Abstract: The behaviour of circular plates with internal rigid ring supports is investigated. The material of plates is assumed to be an ideal elastic material obeying the Hooke’s law. The case of an elastic circular plate supported at the edge and resting on an absolutely rigid ring support is studied in a greater detail. Various optimization problems with unknown positions of extra supports are discussed and the problem of optimal location of the internal support is solved under the condition that the cost of the support is proportional to its length. Making use of the variational methods of the optimal control theory necessary conditions of optimality are deduced analytically. Numerical results are presented for the case of uniformly distributed transverse pressure.

Keywords: Plate, internal support, optimization, optimal control

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