Generalized finite difference method for solving the bending problem of variable thickness thin plate

Abstract

In this work, a meshless generalized finite difference method (GFDM), based on the Taylor series expansion and weighted moving-least square approximation, is proposed to solve the bending problem of variable thickness thin plate under various combinations of boundary conditions. The proposed method can treat the plates of complex shapes with an arbitrary continuous varying thickness in a simple and modular way. Besides, the method proposed a new strategy to create a well-determined linear system by introducing supplementary nodes on the boundary. Numerical examples are provided to demonstrate the accuracy and stability of the proposed method.