Analysis of Tensile Structures with the Element Free Galerkin Method

In this work an implementation of a meshless method, the element free Galerkin method proposed by Belytschko et al. [1], for the analysis of three-dimensional laminar (thin) anisotropic structures is presented. By using the mapping technique proposed by Noguchi [5] the geometry of arbitrary curved surfaces is expanded in the two-dimensional space and the bases of convected co-ordinate system are utilized for expressing the strain and stress components in the virtual work principle. The nodes are generated in this two-dimensional space and the convected co-ordinates are used in the moving least-squares approximation of the displacement field. Generally shaped three-dimensional tensile structures require geometrically non-linear analysis. In the work described herein these effects are formulated in terms of the total Lagrangian method.