Numerical simulation with element-free method based on the wavelet basis function in the sheet metal forming

There are severe deformation and high stress gradient field in the sheet metal forming. Traditional finite element analysis of sheet metal forming processes often requires not only explicit mesh or element shape function with high order but also the post-processing for the ideal precision. Because of the element mesh property it is difficult to get high quality distributed node by the method of discrete node or refinement node, and at the same time the technology of post-processing also affects the computation precision. Element-free method breaks away the restriction of element mesh. Firstly, the adaptive refinement and discretization can be easily achieved, so it well adapts to analyze high stress gradient; Secondly, it substitutes wavelet basis for the polynomial series which are usually used in traditional element-free method, so it has the excellent property of wavelet transform, localization and multi-resolution character, and can overcome the mesh-sensitivity or the stress field discontinuity of finite element method. Forming processes for a square cup deep drawing is analyzed by this element-free method and the results are satisfied very well with the software DYNAFORM solutions.