Sensitivity Analysis and Optimal Design of Elastic Plates with Unilateral Point Supports

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Abstract
The deflection of a linearly elastic, thin plate subjected to a transverse load and supported by a finite number of unilateral point supports depends on the thickness and elastic properties of the plate as well as on the force. From a variational problem statement for the deflection, it is shown that the right and left directional derivatives of the deflection with respect to these parameters exist and that they are solutions of auxiliary variational problems. This result on sensitivities is then employed in the solution procedure for the problem of minimizing compliance of the plate, using thickness as a distributed design variable.