Modelling and numerical solution of problems of structural mechanics with unilateral constraints and friction

Abstract

Abstract The article deals with the problems of calculation of elastically deformable systems with unilateral constraints and Coulomb friction. For the numerical solution of the problem, the finite element method is used, the contact interaction is modeled by means of the contact finite elements (CFE) of the frame-rod type. The basic relations and statements of static and dynamic contact problems for the interacting elastic bodies are given. To comply with the limitations under the conditions of ultimate friction-sliding, the method of compensating loads is applied. On the basis of the proposed discrete contact model and step-by-step loading schemes, the numerical algorithms are developed, which allows calculating structures with unilateral constraints and Coulomb friction, both under static and dynamic loads, as well as taking into account the different contact conditions that approximate the calculation scheme to the real operating conditions of a structure or construction. With the help of the proposed approach, numerical solutions of the problem of contact of the structure with the base under dynamic load are obtained and analyzed.