Formulation of Geometrically Nonlinear Element Free Galerkin Method and its Application to Analysis of Membrane Structures

The element free Galerkin method (EFGM) is a meshless method presented by Belytschko, Lu and Gu in 1994. A feature of the method is that only nodes are required in modeling of objects. Another feature is that distributions of stresses become continuous because the interpolation function used in EFGM is based on the moving least-squares method (MLSM). In this paper a formulation for geometrically nonlinear EFGM is presented, and it is applied to the analysis of membrane structures that are generally supported by the geometrical stiffness. As an illustrative example, a membrane structure whose shape is represented by bi-quadratic function is analyzed. It is also analyzed by finite element method, and results are compared.