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Boundary element method(BEM)has been applied to analyze contact problems in two or three dimensions in last three decades,and the direct constraint method is widely used to establish contact conditions where the contact equations can be explicitly expressed with the displacements and tractions of the contact zone.At early time,the conforming discretization is used for establishing the contact equations between contact node pairs.However,the conforming discretization has some unavoidable limitations on its performance when the geometries are too complicated to generate conforming meshes or finite sliding should be considered.Therefore,the non-conforming discretization using the shape functions to establish the contact equations has been presented later.