A finite element method for contact problems between three-dimensional curved bodies

A finite element method for practically solving contact problems between three-dimensional curved bodies is presented. The method is in a framework of a standard incremental scheme. Contact constraints are described as relations between nodes on the two contacting bodies using quadratic shape functions. Each time the contact state changes; variables corresponding to the degrees of freedom to be constrained are eliminated, and a system of equations including the contact constraints is assembled and transformed so as to retain the symmetry and positive definite form of the global stiffness matrix. The resulting system of equations can be solved by the currently used ICCG or sky-line methods, which are common in general-purpose finite element programs. The effectiveness of the developed method is demonstrated by simple examples including a three dimensional Hertzian contact problem.