Shape optimization of elastic axisymmetric plate on an elastic foundation. (English) Zbl 0839.73036

This work concerns the two-dimensional optimal design problem for an axisymmetric loaded elastic circular plate of variable thickness fixed on an elastic foundation. Under the condition of constant volume of the plate, the function of thickness is optimized in the class of Lipschitz functions bounded simultaneously from above and below by a positive constant. It is assumed that on the plate act its own weight, a force concentrated at the centre, forces concentrated on the circle, and the so-called rotational symmetrical load. The cost functional is the norm in the weighted Sobolev space consisting of the radial deflection functions. Existence of an optimal solution is proved, an approximate problem is introduced, and convergence of approximate solutions to the exact one is established.


74P99 Optimization problems in solid mechanics
74K20 Plates
74B99 Elastic materials
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