The Isoparametric Reproducing Kernel Particle Method for nonlinear deformation of plates

This paper proposed the new Isoparametric Reproducing Kernel Particle Method (IsoRKPM) for modeling nonlinear plate and shell deformation problems. The Reproducing Kernel shape functions are constructed on a two-dimensional parent domain. Following the concept of isoparametric mapping, the RK shape functions are directly used to approximate the plate geometry. A High Order Nodal Integration (HONI) is developed to integrate the Galerkin weak form of the Mindlin plate equilibrium equations. The proposed IsoRKPM with HONI is applied to solve several benchmark problems. Both modal and convergence analyses show that HONI provides more stable and accurate solutions than the nodal integration method.