A formulation of conserving impact system based on localized Lagrange multipliers

This paper proposes a new finite element method of frictional impact of elastic bodies. The formulation introduces a contact frame that is placed in between contacting bodies and represents the contact surface. The nonpenetration condition and the slip–stick condition are defined between the contacting body and the contact frame with the aid of the independent localized Lagrange multipliers representing the contact forces. The position of the contact frame and the local coordinate of the contacting node along the contact frame are also treated as the independent variable, which enables the exact satisfaction of the constraint conditions without the deficiency or redundant constraint. The energy and momentum conservation algorithm is applied to the proposed impact system. For the case of frictional impact, the linear momentum is exactly conserved and the angular momentum is approximately conserved with negligible error. Copyright 2006 John Wiley & Sons, Ltd.