Energy conserving algorithms for dynamic contact analysis using Newmark methods

In this paper, two numerically robust algorithms based on Lagrangian velocity constraint and regularised penalty method are proposed for frictionless dynamic contact analysis utilising the standard Newmark method. It is shown that the Lagrangian velocity constraint method achieves energy conservation and a zero gap constraint approximately, where the errors can be reduced by temporal refinement. In addition to this, a regularised penalty force is devised to ensure exact energy conservation for frictionless contact analysis using the trapezoidal rule. Therefore, unlike the conventional penalty method, the proposed method achieves better accuracy in the impenetrability constraint whilst maintaining the energy stability with no need for extra refinement of the temporal discretisation.