A Penalty Function Type of Virtual Work Principle for Impact Contact Problems of Two Bodies

Abstract

This paper shows how an impact contact force can be expressed as a product series of penalty functions and subsidiary contact conditions having relative movement components between two bodies on a contact surface. A penalty function type of virtual work principle for various contact and separate states of two bodies is formulated by using the expression of the impact force. This principle is most effective for solving a general impact response of the alternation between contact and separation, and a stress wave propagation response of cracked structures with open and/or closed states on a cracked surface, because of both the use of the relative components and the relaxation of all the subsidiary conditions in this principle. A finite element method (FEM) based on this principle is applied to a two-dimensional analysis for longitudinal impact of two uniform rods. The mean value of impact force by FEM results coincides well with the value from the theory of one-dimensional elastic stress wave propagation.