Quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method (QACM‐II)

Abstract

Abstract A novel strategy for developing low‐order membrane elements with analytical element stiffness matrices is proposed. First, some complete low‐order basic analytical solutions for plane stress problems are given in terms of the new quadrilateral area coordinates method (QACM‐II). Then, these solutions are taken as the trial functions for developing new membrane elements. Thus, the interpolation formulae for displacement fields naturally possess second‐order completeness in physical space (Cartesian coordinates). Finally, by introducing nodal conforming conditions, new 4‐node and 5‐node membrane elements with analytical element stiffness matrices are successfully constructed. The resulting models, denoted as QAC‐ATF4 and QAC‐ATF5, have high computational efficiency since the element stiffness matrices are formulated explicitly and no internal parameter is added. These two elements exhibit excellent performance in various bending problems with mesh distortion. It is demonstrated that the proposed strategy possesses advantages of both the analytical and the discrete method, and the QACM‐II is a powerful tool for constructing high‐performance quadrilateral finite element models. Copyright © 2008 John Wiley & Sons, Ltd.