THE BENDING OF THIN PLATES WITH VARYING THICKNESS BASED ON MESHLESS LOCAL PETROV-GALERKIN METHOD

The bending of a thin plate with varying gently thickness is analyzed based on the Meshless Local Petrov-Galerkin method. The plate is assumed to be divided equally by its middle plane. The nodal points are firstly distributed on the plate, the radius of the nodal support domain and proper weighted functions are chosen. And then the shape functions of the nodal points within the support domain are obtained by the moving least square approximation. Substituting the shape functions into the governing equations leads to the stiffness and forces of these nodes in a support domain. The stiffness and forces of all the nodes are assembled into the total stiffness matrix and force vector. The displacements and inner forces of all the nodes are solved by the solution of the governing equation. The software ANSYS is used to analyze identical problems. The present numerical results compared to ANSYS illustrate that the Meshless Local Petrov-Galerkin (MLPG) method is easy to use and with high accuracy for solving the bending problem of variable thickness thin plates.