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A knowledge‐based system for forming quadrilateral finite elements, XFORMQ, was developed at the Centre of Flexible Manufacturing Research and Development of McMaster University, Canada. It automatically forms quadrilateral elements of good quality in conjunction with existing triangular mesh generators. XFORMQ can model geometries as complicated as those handled by triangular mesh generators. It allows for pre‐specified element sizes and rapid transition of element density. The concepts of ‘layer’ and ‘polygon patterns’, which considerably simplify the mesh generation rules and ensure the quality of formed elements, are introduced. Several test cases with different degrees of difficulties were used to evaluate XFORMQ's capabilities with satisfactory results. XFORMQ has the potential of generating meshes arising from the adaptive finite element analysis with quadrilateral elements.

Arbitrary constraints might be included into the problem domain in many engineering applications, which represent specific features such as multi-domain interfaces, cracks with small yield stresses, stiffeners attached on the plate for reinforcement and so on. To imprint these constraints into the final mesh, additional techniques need to be developed to treat these constraints properly.

This paper proposes an automatic approach to generate quadrilateral meshes for the geometric models with complex feature constraints. Firstly, the region is decomposed into sub-regions by the constraints, and then the quadrilateral mesh is generated in each sub-region that satisfies the constraints. A method that deals with constraint lines and points is presented. A distribution function is proposed to represent the distribution of mesh size over the region by using the Laplace equation. The density lines and points can be specified inside the region and reasonable mesh size distribution can be obtained by solving the Laplace equation.

An automatic method to define sub-regions is presented, and the user interaction can be avoided. An algorithm for constructing loops from constraint lines is proposed, which can deal with the randomly distributed constraint lines in a general way. A method is developed to deal with constraint points and quality elements can be generated around constraint points. A function defining the distribution of mesh size is put forward. The examples of constrained quadrilateral mesh generation in actual engineering analysis are presented to show the performance of the approach.

An automatic approach to constrained quadrilateral mesh generation is presented in this paper. It can generate required quality meshes for special applications with complex internal feature constraints.

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 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 quadrilateral 2‐D finite element for linear and non‐linear analysis of solids is presented. The element is based on the technique of mixed interpolation of tensorial components. It is shown that the new element is reliable and efficient, being apt, therefore, to be used in routine engineering applications.

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.

Gives a bibliographical review of the finite element meshing and remeshing from the theoretical as well as practical points of view. Topics such as adaptive techniques for meshing and remeshing, parallel processing in the finite element modelling, etc. are also included. The bibliography at the end of this paper contains 1,727 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1990 and 2001.

A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method.

This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary.

The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software.

This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.

The purpose of this paper is to apply the element decomposition method (EDM) in the study of the bending and vibration properties of plate and shell.

In the present method, each quadrilateral element is first divided into four sub-triangular cells, and the local strains are obtained in those sub-triangles based on linear interpolation. The whole strain filed is formulated through a weighted averaging operation of local strains, implying that only one integration point is adopted to construct the stiffness matrix. To reduce the instability of one-point integration and increase the accuracy of the present method, a stabilization item of the stiffness matrix is formulated by variance of the local strains. A mixed interpolated tensorial components (MITC) method is used in eliminating the shear locking phenomenon.

The novel EDM based on linear interpolation is effective in bending and vibration analyses of plate and shell, and the present method used in practical problems is reliable for static and free vibration analysis.

This method eliminated the instability of one-point integration and increased the accuracy by a stabilization item and performed stably in engineering analysis including large-scale problems of vehicle components.

The paper aims to presents a numerical analysis of free vibration of micromorphic structures subjected to various boundary conditions.

To accomplish this objective, first, a two-dimensional (2D) micromorphic formulation is presented and the matrix representation of this formulation is given. Then, two size-dependent quadrilateral and triangular elements are developed within the commercial finite element software ABAQUS. User element subroutine (UEL) is used to implement the micromorphic elements. These non-classical elements are capable of capturing the micro-structure effects by considering the micro-motion of materials. The effects of the side length-to-length scale parameter ratio and boundary conditions on the vibration behavior of 2D micro-structures are discussed in detail. The reliability of the present finite element method (FEM) is confirmed by the convergence studies and the obtained results are validated with the results available in the literature. Also, the results of micromorphic theory (MMT) are compared with those of micropolar and classical elasticity theories.

The study found that the size effect becomes very significant when the side length of micro-structures is close to the length scale parameter.

The study is to analyze the free vibrations of 2D micro-structures based on MMT; to develop a 2D formulation for micromorphic continua within ABAQUS; to propose quadrilateral and triangular micromorphic elements using UEL and to investigate size effects on the vibrational behavior of micro-structures with various geometries.