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Optimal control for elasto-orthotropic plate

Lovišek J., Králik J.

Control and Cybernetics

2006

Vol. 35, no 2

219-278

The optimal control problems and a weight minimization problem are considered for elastic three-layered plate with inner obstacle and friction condition on a part of the boundary. The state problem is represented by a variational inequality and the design variables influence both the coefficients and the set of admissible state functions. We prove the existence of a solution to the above-mentioned problem on the basis of a general theorem on the control of variational inequalities. Next, the approximate optimization problem is proved on the basis of the general theorem for the continuous problem. When the mesh/size tends to zero, then any sequence of appropriate solutions converges uniformly to a solution of the continuous problem. Finally, the application to the optimal design of unilaterally supported of rotational symmetrical load elastic annular plate is presented.

On thickness optimization of an unilaterally supported anisotropic plate subjected to buckling

Bock I., Lovišek J.

Computer Assisted Mechanics and Engineering Sciences

2002

Vol. 9, No. 4

447-458

We shall be dealing with the eigenvalue optimization problem for an anisotropic plate. The plate is partly unilaterally supported on its boundary and subjected to longitudinal forces causing its buckling. The state problem has then the form of an eigenvalue variational inequality expressing the deflection of the plate and the maximal possible value of the acting forces keeping its stability which corresponds to the first eigenvalue. The demand of the maximal first eigenvalue with respect to variable thicknesses of the plate means to solve the optimal design problem with eigenvalue variational inequality as the state problem. The existence of a solution in the framework of the general theory will be examined. The necessary optimality conditions will be derived. The convergence of the finite elements approximation will be verified.