Smoothed element-free Galerkin methods
A smoothed element-free Galerkin (EFG) method is formulated for incorporating cell-wise strain smoothing operation into EFG method. In present method, the field nodes can be divided into two types: boundary field nodes and interior field nodes. The background cells are divided into SC smoothing cells, and the strains in each smoothing cell are obtained using a gradient smoothing technique which can avoid evaluating derivatives of meshfree shape functions at integration point. The field variables of boundary points are approximated using linear interpolation of neighbour boundary field nodes, and the shape functions possess the Kronecker Delta property and facilitate the impositions of essential boundary conditions. The field variables of interior points are approximated using moving least-squares approximation using the support field nodes around them, which is same as in EFG method. Two schemes for constructing the shape function at the integration point are introduced and named SEFG-1 and SEFG-2. The effect of the number of divisions smoothing cells in both triangular and quadrilateral background cells is investigated in detail. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied and effective results are obtained. The numerical examples have confirmed the significant features of the present methods: (1) can pass the standard patch test; (2) can easily impose essential boundary conditions as those in finite element method; (3) can avoid evaluating derivatives of meshfree shape functions; (4) no numerical parameter is required.
meshfree element-free Galerkin (EFG) smoothed element-free Galerkin (SEFG) gradient smoothing operation finite element method (FEM)
GY. Li X.Y. Cui
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, 410082, PR China
国际会议
南京
英文
63-76
2009-10-12（万方平台首次上网日期，不代表论文的发表时间）