摘要:

AbstractThe main equations for the equilibrium, stability and critical state analysis of discrete elastic systems are presented following the works of Thompson, but in such a way that the original set of generalized coordinates and loads are preserved in the Total Potential Energy. This introduces differences in the resulting equations in bifurcation analysis but does not introduce any new feature regarding the physics of the problem. The new formulation is approximated by means of a standard finite element approach based on interpolation of displacements, in which the derivatives of the potential energy are approximated. The terms retained are those of moderately large rotation theory. The energy analysis is finally related to the more conventional finite element notation in terms of stiffness matrices, and it is shown how in such a way it can be included in present day codes.Part 2 of the paper deals with applications to the analysis of shells of revolution using a semi‐analytical approximation. Two cases are presented in detail: bifurcation in axisymmetric and in asymmetric modes, and the results show good correlation with those of other authors. The influence of load and geometric imperfections is evaluate

ISSN:0029-5981    

DOI:10.1002/nme.1620330902

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe derivation of more efficient algorithms for finite element applications is not the primary goal of this article, but rather the efficient implementation of existing algorithms using dynamic data structures. In some cases the algorithms may be far from optimal, but serve to illustrate the advantages of dynamic data structures. In the first section, a tree data structure termed a PATRICIA tree is described and is shown to be suitable for storing data associated with finite element meshes. The manner in which the tree is constructed guarantees to provide rapid data retrieval times, competitive with those associated with static array data structures, whilst providing the added advantages of a dynamic data structure. The second section introduces a list of lists (LOL) data structure which is used to produce an efficient implementation of an example of a bandwidth reduction algorithm. Furthermore, the LOL data structure is also shown to be appropriate for implementing a novel method for extracting the domain boundary, with its orientation, from a given finite element connectivity matrix.

ISSN:0029-5981    

DOI:10.1002/nme.1620330903

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the problem of modelling the motion of a bubble close to a rigid structure in an infinite fluid. It is well known that the boundary integral method is a powerful technique for modelling the motion of a single bubble in a fluid. In this paper we shall present a modified boundary integral method for modelling the motion of a bubble close to a fixed finite rigid structure, and discuss a numerical scheme for solving the resulting integral equation for three‐dimensional problems. Finally, we illustrate our method with some typical numerical result

ISSN:0029-5981    

DOI:10.1002/nme.1620330904

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe present paper is concerned with the application of iterative techniques to solve boundary element method (BEM) systems of equations.Initially, a brief description of some algorithms which have been employed for symmetric positive‐definite matrices is given (finite element method matrices, for instance). Subsequently, non‐symmetric versions of these algorithms are described and their performance is checked for BEM matrices, through various numerical experiments.Preconditioned algorithms were found to work quite w

ISSN:0029-5981    

DOI:10.1002/nme.1620330905

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA general, well‐structured and efficient method is advanced for the solution of‐a large class of dynamic interaction problems including a non‐linear dynamic system running at a prescribed time‐dependent speed on a linear track or guideway. The method uses an extended state‐space vector approach in conjunction with a complex modal superposition. It allows for the analysis of structures containing both physical and modal components. The physical components studied here are vehicles modelled as linear or non‐linear discrete mass–spring–damper systems. The modal component studied is a linear continuous model of a track structure containing beam elements which can be generally damped and which can be embedded in a three‐parameter damped Winkler‐type foundation. The complex modal parameters of the track structure are solved for. Algebraic equations are established which impose constraints on the transverse forces and accelerations at the interfaces between the moving dynamic systems and the track. An irregularity function modelling a given non‐straight profile of the non‐loaded track or a non‐circular periphery of the wheels is also accounted for. Loss of contact and recovered contact between a vehicle and the track can be treated. The system of coupled first‐order differential equations governing the motion of the vehicles and the trackandthe set of algebraic constraint equations aretogethercompactly expressed in one unified matrix format. A time‐variant initial‐value problem is thereby formulated such that its solution can be found in a straightforward way by use of standard time‐stepping methods implemented in existing subroutine libraries. Examples for verification and application of the proposed method are given. The present study should be of partic

