Nonlinear formulations of the Element-Free Galerkin Method (EFGM) are
presented for the large deformation analysis of Ogden’s hyperelastic materials, which
are considered incompressible. The EFGM requires no explicit mesh in computation
and therefore avoids mesh distortion difficulties. In this study, the implementation of
the Moving Least Squares (MLS) approximation with the quartic spline weight
function is used to obtain the shape function and the transformation method is proposed
to impose the essential boundary conditions. Numerical results for a typical example
show that the present method is effective in dealing with large deformation hyperelastic
materials problems.
Keywords: Element-free galerkin method, Hyperelasticity, Moving least squares, Numerical analysis, Transformation method.
