An isogeometric-meshfree coupling approach for contact problems by using the third medium method

Abstract

This paper presents a concurrent simulation method to integrate the isogeometric-meshfree (IMF) coupling approach with the third medium method for contact problems. The third medium method has been recently proposed as an alternative to conventional contact treatments [1]. This method is based on the concept of formulating a fictive medium in which contacting bodies are free to move and interact. To satisfy contact constraints, the medium is set to change from an isotropic material into an anisotropic one with respect to the movement of contacting bodies. In this way, the penetration of contacting surfaces can be avoided without the aid of an additional gap search algorithm. By further incorporating the IMF coupling approach into the third medium method, the overall problem domain is divided into two sub-domains which are formulated by isogeometric analysis (IGA) and meshfree method, respectively. IGA is applied along the domain boundary while the meshfree approximation is adopted within the interior area. The IMF coupling approach is expected to not only take advantage of both IGA and meshfree methods but also preserve a good convergence based upon the reproducing condition. The accuracy and effectiveness of the present approach are demonstrated by solving a series of benchmark contact problems.