A 4-node hybrid stress-function (HS-F) plane element with drilling degrees of freedom less sensitive to severe mesh distortions

A mixed isostatic 16 dof quadrilateral membrane element with drilling rotations, based on Airy stresses

“…" # So, the assumed stress interpolation corresponds to a combination of the Airy stress solutions, used in hierarchical polynomial order as proposed by Cen et al [3,4]. Apart from other advantages, this choice will allow relevant element matrices to be evaluated more easily through line integration on the element contour as will be detailed in the following sections.…”

“…The results are very accurate over different benchmarks. In a further paper [4], the same authors proposed the use of Airy based stress in the setup of a 4-node statically determined mixed quadrilateral element with Allman drilling rotations. The use of Airy functions in the interpolation of the stress field has also been proposed by A. Cannarozzi and M. Cannarozzi in [34] for deriving 4 and 8 node mixed elements.…”

“…Research in developing high performance membrane finite elements, accurate for coarse meshes and less sensitive to geometry distortion, is even nowparticularly active [1][2][3][4][5][6][7][8][9]. Often, membrane elements are coupled with bending discretization to be used in linear and geometrically nonlinear analysis of folded plates, box structures also assembled with other type of element, as was given in [10,11].…”

Incompatible modes with Cartesian coordinates and application in quadrilateral finite element formulation

“…Development of low-order elements with high accuracy in coarse mesh has always been a hot topic in the research of the finite element method (Cen et al 2011b;Mostafa et al 2013;Pian 1964;Simo and Rifai 1990;Tang et al 1980 should have the following characteristics: (a) numerically efficient, (b) easy to formulate, (c) passes the numerical patch test, (d) without excess rigid body motion, (e) high accuracy, (f) without spurious locking in bending or nearly incompressible limit, (g) with a theoretically optimized convergence rate. It is difficult and meaningful to achieve all these advantages within a low order element, and many methods have been proposed for this purpose.…”

Trefftz- type FEM for solving orthotropic potential problems

“…Due to the fact that no domain integrals are involved in the formulation of TFEM, the Trefftz-type elements are less sensitive to mesh distortion in practical applications. This feature has been investigated by Jirousek and Wroblewski (1995); Jirousek and Qin (1996); Choi et al (2006); Cen et al (2011); using different 4-node quadrilateral elements. On the other hand, the employment of two independent fields also makes the TFEM easier to generate arbitrary polygonal or polyhedral elements with or without inclusions, which are accurate, efficient and natural for micromechanical modeling of heterogeneous materials (Dong and Atluri, 2012a,b,c).…”