A direct constraint-Trefftz FEM for analysing elastic contact problems

A direct constraint technique, based on the hybrid-Trefftz finite element method, is first presented to solve elastic contact problems without friction. For efficiency, static condensation is employed to condense a large model down to a smaller one which involves nodes within the potential contact surfaces only. This model can remarkably reduce computational time and effort. Subsequently, the contact interface equation is constructed by introducing the contact conditions of compatibility and equilibrium. Based on the formulation developed, a general solution strategy, which is applicable to the well-known three classical situations (receding, conforming and advancing) is developed. Finally, three typical examples related to the three situations mentioned are provided to verify the reliability and applicability of the approach.