Optimal design of an elastic circular plate on a unilateral elastic foundation. I: Continuous problems

An elastic simply supported axisymmetric plate, resting on a unilateral elastic foundation, is considered. The design variables are taken to be the thickness of the plate and the stiffness of the unilateral foundation. The thickness, the stiffness, and their partial derivatives of the first order are bounded. The load consists of a concentrated force acting in the centre of the plate, forces concentrated on the circle, an axisymmetric load, and the weight of the plate. The cost functionals are the integral of the intensity of shear stress the extreme fibers of the elastic plate and the norm in the weighted Sobolev space of the deflection curve of radius. The existence of solutions of the optimization, problems of the state problems is proved.