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.

This paper presents an implementation of the node-based smoothed finite element method and Reissner-Mindlin plate theory for a four node isoparametric shell element to improve the numerical precision and computational efficiency subjected to free vibration analysis of textile-like sheet materials. A one smoothing cell integration scheme in the strain smoothing technique is implemented to contrast the shear locking phenomenon that may exists in the analysis for moderately-thick and thick shell models. Various numerical results of free vibration analysis for a multi-layer nonwoven fabric sample are compared with other existing analytical solutions and numerical solutions in literatures to demonstrate the effectiveness of the present method. An advantage of the present formulation is that it can improve the numerical precision without decreasing the computational efficiency.

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