New boundary condition treatments in meshfree computation of contact problems Original Research Article

Due to the loss of Kronecker delta properties in the meshfree shape functions, the imposition of essential boundary conditions consumes significant CPU time in meshfree computation. In this work, two boundary condition treatments are proposed to enhance the computational efficiency of meshfree methods for contact problems. The mixed transformation method is modified from the previous full transformation method by introducing a node partitioning and a mixed coordinate so that the matrix inversion and multiplication of coordinate transformation involves operations only on the sub-degrees of freedom associated with the boundary group. The boundary singular kernel method introduces singularities to the kernel functions of the essential and contact boundary nodes so that the corresponding coefficients of the singular kernel shape functions recover nodal values, and consequently kinematic constraints can be imposed directly. The effectiveness of the proposed methods is demonstrated in several numerical examples.