Open Access

ARTICLE

Element Free Galerkin Method for Three-dimensional Structural Analysis

by Wen-Hwa Chen¹, Xhu-Ming Guo²

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

Computer Modeling in Engineering & Sciences 2001, 2(4), 497-508. https://doi.org/10.3970/cmes.2001.002.497

Abstract

An Element Free Galerkin Method is developed for the analysis of three-dimensional structures. A highly accurate and reliable relation between the number of the quadrature orders n_Q and nodes in a three-dimensional cell n_c, n_Q ≥ ³√n_c + 3, is established to accomplish the required integral calculation in the cell. Based on the theory of topology, the generation of nodes in the solution procedure consists of three sequential steps, say, defining the geometric boundary, arranging inside of the body, and improving numerical accuracy. In addition, by selecting the Dirac Delta function as the weighting function, a three-dimensional scattering sub-domain is devised by linking the node studied to neighbor nodes. Since the size of this newly defined sub-domain is adjustable with the nodal density, the three-dimensional scattering sub-domain can execute the moving least square approximation resiliently, but excellent accuracy is still maintained. Several numerical examples have been studied successfully to demonstrate the proposed techniques.

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