摘要:

AbstractIn 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.

ISSN:0029-5981    

DOI:10.1002/nme.1620310703

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAcoustic 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

ISSN:0029-5981    

DOI:10.1002/nme.1620310704

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractIn 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 she

ISSN:0029-5981    

DOI:10.1002/nme.1620310705

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA 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 mo

ISSN:0029-5981    

DOI:10.1002/nme.1620310706

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractAn 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

ISSN:0029-5981    

DOI:10.1002/nme.1620310707

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractNumerical 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 adaptatio

ISSN:0029-5981    

DOI:10.1002/nme.1620310708

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractFor 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 examp

ISSN:0029-5981    

DOI:10.1002/nme.1620310709

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractA 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 SP

ISSN:0029-5981    

DOI:10.1002/nme.1620310710

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThick 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 problem

ISSN:0029-5981    

DOI:10.1002/nme.1620310711

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY

摘要:

AbstractThree 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.

ISSN:0029-5981    

DOI:10.1002/nme.1620310712

出版商:John Wiley&Sons, Ltd    

年代:1991

数据来源: WILEY