Finite rotation meshfree formulation for geometrically nonlinear analysis of flat, curved and folded shells

Abstract

Geometrically nonlinear analysis of flat, curved and folded shells under finite rotations is performed by enhanced six degrees of freedom (6-DOFs) meshfree formulation. Curvilinear surfaces are dealt with the concept of convected coordinates. Equilibrium equations are derived by total Lagrangian formulation with Green–Lagrange strain and Second Piola–Kirchhoff stress. Both shell geometry and its deformation are approximated by Reproducing Kernels (RKs). Transverse shear strains are considered by Mindlin–Reissner theory. Numerical integration of the stiffness matrix is estimated by using the Stabilized Conforming Nodal Integration (SCNI) method. To show accuracy and effectiveness of the proposed formulation and discretization, benchmark problems from the literatures are considered. Apart from reference solutions available in the literature, additional reference results based on finite element method (FEM) conducted by the present authors are also presented.