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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.

Presents a review on implementing finite element methods on supercomputers, workstations and PCs and gives main trends in hardware and software developments. An appendix included at the end of the paper presents a bibliography on the subjects retrospectively to 1985 and approximately 1,100 references are listed.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

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.

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.

This bibliography is offered as a practical guide to published papers, conference proceedings papers and theses/dissertations on the finite element (FE) and boundary element (BE) applications in different fields of biomechanics between 1976 and 1991. The aim of this paper is to help the users of FE and BE techniques to get better value from a large collection of papers on the subjects. Categories in biomechanics included in this survey are: orthopaedic mechanics, dental mechanics, cardiovascular mechanics, soft tissue mechanics, biological flow, impact injury, and other fields of applications. More than 900 references are listed.

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

This paper aims to propose a new adaptive strategy for two-dimensional (2D) nonlinear finite element (FE) analysis of the minimal surface problem (MSP) based on the element energy projection (EEP) technique.

By linearizing nonlinear problems into a series of linear problems via the Newton method, the EEP technique, which is an effective and reliable point-wise super-convergent displacement recovery strategy for linear FE analysis, can be directly incorporated into the solution procedure. Accordingly, a posteriori error estimate in maximum norm was established and an adaptive 2D nonlinear FE strategy of h-version mesh refinement was developed.

Three classical known surfaces, including a singularity problem, were analysed. Moreover, an example whose analytic solution is unavailable was considered and a comparison was made between present results and those computed by the MATLAB PDE toolbox. The results show that the adaptively-generated meshes reflect the difficulties inherent in the problems and the proposed adaptive analysis can produce FE solutions satisfying the user-preset error tolerance in maximum norm with a fair adaptive convergence rate.

The EEP technique for linear FE analysis was extended to the nonlinear procedure of MSP and can be expected to apply to other 2D nonlinear problems. The employment of the maximum norm makes point-wisely error control on the sought surfaces possible and makes the proposed method distinguished from other adaptive FE analyses.

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.