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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.

A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

Implementation details of the assumed shear strain method in a novel finite rotation shell theory are discussed. Careful considerations of the pertinent aspects of the Newton solution procedure are given. The latter results in a very robust performance of the presented 4–node shell element in some challenging finite rotation problems.

The purpose of this paper is to present a quadrilateral shell element using 16 degrees of freedom (dof) (12 translations and four rotations) which makes a pair with Morley's triangle at 12 dof. This latter has been updated by Batoz who later proposed an extension to a quadrilateral (“DKQ16”) but only with special interpolation functions for an elastic behaviour of the material. Precisely, it is in order to release from this strong limitation that a completely different formulation is proposed here.

The development of this new quadrilateral called “DKS16” involves three stages. The first one starts from Morley's triangle updated by Batoz (“DKT12”) to derive a rotation‐free (RF) triangular element (“S3”). The second stage consists in generalising this triangle to a RF quadrilateral (“S4”). During the final leg, the S4 and DKT12 main features are combined to give the quadrilateral “DKS16”.

Other parameters being equal, the type of finite element chosen for the forming stage simulation has a great influence on further springback result even in software with automatic remeshing. Particularly, it is pointed out that the RF shell elements S3 and S4 as well as the triangle DKT12 are less sensitive to the mesh size than classical shell elements with six dof per node. But, even if some improvements of in‐plane shear have been proposed, stamping codes users are reluctant to use triangles. That is why this paper presents an attempt to extrapolate a quadrilateral (DKS16) from the triangle DKT12 via S3 and S4 elements formulation. Numerous examples showing convergence and accuracy are presented: irregular meshes, large displacement analyses and deep‐drawing simulations.

The triangular “S3” element is already implemented in RADIOSS^® software and its implementation – as well as the one of “DKT12” – is in progress in Pam‐Stamp, both as “user elements”. The next step will be the implementation of the quadrilateral “S4” (RF) and, maybe, the element “DKS16” since both are cheaper in terms of computation time and are found interesting for sheet forming.

It seems obvious that curvatures are more exactly captured in RF elements (when nodes slide on die radius) since they are imposed in terms of translations instead of traditional nodal rotations not managed by contact conditions. As the neighbours are involved, a drawback of these RF elements is their complex formulation in case of branching surfaces and/or abrupt variations in material behaviour and/or thickness. This is not the case for elements such as DKT12 or DKS16, good candidates to add to the (long) list of cheap shell elements for large scale computations typical of sheet metal forming.

A fully mixed hybrid 4‐node shell element for linear analyses is presented and compared to the current state‐of‐the‐art. The specific improvements developed concern the stress assumptions for the transverse shear stresses in the in‐plane directions, such that the element is applicable for arbitrary element geometries without shear locking and satisfies the patch test exactly. Furthermore, in analogy to the membrane and bending part the shear part of the stiffness matrix can be formulated as a one‐point integrated constant part with a rank‐two update representing the linear parts. However, this efficient formulation leads to additional approximations concerning the geometry of arbitrarily curved elements. The latter aspect is discussed with some numerical examples, which demonstrate the capabilities of the developed element.

The numerical quadrature of the stiffness matrices and force vectors is a major factor in the accuracy and efficiency of the finite element methods. Even in the analysis of linear problems, the use of too many quadrature points results in a phenomenon called locking whereas the use of insufficient quadrature points results in a phenomenon called spurious singular mode. Therefore, efficient numerical quadrature schemes for structural dynamics are developed. It is expected that these improved finite elements can be used more reliably in many structural applications. The proposed developed quadrature schemes for the continuum and shell elements are straightforward and are modularized so that many existing finite element computer codes can be easily modified to accommodate the proposed capabilities. This should prove of great benefit to many computer codes which are currently used in structural engineering applications.

The purpose of this paper is to present integrated methodologies based on multilevel modelling concepts for finite element analysis (FEA) of reinforced concrete (RC) shell structures, with specific reference to account for the nonlinear behaviour of cracked concrete and the other associated features.

Geometric representation of the shell is enabled through multiple concrete layers. Composite characteristic of concrete is accounted by assigning different material properties to the layers. Steel reinforcement is smeared into selected concrete layers according to its position in the RC shell. The integrated model concurrently accounts for nonlinear effects due to tensile cracking, bond slip and nonlinear stress‐strain relation of concrete in compression. Smeared crack model having crack rotation capability is used to include the influence of tensile cracking of concrete. Propagation and change in direction of crack along thickness of shell with increase in load and deformation are traced using the layered geometry model. Relative movement between reinforcing steel and adjacent concrete is modelled using a compatible bond‐slip model validated earlier by the authors. Nonlinear iterative solution technique with imposed displacement in incremental form is adopted so that structures with local instabilities or strain softening can also be analysed.

Proposed methodologies are validated by evaluating ultimate strength of two RC shell structures. Nonlinear response of McNeice slab is found to compare well with that of experiment available in literature. Then, a RC cooling tower is analysed for factored wind loads to study its behaviour near ultimate load. Numerical validation demonstrates efficacy and usefullness of the proposed methodologies for nonlinear FEA of RC shell structures.

The present paper integrates critical methodologies used for behaviour modelling of concrete and reinforcement with the physical interaction among them. The study is unique by considering interaction of tensile cracking and bond‐slip which are the main contributors to nonlinearity in the nonlinear response of RC shell structures. Further, industrial application of the proposed modelling strategy is demonstrated by analysing a RC cooling tower shell for its nonlinear response. It is observed that the proposed methodologies in the integrated manner are unique and provide stability in nonlinear analysis of RC shell structures.

The 4‐node assumed strain elements are among the best elements available today but the bending moments at their full integration points oscillate severely. This paper presents a one point integrated version of the 4‐node assumed strain plate element of Bathe‐Dvorkin. A Taylor series expansion approach is used to accommodate the linear variation of strains/stresses within the element and hence to stabilize the spurious zero energy modes. An extensive number of benchmark results are presented and compared.

This paper focuses on the development of a new class of eight‐node solid finite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used efficiently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement‐based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are defined related to nearly‐incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and benefiting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of efficient solid and shell formulations is obtained. Numerical results attest the robustness and efficiency of the proposed approach, when compared to solid and shell elements well‐established in the literature.

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.

Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.

Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.

The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.