Open Access

ARTICLE

A Three-dimensional Adaptive Strategy with Uniform Background Grid in Element-free Galerkin Method for Extremely Large Deformation Problems

Cheng-Te Chi¹, Ming-Hsiao Lee², Wen-Hwa Chen^1,3

1 Dept. of Power Mech. Engng., National Tsing Hua University, Hsinchu, Taiwan, Republic of China
2 National Center for High-performance Computing, National Applied Research Laboratories, Hsinchu, Taiwan, Republic of China
3 National Applied Research Laboratories, Taipei, Taiwan, Republic of China

Computers, Materials & Continua 2011, 24(3), 239-256. https://doi.org/10.3970/cmc.2011.024.239

Abstract

A novel three-dimensional adaptive element-free Galerkin method (EFGM) based on a uniform background grid is proposed to cope with the problems with extremely large deformation. On the basis of this uniform background grid, an interior adaptive strategy through an error estimation within the analysis domain is developed. By this interior adaptive scheme, additional adaptive nodes are inserted in those regions where the solution accuracy needs to be improved. As opposed to the fixed uniform background grid, these inserted nodes can move along with deformation to describe the particular local deformation of the structure. In addition, a triangular surface technique is adopted to depict the geometry of the three-dimensional structure and a new surface adaptive strategy on the surface of the structure is also proposed. The complicated geometry of the three-dimensional structure can be thus analyzed precisely even under extremely large deformation. Besides, the contact regions of the structure can be determined accurately when the contact behavior occurs. Therefore, the present EFGM adaptive strategy not only retains the advantage of the uniform background grid for solving the extremely deformed problems, but also enhances the solution accuracy in the interior and surface of the structure.

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Keywords

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