Constrained variational approach for dynamic analysis of elastic contact problems

Abstract

A solution method for dynamic analysis of elastic contact problems with rigid body motion under small deformation is presented. The contact surface is assumed unbounded and frictionless. A variational statement constrained by the geometric compatibility conditions on the contact surface is formulated as the basic principle of the dynamics and its equivalence to the governing equation of equilibrium is shown. Introducing increments in rigid body motion, the variational statement is described in an incremental form and the geometric compatibility conditions are linearized. The finite element method is adopted as a numerical approximation technique. For the time integration of dynamic response, the displacements are approximated by admissible functions and discontinuities of the velocities due to contact are considered. The resulting discretized system is described as a form of linear complementarity problem, suitable for numerical solution. The formulation is illustrated by means of two numerical examples.