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On stiffness maximization of variable thickness sheet with unilateral contact. (English) Zbl 0871.73046
Summary: 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.
By using saddle point theory, the existence of solutions, i.e. thickness functions and corresponding displacement states, is proved. In general, one cannot expect uniqueness of solutions, unless the lower bound is strictly positive, and the uniqueness of optimal states is shown in this case.

74P99 Optimization problems in solid mechanics
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
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