OPTIMAL-CONTROL OF A VARIATIONAL INEQUALITY WITH APPLICATION TO EQUILIBRIUM PROBLEM OF AN ELASTIC NONHOMOGENEOUS AND ANISOTROPIC PLATE RESTING ON UNILATERAL ELASTIC-FOUNDATION

Several optimal control problems with the same state problem-a variati onal inequality with a monotone operator-are considered. The inequalit y represents bending of an elastic, nonhomogeneous, anisotropic Kirchh off plate resting on some unilateral elasto-rigid foundation and point supports, Both the thickness of the plate and the coefficient of the unilateral elastic foundation play the role of design variables. Cost functionals include the work of external forces (compliance), total re action forces of the foundation or the weight of the plate. The solvab ility of all the problems is proved. Moreover, approximate methods for the optimal control and weight minimization problems are proposed, ma king use of finite elements. The design variables are approximated by piecewise affine functions. The solvability of the approximate problem s is proved and some convergence analysis is presented.