ISSN:0029-5981    

DOI:10.1002/nme.1620330906

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn recent years progress has been made in applying moving and deforming mesh systems to phase change problems. This allows the numerical attention where it is needed, near the migrating phase change zone. In spatially unbounded problems one hopes that numerically finite outer boundaries either escape significant activity or are automatically pushed further away as activity nears. Not infrequently this approach fails. Temperature activity often spreads more rapidly than phase change, thereby reaching far boundaries; stretching of the mesh by movement of far boundaries can challenge mesh control and cause ill‐conditioning. In this paper the advantages of time dependent mesh adaption are enhanced by the joining of a new formulation for infinite elements to far boundaries. This is accomplished through a co‐ordinate transformation within the framework of conventional 2‐D quadratic, biquadratic, and linear–quadratic elements. Standard 2 by 2 Gauss–Legendre quadrature suffices throughout and normal Galerkin finite element features are undisturbed, including strict conservation of energy. The formulation is independent of global co‐ordinates, entails no restrictions on the unknown function and should be applicable to other problem types. All test cases on quadrilateral and triangular grids show very significant improvements with infinite elements relative to comparable solution systems using strictly f

ISSN:0029-5981    

DOI:10.1002/nme.1620330907

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractIn order to obtain the curvature changes of the exterior surface of a shell subjected to an internal pressure, it is necessary to evaluate the displacement derivatives up to the second order. To this end, a hexahedronal element is developed with three‐dimensional elastic properties utilized. At a nodal point on the surface of the shell, the first‐order derivatives of the three displacement components are used as degrees of freedom (d.o.f.) in addition to the components themselves. However, at a nodal point not on the surface, only the three displacement components are used. Therefore, an element with aii exterior surface has a total of 48 d.o.f. and other elements have 24 d.o.f.The stiffness matrix of the 8‐node subparametric hexahedronal high‐order element is derived from the strain energy consideration. The cubic shape functions in the surface co‐ordinates and linear shape functions through the shell thickness are used. The second derivatives of displacement components are continuous at any point on the exterior surface of the element, although they may not be continuous across the nodal line of two adjacent

ISSN:0029-5981    

DOI:10.1002/nme.1620330908

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractThe primary aim of this research is to implement the arbitrary Lagrangian–Eulerian finite element description to model large deformation of interacting bodies. A pure Lagrangian description is often incapable of representing their contact with sufficient precision. In this work, the arbitrary Lagrangian‐Eulerian (ALE) description has been extended to the surface nodes of interacting bodies to overcome these limitations. A penalty formulation has been implemented to account for the impenetrability constraint. The materials have been characterized as elastic‐viscoplastic. Implicit integration schemes have been used at the global and constitutive levels for'improved stab

ISSN:0029-5981    

DOI:10.1002/nme.1620330909

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractAn efficient method is developed to compute the sensitivities of eigenvalues, eigenvectors and frequency responses in a reduced approximate rnodel. The reanalyses of a modified structure for those dynamic responses are also derived in the approximate model. An optimization process utilizing the efficiently calculated sensitivities and reanalyses of the modified structure is formed. The difficulties of finding eigenvector sensitivities for repeated modes have also been addressed and averted in the approximate model. Two numerical examples show satisfactory outcomes by using this proposed approach.

ISSN:0029-5981    

DOI:10.1002/nme.1620330910

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractA distributed method of solving sparse, positive‐definite systems of equations, like those arising from many finite‐element problems, on a hypercube computer is studied. A domain‐decomposition method is introduced wherein the domain of the problem to be solved is physically split into several subdomains. Each of these subdomains is then distributed to a separate processor on the hypercube where the fill, factorization and solution of the system of equations proceeds. This physical split is based on a nodal ordering known as one‐way dissection.4The method is applied to two‐dimensional electrostatic problems which are governed by Laplace's equation. Since the finite‐element method is used to discretize the problem, the algorithm is developed to take full advantage of the inherent sparsity in the system of equations by using an envelope storage scheme. The method is applied to several geometries, and results as well as performance data for the algorithm wi

ISSN:0029-5981    

DOI:10.1002/nme.1620330911

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY