seminar: The compliance of thin plates: modelling and optimization
speaker: Ilaria Fragalà (Politecnico di Milano)abstract: We consider an optimal design problem, which consists in finding the optimal distribution of a prescribed amount of plate-like material in a certain design region, in order to minimize the compliance under a given system of forces. We identify admissible mass distributions to positive measures with prescribed integral mean, thus allowing both diffused and concentrated solutions. By this way, we immediately get the existence of an optimal design, and the minimal compliance can be recovered simply by maximizing a linear form under an Hessian constraint.
In the first part of the talk I will show how this model can be derived from 3D-linear elasticity, by discussing the asymptotic behaviour of a sequence of optimal elastic compliance problems, in the double limit when both the maximal height of the design region and the total volume of the material tend to zero.
In the second part I will give necessary and sufficient optimality conditions, which can be used in order to compute the minimal value of the compliance and to determine analytically some optimal plates.
The results are contained in recent joint works with G. Bouchitté.
timetable:
Fri 13 Oct, 17:00 - 17:55, Aula Dini
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