Displaying similar documents to “Nonsmooth optimal design problems for the Kirchhoff plate with unilateral conditions”

Optimal design of cylindrical shells

Peter Nestler, Werner H. Schmidt (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the...

Shape optimization of an elasto-plastic body for the model with strain- hardening

Vladislav Pištora (1990)

Aplikace matematiky

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The state problem of elasto-plasticity (for the model with strain-hardening) is formulated in terms of stresses and hardening parameters by means of a time-dependent variational inequality. The optimal design problem is to find the shape of a part of the boundary such that a given cost functional is minimized. For the approximate solutions piecewise linear approximations of the unknown boundary, piecewise constant triangular elements for the stress and the hardening parameter, and backward...

On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

Igor Bock, Ján Lovíšek (2001)

Mathematica Bohemica

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An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.

Control in obstacle-pseudoplate problems with friction on the boundary. approximate optimal design and worst scenario problems

Ivan Hlaváček, Ján Lovíšek (2002)

Applicationes Mathematicae

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In addition to the optimal design and worst scenario problems formulated in a previous paper [3], approximate optimization problems are introduced, making use of the finite element method. The solvability of the approximate problems is proved on the basis of a general theorem of [3]. When the mesh size tends to zero, a subsequence of any sequence of approximate solutions converges uniformly to a solution of the continuous problem.

Optimal design of laminated plate with obstacle

Ján Lovíšek (1992)

Applications of Mathematics

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The aim of the present paper is to study problems of optimal design in mechanics, whose variational form is given by inequalities expressing the principle of virtual power in its inequality form. The elliptic, linear symmetric operators as well as convex sets of possible states depend on the control parameter. The existence theorem for the optimal control is applied to design problems for an elastic laminated plate whose variable thickness appears as a control variable.