A meshless method for geometric nonlinear analysis of arbitrary polygonal and circular stiffened plates

Abstract

Based on the first-order shear deformation theory, a meshless Galerkin method for geometric nonlinear analysis of arbitrary polygonal and circular stiffened plates is proposed. The arbitrary polygonal and circular stiffened plates are modeled as composite structures that consist of flat plates and stiffeners. A series of points are used to discretize the flat plate and stiffeners to obtain the meshless model of the stiffened plates. The moving least-squares approximation is used to construct the shape functions and the displacement fields. The large deflection theory of von Karman is adopted for the geometric nonlinear analysis of the stiffened plates, and flexure and extensional properties of the stiffened plates are derived. The stiffeners are fitted to the flat plate by implementing displacement compatibility conditions between the flat plates and the stiffeners. The boundary conditions are enforced by the full transformation method. To demonstrate the convergence and accuracy of the proposed method, several numerical examples are employed. The solutions that are computed by the proposed method are compared with the finite element solutions that are given by ABAQUS and with the results of other research work. The results show that the agreement is good. Because no mesh is required in the model, the stiffeners can be placed anywhere on the flat plates, and changes to the positions of the stiffeners do not entail the remeshing of the plates.