On Obtaining a Solution to Optimization Problems for Solid,Elastic Plates by Restriction of the Design Space*

The problem of minimizing the static compliance of a solid elastic plate, for given total plate volume, is considered. Nonexistence of solutions in the case of a design space consisting of thickness functions for an isotropic, homogeneous plate is identified as being caused by the nonclosedness of the corresponding set of responses (deflections). It is shown that existence can be obtained if a bound on the gradient of the thickness function is imposed. It is also shown that this restriction of the design space ensures the existence of solutions to a broad class of plate optimization problems, static as well as dynamic.