On finite deformation of hyperelastic shell-type structures: Cartesian formulation-based VDQ approach

Abstract

In this article, a numerical approach is presented for the large deformation analysis of shell-type structures made of Neo-Hookean and Kirchhoff–St Venant materials within the framework of the seven-parameter shell theory. Work conjugate pair of the second Piola–Kirchhoff stress and Green–Lagrange strain tensors are taken for the macroscopic stress and strain measures in this total Lagrangian formulation. By defining displacement vector, deformation gradient and stress tensor in the Cartesian coordinate system, and using the chain rule for taking derivative of tensors, the complications of using the curvilinear coordinate system are bypassed. The variational differential quadrature (VDQ) technique as an effective numerical solution method is applied to obtain the weak form of governing equations. Being locking-free, simple implementation, computational efficiency and fast convergence rate are the main features of the proposed numerical approach. A number of well-known benchmark problems are solved in order to reveal the accuracy and efficiency of the method. It is shown that this approach is able to predict the large deformations of hyperelastic shell-type structures in an efficient way.