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Reissner-Mindlin plate model with uncertain input data. (English) Zbl 1367.74032

Summary: A Reissner-Mindlin model of a plate resting on unilateral rigid piers and a unilateral elastic foundation is considered. Since the material coefficients of the orthotropic plate, stiffness of the foundation, and the lateral loading are uncertain, a method of the worst scenario (anti-optimization) is employed to find maximal values of some quantity of interest.The state problem is formulated in terms of a variational inequality with a monotone operator. Using mixed-interpolated finite elements, approximations are proposed for the state problem and for the worst scenario problem. The solvability of the problems and a convergence of approximations is proved.

MSC:

74K20 Plates
49J40 Variational inequalities
74P05 Compliance or weight optimization in solid mechanics
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