Research On Bending And Free Vibrations Of The Thin Plates With Varying Thickness Based On Meshless Method

Meshless method is a new numerical method, which is in essences similar to Finite element method.It is mainly by virtue of node and shape function in local support domain to realize the numerical value of calculation within the global scope, which can partly or thoroughly eliminate the mesh, thus avoiding the dependence of mesh to approximate function and complicated process of meshing and reconstruction. It not only has more flexibility and validity but also can keep the exactness. Therefore, meshless method has important research value and applies value.The paper first reviewed the development and basic theory of meshless method in which Some methods of weighted residuals and approximate functions are described emphatically.Secondly in this paper Meshless method is used to analyze the bending and the free vibrations of a variable thickness thin plate.The nodal points were first 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 were gotten by the solution of the governing equation. The software ANSYS is used to analyze the same problem, to prove the feasibility of method and the correctness of programs.Finally, a summary of the paper and the future research directions are forecasted.