The problem of maximizing the stiffness of a linearly elastic sheet, in unilateral contact with a rigid frictionless support, is considered. The design variable is the thickness distribution, which is subject to an isoperimetric volume constraint and upper and lower bounds. The bounds may vary over the domain of the sheet, and the lower one is allowed to be zero, hence giving the possibility of obtaining topology information about an optimal design.
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Joakim Petersson (1996) studied this question.
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