Displaying similar documents to “Contact shape optimization based on the reciprocal variational formulation”

Shape optimization of materially non-linear bodies in contact

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.

Shape optimization of elasto-plastic bodies

Zuzana Dimitrovová (2001)

Applications of Mathematics

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Existence of an optimal shape of a deformable body made from a physically nonlinear material obeying a specific nonlinear generalized Hooke’s law (in fact, the so called deformation theory of plasticity is invoked in this case) is proved. Approximation of the problem by finite elements is also discussed.

Shape optimization for dynamic contact problems

Andrzej Myśliński (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The paper deals with shape optimization of dynamic contact problem with Coulomb friction for viscoelastic bodies. The mass nonpenetrability condition is formulated in velocities. The friction coefficient is assumed to be bounded. Using material derivative method as well as the results concerning the regularity of solution to dynamic variational inequality the directional derivative of the cost functional is calculated and the necessary optimality condition is formulated.

Shape optimization of elasto-plastic axisymmetric bodies

Ivan Hlaváček (1991)

Applications of Mathematics

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A minimization of a cost functional with respect to a part of a boundary is considered for an elasto-plastic axisymmetric body obeying Hencky's law. The principle of Haar-Kármán and piecewise linear stress approximations are used to solve the state problem. A convergence result and the existence of an optimal boundary is proved.