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Ivan Hlaváček, Raino Mäkinen (1991)
Applications of Mathematics
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An axisymmetric second order elliptic problem with mixed boundarz conditions is considered. A part of the boundary has to be found so as to minimize one of four types of cost functionals. The numerical realization is presented in detail. The convergence of piecewise linear approximations is proved. Several numerical examples are given.
Jaroslav Haslinger, Raino Mäkinen (1997)
Applications of Mathematics
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Optimal shape design problem for a deformable body in contact with a rigid foundation is studied. The body is made from material obeying a nonlinear Hooke’s law. We study the existence of an optimal shape as well as its approximation with the finite element method. Practical realization with nonlinear programming is discussed. A numerical example is included.
Zdeněk Kestřánek (1988)
Aplikace matematiky
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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...
Silveira, Ricardo A.M., Pereira, Wellington L.A., Gonçalves, Paulo B. (2008)
Mathematical Problems in Engineering
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Jaroslav Haslinger, Pekka Neittaanmäki, Timo Tiihonen (1986)
Aplikace matematiky
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The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.