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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.

Most studies of power‐law fluids are carried out using stress‐based system of Navier‐Stokes equations; and least‐squares finite element models for vorticity‐based equations of power‐law fluids have not been explored yet. Also, there has been no study of the weak‐form Galerkin formulation using the reduced integration penalty method (RIP) for power‐law fluids. Based on these observations, the purpose of this paper is to fulfill the two‐fold objective of formulating the least‐squares finite element model for power‐law fluids, and the weak‐form RIP Galerkin model of power‐law fluids, and compare it with the least‐squares finite element model.

For least‐squares finite element model, the original governing partial differential equations are transformed into an equivalent first‐order system by introducing additional independent variables, and then formulating the least‐squares model based on the lower‐order system. For RIP Galerkin model, the penalty function method is used to reformulate the original problem as a variational problem subjected to a constraint that is satisfied in a least‐squares (i.e. approximate) sense. The advantage of the constrained problem is that the pressure variable does not appear in the formulation.

The non‐Newtonian fluids require higher‐order polynomial approximation functions and higher‐order Gaussian quadrature compared to Newtonian fluids. There is some tangible effect of linearization before and after minimization on the accuracy of the solution, which is more pronounced for lower power‐law indices compared to higher power‐law indices. The case of linearization before minimization converges at a faster rate compared to the case of linearization after minimization. There is slight locking that causes the matrices to be ill‐conditioned especially for lower values of power‐law indices. Also, the results obtained with RIP penalty model are equally good at higher values of penalty parameters.

Vorticity‐based least‐squares finite element models are developed for power‐law fluids and effects of linearizations are explored. Also, the weak‐form RIP Galerkin model is developed.

Gives a bibliographical review of the error estimates and adaptive finite element methods from the theoretical as well as the application point of view. The bibliography at the end contains 2,177 references to papers, conference proceedings and theses/dissertations dealing with the subjects that were published in 1990‐2000.

This paper aims to introduce a multiscale computational method for structural failure analysis with inheriting simulation of moving trans-scale boundary (MTB). This method is motivated from the error in domain bridging caused by cross-scale damage evolution, which is common in structural failure induced by damage accumulation.

Within the method, vulnerable regions with high stress level are described by continuum damage mechanics, while elastic structural theory is sufficient for the rest, dividing the structural model into two scale domains. The two domains are bridged to generate mixed dimensional finite element equation of the whole system. Inheriting simulation is developed to make the computation of MTB sustainable.

Numerical tests of a notched three-point bending beam and a steel frame show that this MTB method can improve efficiency and ensure accuracy while capturing the effect of material damage on deterioration of components and structure.

The proposed MTB method with inheriting simulation is an extension of multiscale simulation to structural failure analysis. Most importantly, it can deal with cross-scale damage evolution and improve computation efficiency significantly.

This paper aims to present an extension of two recently published elements (which are based on Petrov‐Galerkin formulation) to geometric nonlinear (GNL) problems.

Two different sets of shape functions, namely isoparametric and metric, suitably chosen to satisfy the necessary compatibility and completeness conditions, are used as test and trial functions, respectively. Total Lagrangian formulation is used for the implementation of the element.

In implementing the unsymmetric formulation for nonlinear problems, the deformation gradient tensor can be evaluated invariably using either isoparametric or metric shape functions. The developed elements are found to exhibit improved performance in the presence of mesh distortions.

The numerical problems in this paper involve linear elastic materials.

Extension of US‐QUAD8 and US‐HEXA20 for GNL problems is new.

There are industrial applications for varying speed lid-driven flow and heat transfer such as the float glass process where the glass film stretches or thickens depending on the desired thickness. Hence the tin cavity underneath or the nitrogen cavity above is being driven by a variable speed. The purpose of this paper is to simulate such behavior.

Numerical solution of variable speed lid-driven cavity is carried out with thermal radiation being considered using control volume approach and staggered grid and applying the SIMPLE algorithm. Transient simulation is used for 2D model in the present study. Second order upwind schemes were used for discretization of momentum, energy equations and time.

Under laminar conditions, thermal radiation plays a significant role in the heat transfer characteristics of the lid-driven cavity. This effect is more significant for blackbody radiation and decreases as the surface emissivity decreases. Nusselt number (Nu) behavior lies between these two limiting case profiles considering constant speed profiles of both maximum and minimum lid velocities, respectively. In addition, local Nu values at the tip where higher than those at the top of the cavity that is stagnant.

The study is limited to laminar flow case.

The applications of this study can be found in float glass process where the glass film stretches or thickens depending on the desired thickness. Hence the tin cavity underneath or the nitrogen cavity above is being driven by a variable speed. Another application involves casting of plastic films. The molten polymer leaves the die with a considerable thickness and high temperature. The film is then trenched to reach its final thickness. In this case, usually there is no actual cavity above or below the film but one can approximate the problem as such. Other similar applications do exist in food drying and processing where the conveyer belt is in portions and their speed may not be the same in different section of the processing oven.

To the best of the authors knowledge, no study in the literature addressed the effect of thermal radiation in lid-driven cavities with variable speed

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 the present work a rigid‐plastic finite element formulation using a dynamic explicit time integration scheme is proposed for numerical analysis of sheet metal forming processes. The rigid‐plastic finite element method, based on membrane elements, has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme, in general, is based on the elastic‐plastic modelling of material requiring large computation time. The resort to rigid‐plastic modelling would improve the computational efficiency, but this involves new points of consideration such as zero energy mode instability. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM (abbreviated from Bending Energy Augmented Membrane) elements, are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and a direct trial‐and‐error method. Computations are carried out for analysis of complicated sheet metal forming processes such as forming of an oilpan and a front fender. The numerical results of explicit analysis are compared with the implicit results, with good agreement, and it is shown that the explicit scheme requires much shorter computational times, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid‐plastic finite element enables an effective computation for complicated sheet metal processes.

The purpose of this paper is to propose a hybrid mesh-free method based on generalized finite difference (GFD) and Newmark finite difference methods to study the elastic wave propagation in functionally graded nanocomposite reinforced by carbon nanotubes (FGNRCN). The presented hybrid mesh-free method is applied for a thick hollow cylinder, which is made of FGNRCN and excited by various mechanical shock loadings.

The FG nanocomposite cylinder is assumed to be under shock loading. The elastic wave propagation is obtained and studied for various nonlinear grading patterns and distributions of the aligned carbon nanotubes. The distribution of carbon naotubes in FG nanocomposite are considered to vary as nonlinear function of radius, which varies with various nonlinear grading patterns continuously through radial direction. The effective material properties of functionally graded carbon nanotube are estimated using a micro-mechanical model.

The mechanical shock analysis of FGNRCN thick hollow cylinder is carried out and the dynamic behavior of displacement field and the time history of radial displacement are obtained for various grading patterns. An effective hybrid mesh-free method based on GFD and Newmark finite difference methods is presented to calculate the average velocity of elastic wave propagation in FGNRCN. The average velocity of elastic wave propagation is obtained for various grading patterns and various kinds of volume fraction. The effects of some parameters on average velocity of elastic wave propagation are obtained and studied in detail.

The calculation of elastic radial wave propagation in a FGNRCN thick hollow cylinder is presented using a hybrid mesh-free method. The effects of some parameters on wave propagation such as various grading patterns of distribution of carbon nanotubes are studied in details.