A RIGID PLASTIC FINITE-ELEMENT FORMULATION FOR THE ANALYSIS OF GENERAL DEFORMATION OF PLANAR ANISOTROPIC SHEET METALS AND ITS APPLICATIONS

General three-dimensional deformation of a planar anisotropic rigid-plastic sheet metal which obeys Hill's quadratic yield function is considered in the present analysis. The explicit expressions of the yield criterion and the related equations are given in the surface curvilinear co-ordinate system. A convective co-ordinate system is used in order to take into account the effect of geometric change during one step in the incremental analysis. The expression of the effective strain increment during one step is obtained in closed form by introducing assumptions on the deformation path and by proper consideration of the rotation of the axes of anisotropy during deformation. Considering the equilibrium at the deformed state, a variational formulation is derived to determine the deformation during a step. The corresponding finite-element equations are found in order to analyze the general deformation of planar anisotropic sheet metals. Two computational examples are chosen to verify the present formulation.