Optimal Control of a Variational Inequality with Application to Equilibrium Problem of an Elastic Nonhomogeneous and Anisotropic Plate Resting on Unilateral Elastic Foundation

  • Authors:

  • Ján Lovíšek

  • Affiliations:

  • Slovak Technical University, Radlinskeno 11, 81368 Bratislave, Slovakia

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 1998

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Abstract

Several optimal control problems with the same stateproblem—a variational inequality with a monotone operator—areconsidered. The inequality represents bending of an elastic,nonhomogeneous, anisotropic Kirchhoff plate resting on someunilateral elasto-rigid foundation and point supports. Both thethickness of the plate and the coefficient of the unilateralelastic foundation play the role of design variables. Costfunctionals include the work of external forces (compliance),total reaction forces of the foundation or the weight of theplate. The solvability of all the problems is proved. Moreover,approximate methods for the optimal control and weightminimization problems are proposed, making use of finiteelements. The design variables are approximated by piecewiseaffine functions. The solvability of the approximate problems isproved and some convergence analysis is presented.