An alpha finite element method for linear static and buckling analysis of textile-like sheet materials

A four node isoparametric shell element (Q4) based on Mindlin/Reissner plate theory and the alpha finite element method (αFEM) was formulated for obtaining 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. The first and fourth author acknowledge FCT for the conceded financial support through Project UID/CTM/00264/2019 of 2C2T – Centro de Ciência e Tecnologia Têxtil, hold by National Founds of FCT/MCTES. The second and third author acknowledge support by FCT/MCTES through national funds and when applicable co-funded EU funds under the project SFRH/BD/136554/2018.