OPTIMAL-DESIGN OF AN ELASTIC PLATE WITH UNILATERAL ELASTIC-FOUNDATIONAND RIGID SUPPORTS, USING THE REISSNER-MINDLIN PLATE MODEL .1. CONTINUOUS PROBLEMS

Several optimal design problems with a variational inequality with a m onotone operator as common state problem are considered. The inequalit y represents the bending of a Reissner-Mindlin plate, resting on a uni lateral elastic foundation and on some unilateral rigid piers. Both th e thickness of the plate and the stiffness of the foundation play the role of design variables. The cost functionals include the intensity o f shear stresses: and reactive forces on the piers or the weight of th e plate. The solvability of all the problems is proved.