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The problem of structural optimization of trusses subject to stress and frequency constraints is considered from a practical viewpoint. Assuming that the choice of members has to be from a discrete set of available sections, the solution is attempted using a mathematical programming approach and an approximate two‐step procedure involving a continuous variable optimization followed by a discrete programming algorithm. The latter approach is highly promising for problems involving stress and frequency constraints. Detailed results are presented using several benchmark problems.

Design sensitivities of plates and shells under transient dynamic loads with constraints on displacements and stresses are likely to be highly erroneous if proper care is not taken in selecting appropriate finite element mesh and time step size to be used in the analysis. An accurate value of design derivative is assured if an optimal mesh coupled with a reasonably fine time step size is used. The optimal mesh can be obtained iteratively and a number of examples are solved to demonstrate the importance of controlling discretization errors in space and time.

Contact problems are among the most difficult ones in mechanics. Due to its practical importance, the problem has been receiving extensive research work over the years. The finite element method has been widely used to solve contact problems with various grades of complexity. Great progress has been made on both theoretical studies and engineering applications. This paper reviews some of the main developments in contact theories and finite element solution techniques for static contact problems. Classical and variational formulations of the problem are first given and then finite element solution techniques are reviewed. Available constraint methods, friction laws and contact searching algorithms are also briefly described. At the end of the paper, a bibliography is included, listing about seven hundred papers which are related to static contact problems and have been published in various journals and conference proceedings from 1976.

The structural design problem can be viewed as an iterative design loop with each iteration involving two stages for topology and shape designs with genetic algorithm (GA) as the optimization tool for both.

The topology optimization problem, which is ill posed, is regularized using a constraint on perimeter and solved using GA. The problem is formulated as one of compliance minimization subject to volume constraint for the single loading case. A dual formulation of this has been used for the multiple loading cases resulting in as many behavioral constraints as there are loading cases. The tentative topology given by the topology optimization module is taken and the domain boundary is approximated using straight lines, B‐splines and cubic spline curves and design variables are selected among the boundary defining points. Optimum boundary shape of the problem has been obtained using GA in two different ways: without stress constraints; and with stress constraints.

The proposed two stage strategy has been tested on benchmark structural optimization problems and its performance is found to be extremely good.

The strategy appears to be eminently suitable for implementation in a general purpose FE software as an add‐on module for structural design optimization.

It has been observed that the integrated topology and shape design method is robust and easy to implement in comparison with other techniques. The computing time requirements for the GA does not appear daunting in the present scenario of high performance parallel computing and improved GA techniques.

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.

Presents a method of obtaining an optimal mesh in the finite element analysis of two‐dimensional linear elastodynamic problems under transient dynamic loading, which is based on a generalization of the Z‐Z criterion for discretization error estimation for time‐dependent problems. The optimal mesh limits the error due to discretization within a prescribed value, and studies of all other possible errors involved in finite element transient dynamic analysis are carried out systematically. Also proposes methods to study and limit the modal truncation error. Numerous examples show the capabilities of the proposed methods and the importance of the optimal mesh and modal truncation error in finite element transient dynamic analysis.

Three‐dimensional transient analysis of a submerged cylindrical shell is presented. Three‐dimensional trilinear eight‐noded isoparametric fluid element with pressure variable as unknown is coupled to a nine‐noded degenerate shell element. Staggered solution scheme is shown to be very effective for this problem. This allows significant flexibility in selecting an explicit or implicit integrator to obtain the solution in an economical way. Three‐dimensional transient analysis of the coupled shell fluid problem demonstrates that inclusion of bending mode is very important for submerged tube design—a factor which has not received attention, since most of the reported results are based on simplified two‐dimensional plane strain analysis.

In this paper an application of structural optimization to the design of structures with constraints in frequency and mode shape is presented. The objective is to obtain an optimum design making adequate changes in the structure to modify its dynamic characteristics. The method is based on an iterative process of optimization that includes structural analysis by the Finite Element Method (FEM), sensitivity analysis, and optimization techniques. An efficient and accurate method is used to calculate the sensitivities of the dynamic behaviour of the structure. The sensitivity analysis is accomplished using a semi‐analytical procedure based on the Nelson method. A Sequential Linear Programming (SLP) algorithm is used to solve the optimization problem. In the minimization process the convergence is assured even in a short number of iterations. The validation of the method is also shown by means of two examples of application.

This paper deals with structural shape and thickness optimization of axisymmetric shell structures loaded symmetrically. In the finite element stress analysis use is made of newly developed linear, quadratic, and cubic, variable thickness, C(0) elements based on axisymmetric Mindlin‐Reissner shell theory. An integrated approach is used to carry out the whole shape optimization process in a fully automatic manner. A robust, versatile and flexible mesh generator is incorporated with facilities for generating either uniform or graded meshes, with constant, linear, or cubic variation of thickness, pressure etc. The midsurface geometry and thickness variations of the axisymmetric shell structure are defined using cubic splines passing through certain key points. The design variables are chosen as the coordinates and/or the thickness at the key points. Variable linking procedures are also included. Sensitivity analysis is carried out using either a semi‐analytical method or a global finite difference method. The objective of the optimization is the weight minimization of the structure. Several examples are presented illustrating optimal shapes and thickness distributions for various shells. The changes in the bending, membrane and shear strain energies during the optimization process are also monitored.

Purpose — The purpose of this paper is to seek improved solution techniques for combined boundary‐initial value problems (IVPs) associated with the time‐dependent creep deformation and rupture of engineering structures at high temperatures and hence to reconfigure a parallel iterative preconditioned conjugate gradient (PCG) solver and the DAMAGE XXX software, for 3‐D finite element creep continuum damage mechanics (CDM) analysis.Design/methodology/approach — The potential to speed up the computer numerical solution of the combined BV‐IVPs is addressed using parallel computers. Since the computational bottleneck is associated with the matrix solver, the parallelisation of a direct and an iterative solver has been studied. The creep deformation and rupture of a tension bar has been computed for a range of the number of degrees of freedom (ndf), and the performance of the two solvers is compared and assessed.Findings — The results show the superior scalability of the iterative solver compared to the direct solver, with larger speed‐ups gained by the PCG solver for higher degrees of freedom. Also, a new algorithm for the first trial solution of the PCG solver provides additional speed‐ups.Research limitations/implications — The results show that the ideal parallel speed‐up of the iterative solver of 16, relative to two processors, is achieved when using 32 processors for a mesh of ndf = 153,238. Originality/value — Techniques have been established in this paper for the parallelisation of CDM creep analysis software using an iterative equation solver. The significant computational speed‐ups achieved will enable the analysis of failures in weldments of industrial significance.