarchical three dimensional solid element without loss of accuracy but significant gain in modelling convenience. Numerical examples are presented to demonstrate the accuracy, efficiency and overall superiority of the present formulation. The results obtained from the present formulation are compared with those available in the literature as well as analytical solutions.
    Additional Material: 13 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310403
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    The multiple Reciprocity boundary element method in elasticity: A new approach for transforming domain integrals to the boundary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 709-727 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a new boundary element approach to transform domain integrals into equivalent boundary integrals. The technique, called the Multiple Reciprocity Method, is applied to 2-D elasticity problems and operates on domain integrals resulting from different types of body forces such as gravitational and centrifugal forces, as well as loadings due to linear and quadratic temperature distributions. Numerical examples are presented to demonstrate the accuracy and efficiency of the method.
    Additional Material: 8 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310406
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    Shear-flexible models for spatial buckling of thin-walled curved beamsThis work is supported NSF under research grant no. EET-8714628 (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 729-757 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The governing non-linear finite element equations for the spatial stability analysis of curved beams, using a simple two-noded model, are derived based on the incremental form of a mixed variational principle with independent discretization for its generalized strain field and the reference line displacements as well as cross-sectional warping and bending/twisting rotations. The formulation is valid for both open-and closed-type thin-walled sections, and this is accomplished by the use of a kinematic description based on a generalized beam theory in which shear deformation due to both flexural-and warping-torsional actions is accounted for. The effect of finite rotations in space is included, resulting in a second-order accurate geometric stiffness matrix and ensuring that all significant instability modes can be predicted. Finally, the results obtained in a number of numerical simulations for lateral-torsional bifurcation buckling of circular arches are presented to illustrate the model effectiveness and practical usefulness, and to provide explanations for the source of discrepancies noted in the results obtained in previous investigations.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310407
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    Simple and efficient shear flexible two-node arch/beam and four-node cylindrical shell/plate finite elements (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 759-776 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Several simple and accurate C° two-node arch/beam and four-node cylindrical shell/plate finite elements are presented in this paper. The formulation used here is based on the refined theory of thick cylindrical shells and the quasi-conforming element technique. Unlike most C° elements, the element stiffness matrix presented here is given explicitly. In spite of their simplicity, these C° finite elements posseses linear bending strains and are free from the deficiencies existing in curved C° elements such as shear and membrane locking, spurious kinematic modes and numerical ill-conditioning. These finite elements are valid not only for thick/thin beams and plates, but also for arches/straight beams and cylindrical shells/plates. Furthermore, these C° elements can automatically reduce to the corresponding C1 beam and plate elements and give the C° beam element obtained by the reduced integration as a special case. Several numerical examples indicate that the simple two-node arch/beam and four-node cylindrical shell/plate elements given in this paper are superior to the existing C° elements with the same element degrees of freedom. Only the formulation of the rectangular cylindrical shell and plate element is presented in this paper. The formulation of an arbitrarily quadrilateral plate element will be presented in a follow-up paper32.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310408
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    Scattering of elastic waves by a crack with spring-mass contact (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 789-801 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The scattering problem of elastic waves by a crack with spring-mass contact is investigated. Such a crack may be regarded as a simplified model of a thin elastic inclusion. Boundary integral equations are formulated for both displacement and traction on crack faces and are solved numerically. Numerical results are presented for stress intensity factors, crack-opening displacements and scattering cross-sections. Our results are in good agreement with other published solutions. It is also found that the effect of a mass can not be neglected in evaluation of scattering cross-sections, even if the mass is small.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310410
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    Finite element formulations that include particular solutions of governing equations (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 777-787 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The correspondence between the homogeneous and particular solutions of differential equations and the related solutions of the discrete equations is brought to light in this study. Guided by this correspondence, the trial functions for finite elements are written in two parts - one the homogeneous and the other a prescribed particular solution. It is shown that this approach allows one to simplify the computations of element matrices and also yields better results, throughout the element, than those obtained by the conventional approach. Two simple examples are provided for illustration.
    Additional Material: 2 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310409
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    On bounding properties of eigenvalues from linear initial FE stability analyses of thin, elastic shells with respect to stability limits from geometrically non-linear prebuckling analyses (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1087-1111 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: There is consensus in the literature that the eigenvalues of smallest absolute value from linear initial stability analyses of thin, elastic shells by the finite element method (FEM) do not posses bounding properties with respect to corresponding stability limites from geometrically non-linear stability analyses. A ‘linear initial stability analysis’ by the FEM representes the first step of an ‘accompanying linear stability analysis’ by this method. In this paper, two modes of such stability analyses of thin, elastic shells will be presented. It will be proved that, for mode 1, in contrast to mode 2, bounding properties of eigenvalues of smallest absolute value with respect to corresponding stability limits from geometrically non-linear stability analyses, in fact, do exist. Moreover, bounding properties of such eigenvalues from mode 1 relative to corresponding eigenvalues from mode 2 will be shown to exist. The existence of these properties is important from the standpoint of engineering practice.
