Meshless numerical method for the contact problems of joint surface

Purpose The partition of unity of the standard meshless Galerkin method is used as basis in expressing the discontinuity of the contact surface displacement, particularly by adding discontinuous terms into the displacement mode, and constructing the discontinuous meshless displacement field function. In this study the contact surface equation is aimed to derive from the improved Coulomb friction contact model. Design/methodology/approach In this paper based on the basic idea of meshless method, an improved moving least squares approximation function (expansion method based on out of unit division) is applied to the analysis of two-dimensional contact problems. Findings On the basis of this equation after discrete processing, it is combined with the discrete form of the virtual work equation with added contact conditions, and eventually transformed into a standard linear complementary problem. Moreover, it is solved by using the Lemke algorithm, and a corresponding example is provided in this research. Originality/value The proposed method can effectively control the mutual embedding of the contact surface, and the stress distribution that is the same as the actual situation can be obtained on the contact surface.