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finite element method; shape optimization; optimal design; method of nonlinear programming; numerical examples; elliptic boundary value problems
Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system is governed by partial differential equations with unilateral boundary conditions. In the paper an efficient method of nonlinear programming for solving optimal shape design problems is presented. The effectiveness of the technique proposed is demonstrated by numerical examples.
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