8-node unsymmetric distortion-immune element based on Airy stress solutions for plane orthotropic problems

Abstract

In this work, a simple but robust 8-node 16-DOF quadrilateral membrane element with exceptional tolerances to mesh distortion is proposed for efficiently analyzing the two-dimensional orthotropic elasticity problems, within the improved framework of the unsymmetric FEM. This unsymmetric element model adopts a self-equilibrium metric stress field, which is formulated at the basis of Airy stress solutions of the plane problem, to be the trial functions. Meanwhile, to ensure the interelement compatibility, the standard isoparametric displacement field is employed to be the element’s test function. Numerical tests reveal that this quadratic element is always capable of producing exact solutions in constant and linear stress/strain problems and delivering quite satisfactory results in other higher-order benchmark problems. In particular, it can still work very well even when the element shape deteriorates severely into a concave quadrangle or degenerated triangle.