Bending analysis of skew ribbed plates with a meshfree method

Abstract

Based on the first - order shear deformation theory (FSDT), a meshless method for solving the free vibration problem of the skew ribbed plates is proposed. The plates and ribs are discretized with a series of points to obtain a meshless model of the ribbed plate by simulating the ribs with beams. The FSDT and the moving least - squares approximation are used to establish the displacement field. The displacement fields of the stiffener can be expressed in terms of the mid-surface displacement of the plate by imposing displacement compatible conditions between the plate and the stiffener. Then the stiffness equation of the entire skew ribbed plate can be derived by superimposing the strain energy of plate and stiffener. And the boundary condition is introduced by the full transformation method. Several examples are calculated, and the results given by the proposed method are compared with those from other researchers or ABAQUS. The results show that the method can effectively analyze the bending problem of the skew ribbed plate, and it avoids redistribution of plate nodes when rib position changes.