A Mesh-free Analysis of Shell Structures

A mesh-free formulation based on the Mindlin-Reissner shell theory for geometrical and material nonlinear analysis of shells is presented. In this mesh-free formulation, two projection methods are developed to generate the shell surface using the Lagrangian mesh-free interpolations. The updated Lagrangian theory underlying the co-rotational procedure is adopted for the local strain, stress and internal force updating. A local boundary integration method in conjunction with the selective reduced integration method is introduced to enforce the linear exactness and relieve shear locking. Both nonlinear static and dynamic analysis of shell structures with finite rotations are considered. Several numerical examples are presented to demonstrate the accuracy and applicability of the proposed formulation.