Book review: "Variational Methods in Shape Optimization Problems"
Andrzej Myśliński (2006)
Control and Cybernetics
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Andrzej Myśliński (2006)
Control and Cybernetics
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(2005)
Control and Cybernetics
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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.
Jaroslav Haslinger (1999)
Applications of Mathematics
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The paper deals with a class of optimal shape design problems for elastic bodies unilaterally supported by a rigid foundation. Cost and constraint functionals defining the problem depend on contact stresses, i.e. their control is of primal interest. To this end, the so-called reciprocal variational formulation of contact problems making it possible to approximate directly the contact stresses is used. The existence and approximation results are established. The sensitivity analysis...
Bijan Mohammadi (2010)
Control and Cybernetics
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G. Allaire, C. Dapogny, G. Delgado, G. Michailidis (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves...
Andrzej Myśliński (2012)
International Journal of Applied Mathematics and Computer Science
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This paper deals with the formulation of a necessary optimality condition for a topology optimization problem for an elastic contact problem with Tresca friction. In the paper a quasistatic contact model is considered, rather than a stationary one used in the literature. The functional approximating the normal contact stress is chosen as the shape functional. The aim of the topology optimization problem considered is to find the optimal material distribution inside a design domain occupied...