Element free Galerkin method for three-dimensional structural analysis

An Element Free Galerkin Method is developed for the analysis of three-dime nsional structures. A highly accurate and reliable relation between the num ber of the quadrature orders n(Q) and nodes in a three-dimensional cell n(c ), n(Q) greater than or equal to (3)rootn(c) + 3, is established to accompl ish the required integral calculation in the cell. Based on the theory of t opology, the generation of nodes in the solution procedure consists of thre e sequential steps, say, defining the geometric boundary, arranging inside of the body, and improving numerical accuracy. In addition, by selecting th e Dirac Delta function as the weighting function, a three-dimensional scatt ering subdomain is devised by linking the node studied to neighbor nodes. S ince the size of this newly defined subdomain 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 ma intained. Several numerical examples have been studied successfully to demo nstrate the proposed techniques.