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A fixed grid representation of the finite element domain is used to solve elasticity problems. An integration between CAD and FEM systems is made by using this fixed grid representation. Some considerations about FG approximation and stiffness matrix generation are presented. The element stiffness matrix for an element in the mesh is obtained as a factor of a standard element stiffness matrix. A least squares local approximation of stress field is used to calculate the stress at boundary elements. A problem with an analytical solution is used to measure the displacement and stress error. Several meshes and several geometrical configurations of the problem are used to test the reliability of the fixed grid finite element method.

The accuracy of finite element discretizations modelling one‐dimensional wave propagation problems is presented. The spurious reflections arising from finite/infinite element discretizations for unbounded domain problems are quantified. The error curves, numerically obtained, yield a criterion for rational mesh design. Formulae for minimum discretization ratios are given.

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.

We describe a visual method—stress band plots—for displaying the stress solution within a two‐dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.

We compare potential‐based (ø‐U‐P0) and displacement‐based finite element methods for static analysis of contained fluids. A general transient formulation may be specialized to static analysis in both cases. In the potential‐based method velocity potentials (ø) and a single pressure (P0) variable are the unknowns in the fluid region. Displacements are the unknowns in the fluid for displacement‐based methods. Higher‐order displace‐ment‐based elements may produce singular matrices for some static analyses, restricting us to four‐node elements for reliability. While both methods can yield excellent results when compared with experimental data, potential‐based methods appear to have computational advantages over displacement‐based methods.

In this paper we derive a simple finite element formulation for geometrical nonlinear shell structures. The formulation bases on a direct introduction of the isoparametric finite element formulation into the shell equations. The element allows the occurrence of finite rotations which are described by two independent angles. A layerwise linear elastic material model for composites has been chosen. A consistent linearization of all equations has been derived for the application of a pure Newton method in the nonlinear solution process. Thus a quadratic convergence behaviour can be achieved in the vicinity of the solution point. Examples show the applicability and effectivity of the developed element.

The paper presents a new technique for a compatible transition from a h‐refined to a p‐refined finite element mesh. At one or more faces of particularly designed pNh‐transition elements a low order h‐discretization may be combined with a usual p‐mesh in the other parts of the elements. The pNh‐elements are conform finite elements which can be applied in an adaptive scheme controlled by a residue based error estimate. Typical applications which require strongly a local mesh refinement within a p‐finite element mesh are, e.g. the approximation of high gradients and the determination of contact areas. Numerical examples demonstrate the efficiency of the pNh‐element technique for such problems.

While calculating internal forces of a structure resulting from temperature it is necessary to know thermal conduction and what goes hand in hand to determine temperature distribution at various points of the analysed structures. Finite strip method (FSM) is very suitable for the analysis of thermal conduction, heating, heat and temperature distribution in engineering structures, especially rectangular of identical edge conditions. The paper presents several examples of FSM application for the analysis of conduction and heat and temperature distribution for various types of engineering structures which can appear, among others, while welding several joined elements with welds made at specified speed as linear and point welds. Bars, shields, square and rectangular plates, steel orthotropic plates, steel and combined girders (steel‐concrete), box girders subject to various loads connected with heat and temperature (loaded with temperature, non‐uniformly heated surface). The obtained results may be useful in engineering practice for determining actual temperature and load capacity in individual elements of the construction.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

This work discusses the use of exponentially and reciprocally decaying infinite elements and assesses their respective value for magnetostatic and eddy current problems. In particular, the need for different decaying parameters for different materials is shown to be detrimental to their application in many practical situations. A simple method, whereby a 2‐D solution is used to find the approximate boundary conditions for a closely truncated 3‐D mesh is presented and shown to give good results without the complications of infinite elements. This method is applied to a large eddy current problem.