Abstract: A new type of numerical method called mesh-free method is presented to implement the simulation of square box part deep drawing in view of the drawback of finite element method. Mechanics equations for dominating the sheet metal forming process based on mesh-free reproducing kernel particle method are developed. The material shape function is adopted to avoid the frequent updates of shape function and influence domain. To impose the essential boundary conditions exactly, mesh-free shape function is re-constructed and the modified shape function called kinematically admissible shape function is interpolatory. The all shape functions associated with nodes within the whole domain are re-constructed in order to enforce the complex essential boundary conditions expediently and exactly. The nodes distributed in the die are used to construct a matrix owning the characteristic which can be used to search the slave node being in contact with the die. Furthermore a data structure called “sparse matrix” is proposed to accelerate the contact searching. The program for simulating the sheet metal forming process is set up, and the mesh-free simulations of deep drawing for the square box part are implemented. The influence of blank holder force on the deep drawing is investigated, and the distributions of thickness, stress and strain are obtained by meshless numerical simulations. The comparison of numerical results with experimental results shows the effectiveness of using mesh-free method to simulate sheet metal forming.

Key words: Finite element method, Mesh-free method, Numerical simulation, Stamping