Bending and free vibration analyses of circular stiffened plates using the FSDT mesh-free method

Abstract Based on the first-order shear deformation theory, a meshless method for bending and free vibration analyses of circular stiffened plates is proposed. The circular stiffened plate is modelled as a composite structure that consists of a flat circular plate and stiffeners. A series of points are used to discretize the flat circular plate and stiffeners to obtain the mesh-free model. The moving least-squares approximation is used to construct the shape functions and to derive the displacement fields of the flat circular plate and stiffeners, respectively. The total potential energy and kinetic energy of the circular stiffened plate are obtained according to the compatibility condition between the flat circular plate and stiffeners. The equations governing the bending and free vibration behaviors of the circular stiffened plate are derived according to the principle of Minimum Potential Energy and Hamilton's Principle, respectively. The boundary conditions are enforced by the full transformation method. The convergence of the proposed method and the domain of influence (DOI) that affects the numerical results are studied. Several examples are calculated by the proposed method and compared with the results available in the literature or given by the finite element software ABAQUS. The results show that the proposed method frees the researchers from determining a nodal line on the plate along every stiffener, which is very beneficial for carrying out optimization studies on stiffener location.