An unsymmetric 8‐node plane element immune to mesh distortion for linear isotropic hardening material

Abstract

An 8-node quadrilateral plane element US-QUAD8 is developed for linear isotropic hardening material in the framework of updated Lagrangian unsymmetric finite formulation where B L matrix is constructed by classical shape function, and B R matrix by the higher-order Lagrangian basis function in global coordinate system. The present element eliminates the influence of Jacobian in the elemental stiffness matrix and guarantees the quadratic completeness of displacement field even under severe distorted mesh. Two typical problems meshed with angular/curved-edge/mid-side distorted elements demonstrate excellent performance of distortion resistance of the present element and good computational efficiency in severe mesh distortion.

Extension of the unsymmetric 8‐node hexahedral solid element US‐ATFH8 to 3D hyper‐elastic finite deformation analysis

“…In formulating the US‐ATFQ4 element, the Jacobi determinant is eliminated in final expression of the element stiffness matrix, removing the damaging effects associated with element distortion 10 . The application of analytical solutions (ATFs) greatly improves the precision of the low‐order element, and naturally overcomes interpolation failure and dependence on frame rotation, defects that are often present in previous unsymmetric formulations 11–16 . Following this work, several similar element models have been proposed, 17,18 including the extension to geometric nonlinear model by designing a rational update strategy for ATFs 19 .…”

“…10 The application of analytical solutions (ATFs) greatly improves the precision of the low-order element, and naturally overcomes interpolation failure and dependence on frame rotation, defects that are often present in previous unsymmetric formulations. [11][12][13][14][15][16] Following this work, several similar element models have been proposed, 17,18 including the extension to geometric nonlinear model by designing a rational update strategy for ATFs. 19 The improved US-ATFQ4 element exhibits much better performance as demonstrated by a series of purposely designed performance tests.…”