Large deformation analysis of shell-type structures using the VDQ-transformed scheme: A two-point formulation based on 3D elasticity

Abstract

Shell-type structures are frequently used in aerospace, marine and civil engineering. In this paper, a numerical approach called as VDQ-transformed is introduced to analyze the large deformations of hyperelastic shell-type structures based on the Saint Venant–Kirchhoff constitutive model in the context of three-dimensional (3D) nonlinear elasticity. According to the Euler–Lagrange description, the kinetic first Piola-Kirchhoff tensor and kinematic deformation gradient tensor are considered for the stress and strain measures in the formulation. By replacing the tensor form of formulations with matricized ones, the governing equations are written in a novel vector-matrix format which can be readily exploited for programming in numerical approaches. Moreover, discretizing is carried out by the variational differential quadrature (VDQ) method as a point-wise numerical method. To apply the VDQ technique, a transformation is used to map the irregular domain into the regular one. Some well-known benchmark problems for the large deformations of shells are solved to assess the approach. Compact matricized formulation, simple implementation, being locking-free, computational efficiency and fast convergence rate can be mentioned as the main features of the introduced numerical approach.