The Contact Patch Test for Linear Contact Pressure Distributions in 2D Frictionless Contact

摘要

It is well known that the classical one-pass node-to-segment algorithms for the enforcement of contact constraints fail the contact patch test. The situation is particularly critical when using the penalty method. In a recent study, the authors proposed a modified one-pass node-to-segment algorithm able to pass the contact patch test also in conjunction with the penalty method. However, in a general situation the pressure distribution transferred across a contact surface is non-uniform. Hence, even for a contact element which passes the contact patch test under a uniform distribution of the contact pressures, the transfer of a non-uniform state of stress across the contact surface may give rise to disturbances related to the discretization. Such disturbances introduce local solution errors and ultimately affect the accuracy of the analysis. This paper, following on from the previous study, develops an enhanced node-to-segment formulation able to pass a modified version of the contact patch test whereby a linear distribution of pressures has to be transmitted across the contact surface.