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 Chin. Phys. B, 2015, Vol. 24(10): 100202    DOI: 10.1088/1674-1056/24/10/100202
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# Analysis of elastoplasticity problems using an improved complex variable element-free Galerkin method

Cheng Yu-Mina, Liu Chaoa, Bai Fu-Nonga, Peng Miao-Juanb
a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
b Department of Civil Engineering, Shanghai University, Shanghai 200072, China
Abstract

In this paper, based on the conjugate of the complex basis function, a new complex variable moving least-squares approximation is discussed. Then using the new approximation to obtain the shape function, an improved complex variable element-free Galerkin (ICVEFG) method is presented for two-dimensional (2D) elastoplasticity problems. Compared with the previous complex variable moving least-squares approximation, the new approximation has greater computational precision and efficiency. Using the penalty method to apply the essential boundary conditions, and using the constrained Galerkin weak form of 2D elastoplasticity to obtain the system equations, we obtain the corresponding formulae of the ICVEFG method for 2D elastoplasticity. Three selected numerical examples are presented using the ICVEFG method to show that the ICVEFG method has the advantages such as greater precision and computational efficiency over the conventional meshless methods.

Keywords:  meshless method      complex variable moving least-squares approximation      improved complex variable element-free Galerkin method      elastoplasticity
Received:  24 March 2015      Revised:  05 May 2015      Published:  05 October 2015
 PACS: 02.60.Cb (Numerical simulation; solution of equations) 02.70.-c (Computational techniques; simulations) 02.90.+p (Other topics in mathematical methods in physics) 46.15.-x (Computational methods in continuum mechanics)
Fund:

Project supported by the National Natural Science Foundation of China (Grant Nos. 11171208 and U1433104).

Corresponding Authors:  Cheng Yu-Min     E-mail:  ymcheng@shu.edu.cn