Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the…
Abstract
Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.
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This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE…
Abstract
This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.
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P.A.J. VAN DEN BOGERT, R. DE BORST, G.T. LUITEN and J. ZEILMAKER
A marked characteristic of rubber‐like materials is the nearly incompressible behaviour. This type of behaviour is best modelled by mixed finite elements with separate…
Abstract
A marked characteristic of rubber‐like materials is the nearly incompressible behaviour. This type of behaviour is best modelled by mixed finite elements with separate interpolation functions for the displacements and the pressure. In this contribution the performance of three‐dimensional elements is investigated using a two‐tiered strategy. First, the ability of some linear and quadratic three‐dimensional elements to deform correctly under nearly isochoric conditions is estimated using the well‐known constraint‐counting method, in which the ratio of the number of degrees‐of‐freedom over the number of kinematic constraints present in the finite element mesh is determined. Next, the performance of the elements is assessed by numerical simulations for three cuboidal rubber blocks with different shape factors. The results turn out to be quite sensitive with respect to the ratio of the number of degrees‐of‐freedom over the number of kinematic constraints, since too many pressure degrees‐of‐freedom make the element overstiff, while too few pressure degrees‐of‐freedom may cause the occurrence of spurious kinematic modes. This observation appears to be not only valid for the global structural behaviour, but also with respect to the specific parts in the structure, where the above‐mentioned ratio is different from the global number, e.g., in corners of the structure.
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J.M.A. Cesar de Sa and D.R.J. Owen
The application of numerical techniques to the solution of practical problems which exist in rubber technology is described. Structures and components in the form of reinforced…
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The application of numerical techniques to the solution of practical problems which exist in rubber technology is described. Structures and components in the form of reinforced rubber shells are widely used in industry and prediction of their performance is complicated by both the anisotropic nature of composite construction and the incompressible behaviour of the basic material. A layered shell element is developed for the solution of such problems with general anisotropic behaviour independently permitted in each layer. The approach adopted permits the easy location of reinforcement patterns. Numerical solution is based on a single field formulation by eliminating at integrating point level the Lagrange multiplier imposing the incompressible constraint. Large deformation, including large rotation, behaviour is accommodated and a total Lagrangian solution process is adopted. The code developed permits the simulation of non‐conservative loading and its versatility is demonstrated by the solution of some practical examples.
A fast assembly scheme for FEM sparse matrices is given. For the solution we compare the conjugate gradient and two preconditionings for this method in the case of plane strain…
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A fast assembly scheme for FEM sparse matrices is given. For the solution we compare the conjugate gradient and two preconditionings for this method in the case of plane strain elasticity and orthotropic materials with very stiff coefficients. The influence of fibre orientation on the number of iterations is tested. It is suggested to use the simple incomplete Crout scheme even when the resulting preconditioning matrix is not positive definite.
Koji FUJIWARA and Takayoshi NAKATA
Benchmark problem 7 of the TEAM workshop consists of an asymmetrical conductor with a hole. 17 computer codes are applied, and 25 solutions are compared with each other and with…
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Benchmark problem 7 of the TEAM workshop consists of an asymmetrical conductor with a hole. 17 computer codes are applied, and 25 solutions are compared with each other and with experimental results for eddy current densities and flux densities. Most of the codes were found to give satisfactory solutions.
Eduardo N. Dvorkin and Sara I. Vassolo
A quadrilateral 2‐D finite element for linear and non‐linear analysis of solids is presented. The element is based on the technique of mixed interpolation of tensorial components…
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A quadrilateral 2‐D finite element for linear and non‐linear analysis of solids is presented. The element is based on the technique of mixed interpolation of tensorial components. It is shown that the new element is reliable and efficient, being apt, therefore, to be used in routine engineering applications.
Eduardo N. Dvorkin and Klaus‐Jürgen Bathe
A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional…
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A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.
C.H. Liu, G. Hofstetter and H.A. Mang
The paper starts with a review of constitutive equations forrubber‐like materials, formulated in the invariants of the rightCauchy—Green deformation tensor. A general framework…
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The paper starts with a review of constitutive equations for rubber‐like materials, formulated in the invariants of the right Cauchy—Green deformation tensor. A general framework for the derivation of the stress tensor and the tangent moduli for invariant‐based models, for both the reference and the current configuration, is presented. The free energy of incompressible rubber‐like materials is extended to a compressible formulation by adding the volumetric part of the free energy. In order to overcome numerical problems encountered with displacement‐based finite element formulations for nearly incompressible materials, three‐dimensional finite elements, based on a penalty‐type formulation, are proposed. They are characterized by applying reduced integration to the volumetric parts of the tangent stiffness matrix and the pressure‐related parts of the internal force vector only. Moreover, hybrid finite elements are proposed. They are based on a three‐field variational principle, characterized by treating the displacements, the dilatation and the hydrostatic pressure as independent variables. Subsequently, this formulation is reduced to a generalized displacement formulation. In the numerical study these formulations are evaluated. The results obtained are compared with numerical results available in the literature. In addition, the proposed formulations are applied to 3D finite element analysis of an automobile tyre. The computed results are compared with experimental data.
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Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing…
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Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.