Optimal prestress of structures with frictional unilateral contact interfaces

Summary The problem of optimal prestress stabilization of elastic structures with frictional contact interfaces subject to static loads is studied in this paper. A linear elastic structure with given unilateral contact at frictional interfaces is considered. The prestressing control is modelled by the pin-load method. The static problem is formulated as a nonsymmetric variational inequality. The goal of the optimal control design is closing of the unilateral contact joints as well as minimization of the friction induced slips with a minimum effort. The resulting optimal control problem is nonsmooth and nonconvex, as it concerns the control of structures governed by variational inequalities. Appropriate techniques of nonsmooth analysis are used for its numerical solution. Effective computer realization and integration into existing finite element software is facilitated by appropriate static condensation techniques, which are outlined in the paper. Numerical examples illustrate the theory.