Geometric Nonlinear Meshless Analysis of Ribbed Rectangular Plates Based on the FSDT and the Moving Least-Squares Approximation

Abstract

Based on the first-order shear deformation theory (FSDT) and the moving least-squares approximation, a new meshless model to study the geometric nonlinear problem of ribbed rectangular plates is presented. Considering the plate and the ribs separately, the displacement field, the stress, and strain of the plate and the ribs are obtained according to the moving least-squares approximation, the von Karman large deflection theory, and the FSDT. The ribs are attached to the plate by considering the displacement compatible condition along the connections between the ribs and the plate. The virtual strain energy formulation of the plate and the ribs is derived separately, and the nonlinear equilibrium equation of the entire ribbed plate is given by the virtual work principle. In the new meshless model for ribbed plates, there is no limitation to the rib position; for example, the ribs need not to be placed along the mesh lines of the plate as they need to be in FEM, and the change of rib positions will not lead to remeshing of the plate. The proposed model is compared with the FEM models from pieces of literature and ANSYS in several numerical examples, which proves the accuracy of the model.