    Additional Material: 9 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310605
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    Optimization analysis of the four-level-time schemes (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1113-1119 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A procedure was implemented to determine some optimum values for the parameters of the four-level-time scheme which can be utilized for the numerical solution of a system of ordinary differential equations. A multi-variable search method was employed to estimate these optimum parameters. Two different optimization studies were performed. The resultant optimum four-level-time schemes produced very accurate results, satisfied physical reality, and did not produce any oscillations for the specific problems that were studied. The optimum values for the three parameters α, β and γ in the four-level-time scheme were α = 16.72, β = 6.26 and γ = 2.46. The optimum value of θ for the Wilson-θ method was θ = 1.42. The optimum schemes were compared to some existing four-level-time schemes. The outcome demonstrated that the optimum schemes were superior. The Houbolt method and the Galerkin weighting procedure were shown to have greater inaccuracies than the optimum schemes.
    Additional Material: 1 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310606
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    On FEM-BEM coupling for fluid-structure interaction analyses in the time domain (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1151-1168 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The investigation of coupled fluid-structure systems, subjected to dynamic loads, calls for the use of discrete techniques such as the finite element method (FEM) and the boundary element method (BEM). This paper reports on the development of a FEM-BEM coupling procedure, where finite elements are used to model the linear elastic structure, while the adjacent fluid is represented by boundary elements. The new approach is formulated entirely in the time domain to be extensible to non-linear problems.Various numerical calculations are presented which clearly demonstrate the applicability and the merits of the hybrid method. The obtained results are in excellent agreement with solutions stemming from a boundary element analysis which uses subdomain techniques.
    Additional Material: 12 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620310609
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    On a new iterative approach of component mode synthesis (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1195-1202 
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    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A wholly new concept of intermediate structure is developed in this paper. Based on this, a new component mode iteration (CMI), or subdomain subspace iteration method, is proposed.In the new CMI method, the ordinarily required step of ensuring interface compatibility is eliminated. An outstanding achievement of this method is that it retains the merit of the standard subspace iteration (SSI) technique concerning the number of vectors required in computation. In the present method iteraton is carried out at subdomain levels. On machines capable of parallel processing, this work can be performed simultaneously.Numerical examples clearly demonstrate the excellence of this new method.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310611
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    A continuum finite element for single-set jointed media (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 31 (1991), S. 1169-1194 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In response to the need for an advanced computational model for wave propagation in jointed-rock media a new finite element for jointed media with a single set of regularly spaced joints is developed. The element is a numerical implementation of the higher-order homogenization model recently proposed by Murakami and Hegemier. Due to the dispersive effects induced by regularly spaced joints, wave phenomena in jointed media are altered significantly. Therefore, in order to improve the interpretation of seismograms for accurate source identification, it is necessary to develop a higher-order continuum element. The accuracy and efficiency of the new element is investigated by applying it to wave-guide and wave-normal problems of a jointed half-space and by comparing the wave response with that of DYNA2D. The analyses by DYNA2D discretize explicitly the details of the joint microstructure, and are adopted as numerically exact measures for the assessment of the proposed finite element; good correlations were obtained. The validation study also confirmed the importance of wave dispersion for non-linear as well as linear joint responses. Finally, as a more practical application of the proposed element, the problem of a jointed full-space with a cylindrical cavity pressurized by step and pulse loadings was solved. Velocities at several observation points were compared with the numerically exact results of DYNA2D. Similar analyses carried out for elastic isotropic media predicted totally different velocity responses and confirmed the need for the proposed element.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620310610
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    Automatic quadrilateral/triangular free-form mesh generation for planar regions (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1441-1483 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Automation of finite element mesh generation holds great benefits for mechanical product development and analysis. In addition to freeing engineers from mundane tasks, automation of mesh generation reduces product cycle design and eliminates human-related errors. Most of the existing mesh generation methods are either semi-automatic or require specific topological information. A fully automatic free-form mesh generation method is described in this paper to alleviate some of these problems. The method is capable of meshing singly or multiply connected convex/concave planar regions. These regions can be viewed as crosssectional areas of 2 1/2 D objects analysed as plane stress, plane strain or axisymmetric stress problems. In addition to being fully automatic, the method produces quadrilateral or triangular elements with aspect rations near one. Moreover, it does not require any topological constraints on the regions to be meshed; i.e. it provides free-form mesh generation. The input to the method includes the region's boundary curves, the element size and the mesh grading information. The method begins by decomposing the planar region to be meshed into convex subregions. Each subregion is meshed by first generating nodes on its boundaries using the input element size. The boundary nodes are then offset to mesh the subregion. The resulting meshes are merged together to form the final mesh. The paper describes the method in detail, algorithms developed to implement it and sample numerical examples. Results on parametric studies of the method performance are also discussed.
    Additional Material: 25 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320705
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    Conference diary (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1527-1528 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320707
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    Multiplier methods for engineering optimization (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1485-1525 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Multiplier methods used to solve the constrained engineering optimization problem are described. These methods solve the problem by minimizing a sequence of unconstrained problems defined using the cost and constraint functions. The methods, proposed in 1969, have been determined to be quite robust, although not as efficient as other algorithms. They can be more effective for some engineering applications, such as optimum design and control of large scale dynamic systems. Since 1969 several modifications and extensions of the methods have been developed. Therefore, it is important to review the theory and computational procedures of these methods so that more efficient and effective ones can be developed for engineering applications. Recent methods that are similar to the multiplier methods are also discussed. These are continuous multiplier update, exact penalty and exponential penalty methods.
    Additional Material: 6 Ill.
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    URL: http://dx.doi.org/10.1002/nme.1620320706
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    Masthead (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991) 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320801
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