Planar multiple-contact problems subject to unilateral and bilateral kinetic constraints with static Coulomb friction

This paper is concerned with contact problems. A planar multiple-contact problem subject to unilateral and bilateral kinetic constraints with static friction is studied using the complementarity method. First, this paper discusses the one-to-one correspondence of solutions of the contact problems of concern and of the corresponding complementarity models. An enhanced complementarity model is proposed by adding missed tangential acceleration constraints into previous complementarity models. Solutions of the proposed complementarity model and solutions of the contact problem are proven to exhibit one-to-one correspondence, which may not be guaranteed in the previous complementarity models. Then, this paper applies linear complementarity theory to investigate the properties of the solutions of the proposed complementarity model. For both unilaterally constrained contact problems and bilaterally constrained contact problems, the existence of solutions and boundedness of solutions are proven. Sufficient conditions for the uniqueness of solutions and finiteness of the number of solutions are also provided. Several numerical examples are given to show the non-uniqueness of solutions or the infiniteness of the number of solutions. Such phenomena demonstrate the non-smoothness of the contact problems discussed herein.