Open Access

ARTICLE

A Novel Element-Free Galerkin Method with Uniform Background Grid for Extremely Deformed Problems

Wen-Hwa Chen¹, Cheng-Te Chi, Ming-Hsiao Lee

1 Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China. E-mail: whchen@pme.nthu.edu.tw

Computer Modeling in Engineering & Sciences 2009, 40(2), 175-200. https://doi.org/10.3970/cmes.2009.040.175

Abstract

Based on an incremental formulation of element-free Galerkin method (EFGM), a highly efficient three-dimensional EFGM analysis procedure is proposed to deal with the structure with extremely large deformation. By this procedure, a fixed and uniform background grid, part of which coincides with the background cells employed in the conventional EFGM for numerical integration, is devised. The background grid is connected by uniformly distributed fictitious nodes which do not move during loading process even if extremely large deformation occurs. A deformable analysis domain, which is discretized by moving boundary nodes and interior nodes, is established for describing the deformation of the structure to be analyzed. When the structure is deformed under loadings, some fictitious nodes of the background grid outside the analysis domain may be included into the analysis domain as new interior nodes. Meanwhile, some interior nodes may be excluded from the analysis domain due to deformation. By a moving least square (MLS) approximation technique, a mapping procedure can then be developed for calculating the nodal displacements/ strains/stresses at those new interior nodes from those of the neighboring influencing boundary/interior nodes existing in the previous analysis domain. Although the interior nodes existing in the deformed structure may be different at each load increment, the distribution of the new interior nodes still remains uniform. Thus, the interpolation functions within the sub-domain can be determined by enough numbers of neighboring influencing boundary/interior nodes even under extremely large deformation. \newline To demonstrate the accuracy and efficiency of the new EFGM analysis procedure developed, two metal forming problems are tackled. Excellent agreement between the present computed results and those available in the literatures is drawn. The application of the present technique using uniform background grid for solving extremely deformed problems can also be extended to other meshless methods.

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