A novel node-to-segment algorithm in smoothed finite element method for contact problems

摘要

Studies have found that the widely-used one-pass node-to-segment (NTS) algorithm for contacts fails to pass the contact patch test. Solution errors at the contacting surfaces resulting from the classical NTS algorithm do not necessarily decrease with the mesh refinement. This paper presents a novel NTS with the explicit dynamic formulation in detail, which can pass the contact patch test. The proposed algorithm consists of the following technical ingredient: (1) A weighted smoothing technique is developed to accurately evaluate contact forces for contact problems; (2) The central difference time integration scheme is utilized for efficiency, to save storage space, and to avoid the use of tangent stiffness matrix; (3) the penalty method is used for ease in implementation; (4) Our NTS algorithm is coded in the smoothed finite element method (S-FEM). Two S-FEM models are adopted for the proposed NTS algorithm: the node-based smoothed finite element method (NS-FEM) and the edge-based smoothed finite element method (ES-FEM) so that automatically generable triangular elements can be used for excellent adaptation. Numerical examples of the proposed algorithm are presented to examine the performance. It is found that the present algorithm alleviates the nonuniformity of contact pressure on both flat and curve boundaries. ES-FEM and NS-FEM combined with the new NTS algorithm have higher convergence rates. In addition, the ES-FEM has more accurate displacement and stress solutions at the same grid level. NS-FEM can even provide an upper bound solution in the strain energy for contact problems.