Control in obstacle-pseudoplate problems with friction on the boundary. Optimal design and problems with uncertain data.

*(English)*Zbl 1042.49036Summary: Four optimal design problems and a weight minimization problem are considered for elastic plates with small bending rigidity, resting on a unilateral elastic foundation, with inner rigid obstacles and a 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. If some input data are allowed to be uncertain a new method of reliable solutions is employed. We prove the existence of a solution to the above-mentioned problems on the basis of a general theorem on the control of variational inequalities.

Reviewer: Reviewer (Berlin)

##### MSC:

49Q10 | Optimization of shapes other than minimal surfaces |

49J40 | Variational inequalities |

74K20 | Plates |

74P05 | Compliance or weight optimization in solid mechanics |

93C30 | Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) |