Optimal design of an elastic plate with unilateral elastic foundation and rigid supports, using the Reissner-Mindlin plate model .1. Continuous problems.

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