A thick shell model based on reproducing kernel particle method and its application in geometrically nonlinear analysis

A meshfree approach to the simulation of the large deformation of a curved shell by the reproducing kernel particle method (RKPM) is presented. Since the kinematic description is based on the Mindlin–Reissner shell theory, only one layer of particles is needed to model the shell and the time increment is not limited by the shell thickness. The reproducing interpolation function is adopted to discretize the kinematic quantities of the shell; thus, the spatial discretization is independent of the finite element mesh, so it can address large deformations without mesh distortion. The governing equation of an arbitrary curved shell is derived in detail based on the principle of virtual power, for which reasonable simplifications have been taken. The Lagrangian kernel and stress points are adopted in the calculation, which are sufficient to eliminate instability. Several numerical examples are performed, verifying the reliability and numerical accuracy of the RKPM shell model. No locking is observed in the numerical solutions.