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shape optimization; axisymmetric elliptic problems; elasticity
An elastic simply supported axisymmetric plate of given volume, fixed on an elastic foundation, is considered. The design variable is taken to be the thickness of the plate. The thickness and its 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 functional is the norm in the weighted Sobolev space of the deflection curve of radius. Existence of a solution of the optimization problem of the state problem is proved. Approximate problem is introduced and convergence of its solutions to that of the continuous problem is established.
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