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Weight minimization of an elastic plate with a unilateral inner obstacle by a mixed finite element method

Ivan Hlaváček (1994)

Applications of Mathematics

Unilateral deflection problem of a clamped plate above a rigid inner obstacle is considered. The variable thickness of the plate is to be optimized to reach minimal weight under some constraints for maximal stresses. Since the constraints are expressed in terms of the bending moments only, Herrmann-Hellan finite element scheme is employed. The existence of an optimal thickness is proved and some convergence analysis for approximate penalized optimal design problem is presented.

Weyl formula with optimal remainder estimate of some elastic networks and applications

Kaïs Ammari, Mouez Dimassi (2010)

Bulletin de la Société Mathématique de France

We consider a network of vibrating elastic strings and Euler-Bernoulli beams. Using a generalized Poisson formula and some Tauberian theorem, we give a Weyl formula with optimal remainder estimate. As a consequence we prove some observability and stabilization results.

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