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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.

This paper aims to develop a hybrid finite difference‐finite element method and apply it to solve the three‐dimensional energy equation in non‐isothermal fluid flow past over a tube.

To implement the hybrid scheme, the tube length is partitioned into uniform segments by choosing grid points along its length, and a plane perpendicular to the tube axis is drawn at each of the points. Subsequently, the Taylor‐Galerkin finite element technique is employed to discretize the energy equation in the planes; while the derivatives along the tube are discretized using the finite difference method.

To demonstrate the validity of the proposed numerical scheme, three‐dimensional test cases have been solved using the method. The variation of L²‐norm of the error with mesh refinement shows that the numerical solution converges to the exact solution with mesh refinement. Moreover, comparison of the computational time duration shows that the proposed method is approximately three times faster than the 3D finite element method. In the non‐isothermal fluid flow around a tube for Re=250 and Pr=0.7, the results show that the Nusselt number decreases with the increase in the tube length and, for the tube length greater than six times the tube diameter, the average Nusselt number converges to the value for the two‐dimensional case.

A hybrid finite difference‐finite element method has been developed and applied to solve the 3D transient energy equation for different test cases. The proposed method is faster, and computationally more efficient, compared with the 3D finite element method.

Based on the recent advances of hybrid stress finite elements, a series of alternative stress assumptions for these elements are investigated. Several new element models are proposed by using different concepts for the stress interpolation. Under a unified formulation presented in this paper for Hellinger—Reissner principle based hybrid stress element models, the element series 5β‐family for plane stress and 18β‐family for three‐dimensional problems are discussed. The extra incompatible displacements sometimes also added are not introduced in this unified formulation. A number of popular benchmark elastic problems are examined for both two element families. In each family, the element model presented in this paper using normalized transformed higher order stress trials usually gives better predictions than the others.

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

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.

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 is given. The bibliography at the end of the paper contains 1,726 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 1996‐1999.

A multi‐variable finite element algorithm based on the generalized Galerkin method is presented. This algorithm takes advantages from the hybrid finite element method and the quasi‐conforming element method. Therefore, it has more flexibility and makes the hybrid and quasi‐conforming concepts easily applied to various physical problems. The formulation of a hybrid quadrilateral finite element with a unified singularity for both thermal and stress analyses has been derived using this algorithm. Some numerical examples are included to illustrate advantages of the hybrid algorithm in both stress and thermal analyses. It is also convenient to employ the algorithm in finite displacement problems.

This paper sets out to implement bounded high‐order (HO) resolution schemes in a hybrid finite volume/finite element method for the solution of the radiative transfer equation.

The hybrid finite volume/finite element method had formerly been developed using the step scheme, which is only first‐order accurate, for the spatial discretization. Here, several bounded HO resolution schemes, namely the MINMOD, CLAM, MUSCL and SMART schemes, formulated using the normalized variable diagram, were implemented using the deferred correction procedure.

The results obtained reveal an interaction between spatial and angular discretization errors, and show that the HO resolution schemes yield improved accuracy over the step scheme if the angular discretization error is small.

Although the HO resolution schemes reduce the spatial discretization error, they do not influence the angular discretization error. Therefore, the global error is only reduced if the angular discretization error is also small.

The use of HO resolution schemes is only effective if the angular refinement yields low‐angular discretization errors. Moreover, spatial and angular refinement should be carried out simultaneously.

The paper extends a methodology formerly developed in computational fluid dynamics, and aimed at the improvement of the solution accuracy, to the hybrid finite volume/finite element method for the solution of the radiative transfer equation.

This paper presents a hybrid finite element — boundary element method for the steady state thermal analysis of energy installations. The coupling of the two techniques is presented: finite elements are used in a bounded region containing thermal sources while the complementary domain is treated with boundary elements. With such a combination the number of unknowns is reduced and an accurate prediction of temperature is obtained. As an example, the temperature rise is computed for the case of three power cables laid in a thermal backfill: the finite element method (FEM) is used for the cables and the backfill while the homogeneous soil is taken into account with the boundary element method (BEM).

The analysis of plate systems (Figure 1) with mixed finite elements is limited to geometric smooth partial systems (Figure 1a) with continuous strains and stresses. This is due to the independent approximation of the parameters of the local generalized displacements (displacements, slopes) and generalized stresses (stress resultants at the cross‐section) in the nodes of the partial systems (Figure 1c). Owing to the simultaneous approximation, an additional static constraint of the generalized stresses, apart from the kinematic constraint of the displacements which is usual in the finite element methods, is needed at the assembly, so that discontinuities of the stresses resulting from the equilibrium conditions cannot be determined.