An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates

In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian-type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one-node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh-dependent sub-optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd.

Polygonal finite elements for topology optimization: A unifying paradigm

This study investigates and reviews approaches to modelling laminated composite plates. It explores theories that have been proposed and developed and assesses their suitability and functionality. The particular focus in this study has been on normal stresses and the through-thickness distributions of transverse shear. These are important for composite plates as stress-induced failures can occur in three different ways. Therefore, it is essential to understand and calculate transverse shear and normal stress through the thickness of the plate accurately. In this study, previous laminated composite plate theories are categorised and reviewed in a general sense, i.e. not problem specific, and the advantages and disadvantages of each model are discussed. This research mainly focuses on how accurate and efficient the models can predict the transverse shear. It starts with displacement-based theories from very basic models such as Classical laminate plate theory to more complicated and higher-order shear deformation theory. Models are furthermore categorised by how the models consider the overall laminate. In this article, the theories are divided into two parts: Single layer theory, where the whole plate is considered as one layer; and Layerwise theory, where each layer is treated separately. The models based on zig-zag and Discrete Theories are then reviewed, and finally the mixed (hybrid) plate theories are studied.

The development of laminated composite plate theories: a review

The present paper is devoted to a state-of-the-art review on the computational treatment of laminated composite and sandwich panels. Over two hundred texts have been included in the survey with the focus put on theoretical models for multilayered plates and shells, and FEM implementation of various computational concepts. As a result of the review, one could notice a lack of a single numerical model capable for a universal representation of all layered composite and sandwich panels. Usually, with the increase of the range of rotations considered in the particular model, one can observe the decrease of the degree of complexity of the through-the-thickness representation of deformation profiles.

https://www.degruyter.com/downloadpdf/j/eng.2011.1.issue-1/s13531-011-0005-x/s13531-011-0005-x.xml

A literature review on computational models for laminated composite and sandwich panels

W artykule przedstawiono przegląd modeli obliczeniowych stosowanych w analizie laminowanych powlok kompozytowych i sandwiczowych. W przeglądzie uwzgledniono ponad 200 pozycji literatury traktujących o modelach teoretycznych dla plyt i powlok wielo-warstowych oraz/lub o implementacjach numerycznych roznych modeli obliczeniowych. Jako podstawową konkluzje z dokonanego przeglądu, nalezy uznac, ze nie istnieje jeden uniwersalny model matematyczny zdolny do efektywnego reprezentowania ogolu konstrukcji warstwowych. Praktyczna przydatnośc roznych sformulowan teoretycznych zalezy istotnie od specyfiki analizowanego problemu. Przy oczywistych ograniczeniach zdolności obliczeniowych, glownie natury sprzetowej i ekonomicznej, calkiem naturalnym zjawiskiem jest zauwazalna tendencja do zmniejszania rzedu dokladności opisu deformacji profilu poprzecznego wraz ze wzrostem stopnia nieliniowości analizowanych zagadnien.

Membrane elements insensitive to distortion using the quadrilateral area coordinate method

The quadrilateral area co-ordinate method is used to formulate a new quadrilateral element for Mindlin–Reissner plate bending problem. Firstly, an independent shear field is assumed based on the locking-free Timoshenko's beam formulae; secondly, a fourth-order deflection field is assumed by introducing some generalized conforming conditions; thirdly, the rotation field is determined by the strain–displacement relations. Furthermore, a hybrid post-processing procedure is suggested to improve the stress/internal force solutions. Following this procedure, a new 4-node, 12-dof quadrilateral element, named AC-MQ4, is successfully constructed. Since all formulations are expressed by the area co-ordinates, element AC-MQ4 presents some different, but beneficial characters when compared with other usual models. Numerical examples show the new element is free of shear locking, insensitive to mesh distortion, and possesses excellent accuracy in the analysis of both thick and thin plates. It has also been demonstrated that the area co-ordinate method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models. Copyright © 2005 John Wiley & Sons, Ltd.

Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate

A simple quadrilateral 12 DOF plate bending element based on Reissner–Mindlin theory for analysis of thick and thin plates is presented in this paper. This element is constructed by the following procedure: 1. the variation functions of the rotation and shear strain along each side of the element are determined using Timoshenko's beam theory; and 2. the rotation, curvature and shear strain fields in the domain of the element are then determined using the technique of improved interpolation. 
The proposed element, denoted by ARS-Q12, is robust and free of shear locking and, thus, it can be employed to analyze very thin plate. Numerical examples show that the proposed element is a high performance element for thick and thin plates.

A new twelve DOF quadrilateral element for analysis of thick and thin plates

The area co-ordinate method has been successfully applied to construct triangular elements. In this paper, this method is generalized to construct quadrilateral elements, and the area co-ordinate theory for quadrilateral elements is systematically developed: (i) the area co-ordinates (L1 , L2 , L3 , L4) of any point in a quadrilateral are defined and two identical equations, which the four area co-ordinates should satisfy, are formulated and proved; (ii) two characteristic parameters for quadrilateral elements are defined and the degeneration conditions under which a quadrilateral degenerates into a parallelogram or a trapezoid or a triangle are given; (iii) transformation relations between the area co-ordinates and the Cartesian or isoparametric co-ordinates are presented, and several important formulae for quadrilateral area co-ordinates are listed. Copyright © 1999 John Wiley & Sons, Ltd.

Yuqiu Long

Papers

Membrane elements insensitive to distortion using the quadrilateral area coordinate method

Application of the quadrilateral area co-ordinate method: a new element for Mindlin–Reissner plate

A new twelve DOF quadrilateral element for analysis of thick and thin plates

Area co-ordinates used in quadrilateral elements

A new 4-node quadrilateral FE model with variable electrical degrees of freedom for the analysis of piezoelectric laminated composite plates