An Alpha Finite Element Method for Linear Static and Buckling Analysis of Textile-Like Sheet Materials

Abstract

A four node isoparametric shell element (Q4) based on Mindlin/Reissner plate theory and the alpha finite element method (αFEM) was formulated for a nearly exact solution of linear static and buckling analysis of textile-like sheet material. The novel idea of αFEM-Q4 is assumed to be similar to the framework of conventional finite element approaches for Q4, but the gradient of strains is scaled by a factor α ∈ [0, 1]. The numerical examples demonstrate that the αFEM-Q4 can improve the accuracy of FEM solution in static and buckling analysis shell structures of non-woven fabric. However, the αFEM-Q4 cannot provide the nearly exact solution to all elasticity problems. In addition, it also requires a quadrilateral mesh that cannot be fully generated by common geometric algorithms for complicated problem domains.