The hybrid complex variable element-free Galerkin method for 3D elasticity problems: Fid-Bau Portal

The hybrid complex variable element-free Galerkin method for 3D elasticity problems

Cheng, Heng / Peng, Miaojuan / Cheng, Yumin / Meng, Zhijuan

Highlights • The dimension splitting method is introduced into a meshless method for 3D elasticity problems. • The equations of 3D problem are translated into a series of 2D ones. • The new Galerkin weak of the dimension splitting method for 3D elasticity problems are obtained. • The hybrid complex variable element-free Galerkin (HCVEFG) method is presented. • The HCVEFG method has greater computational efficiency than the improved EFG method for 3D problems.

Abstract Based on the dimension splitting method (DSM) and the improved complex variable element-free Galerkin (ICVEFG) method, the hybrid complex variable element-free Galerkin (HCVEFG) method for three-dimensional (3D) elasticity is proposed in this paper. The equilibrium equation of a 3D elasticity is written as three sets of equations, which contains the equilibrium equations of any two directions. By introducing the DSM, a set of the equilibrium equation of a 3D elasticity problem is transformed into a series of two-dimensional (2D) problems which are solved by using the ICVEFG method. In splitting direction, the finite difference method is used for coupling those 2D discretized equations. Similarly, the discretized equation of another set of the equilibrium equation can be derived. Then by coupling those two discretized system equations, the numerical solutions of the HCVEFG method for 3D elasticity problems can be obtained. The error and the convergence are analyzed by numerical examples, and the results show that the HCVEFG method has greater computational speed.