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

Abstract

This paper investigates that an impact contact force can be expressed as the product series of the penalty functions and the subsidiary contact conditions on a contact area between two bodies. Using the expression of the impact force, all the subsidiary contact conditions are relaxed in a virtual work principle for two bodies, and a penalty function method can be transformed from the concept of a least square method into that of a virtual work method. The use of a virtual work principle makes it easy to formulate a finite element method (FEM). Then, this paper also presents a virtual work principle with penalty functions for various impact contact states of two bodies. A FEM based on this principle is applied to a two-dimensional problem for the longitudinal impact of two bodies. The mean value of impact force by the FEM agrees well with the value from the theory of propagation of one-dimensional elastic stress wave.