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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.

The mixed assumed strain approach proposed by Simo and Rifai is used to derive three 8‐noded hexahedral mixed strain elements. The approach is also generalized to geometrically non‐linear problems. Based on the Galerkin form of Hu‐Washizu three field variational principle, the Green‐Lagrange strain tensor and the second Piola‐Kirchhoff stress tensor (symmetric) are employed to develop the geometrically non‐linear formulation for 2D and 3D mixed enhanced strain elements. Numerical results are presented to show that the resulting hexahedral mixed strain elements possess all the ideal qualities. They are able to pass the patch test, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. Also, they are less sensitive to distorted meshes than standard isoparametric elements and exhibit high accuracy for both linear and non‐linear problems, permitting coarse discretizations to be utilized. The elements developed in this paper have been implemented in the general purpose FE package LUSAS.

An 8‐node solid element applicable for thin structures is presented. The element employs eighteen assumed stress modes and the conventional displacement interpolation. The formulation starts with the hybrid stress element proposed by Pian and Tong. The higher order stress modes are first decomposed into the ones which do and do not lead to thin‐element locking. The recently established methodology of admissible matrix formulation allows the decoupling of the above two categories of stress modes in the flexibility matrix without triggering element instability or failure of the patch test. The element stiffness can thus be decomposed into a series of matrices. Locking can be eliminated by adjusting the magnitude of the pertinent matrices. Accuracy and convergence rate of the present element are found to be competent to many of the existing plate and shell models.

We describe how to improve the accuracy of stress in the application of the hybrid finite element method. The idea is based on the fact that the assumed stress hybrid method is equivalent to both the principle of minimum complementary energy within the interior of each element and the principle of the minimum potential energy in the entire domain. It is known that when a good hybrid model is used for the displacement solution, the stress model must satisfy equilibrium within individual elements and be comparable with the boundary displacements. However, the compatibility in the elements is usually ignored and through variational operation it may be only approximately satisfied. So the stress model cannot approach a corresponding analytical stress field. In the present study, after nodal displacements are solved, we propose that a different stress model could be used to find the stress coefficients according to the principle of minimum complementary energy in each element in order to get an improved stress field.

The use of enhanced strains leads to an improved performance of low order finite elements. A modified Hu‐Washizu variational formulation with orthogonal stress and strain functions is considered. The use of orthogonal functions leads to a formulation with B (overline) ‐strain matrices which avoids numerical inversion of matrices. Depending on the choice of the stress and strain functions in Cartesian or natural element coordinates one can recover, for example, the hybrid stress element P‐S of Pian‐Sumihara or the Trefftz‐type element QE2 of Piltner and Taylor. With the mixed formulation discussed in this paper a simple extension of the high precision elements P‐S and QE2 to general non‐linear problems is possible, since the final computer implementation of the mixed element is very similar to the implementation of a displacement element. Instead of sparse B‐matrices, sparse B (overline) ‐matrices are used and the typical matrix inversions of hybrid and mixed methods can be avoided. The two most efficient four‐node B (overline) ‐elements for plane strain and plane stress in this study are denoted B (overline)(x, y)‐QE4 and B (overline)(ξ, η)‐QE4.

Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

The purpose of this paper is to investigate steady state creep behavior of a functionally graded rotating disc under varying thermal gradient (TG).

The steady state creep in a rotating FGM disc with linearly varying thickness has been investigated by using von-Mises yield criterion. The disc under investigation is assumed to be made of FGM containing non-linear distribution of silicon carbide particle (SiC_p) in a matrix of pure aluminum along the radial distance. The creep behavior of the FGM composite disc is described by threshold stress-based law. The stresses and strain rates in the FGM disc have been estimated for different kinds of TG.

The results indicate that when the FGM disc is subjected to a radial TG, with temperature increasing with increasing radius, the radial stress in the disc increases over the entire disc but the tangential and effective stresses increase near the inner radius and decrease toward the outer radius. The imposition of such a radial TG in the FGM disc leads to significant reduction in the radial and tangential strain rates. With the increase in magnitude of TG in the FGM disc, the inhomogeneity in creep stresses increases but the inhomogeneity in strain rates decreases significantly, thereby reducing the chances of distortion in the FGM disc.

The creep strain rates in rotating FGM disc could be significantly reduced when the disc is subjected to a radial TG, with temperature increasing with increasing radius.

THREE methods of elastic stress computation are described in the following section.

MOST of the structural analysis problems that have resulted from the use of “thin‐walled” construction seem to fall into two general classes: Stress distribution and buckling. Even these classes cannot be entirely separated, as the stress distribution can be greatly affected by buckling phenomena. A thorough understanding of the general principles of buckling (or structural instability) is therefore essential for efficient and safe design of modern aircraft structures.

The purpose of this paper is to present a new effective integration method for cyclic plasticity models.

By defining an integrating factor and an augmented stress vector, the system of differential equations of the constitutive model is converted into a nonlinear dynamical system, which could be solved by an exponential map algorithm.

The numerical tests show the robustness and high efficiency of the proposed integration scheme.

The von‐Mises yield criterion in the regime of small deformation is assumed. In addition, the model obeys a general nonlinear kinematic hardening and an exponential isotropic hardening.

Integrating the constitutive equations in order to update the material state is one of the most important steps in a nonlinear finite element analysis. The accuracy of the integration method could directly influence the result of the elastoplastic analyses.

The paper deals with integrating the constitutive equations in a nonlinear finite element analysis. This subject could be interesting for the academy as well as industry. The proposed exponential‐based integration method is more efficient than the classical strategies.