Analysis and optimization of nonsmooth mechanical structures
- Ignat, Anca
- Sprekels, Jürgen
- Tiba, Dan
2010 Mathematics Subject Classification
- 49Q10 35J35 34A55
- Lipschitz arches, discontinuous plate thickness, shape optimization
It is our aim to give a new treatment for some classical models of arches and plates and for their optimization. In particular, our approach allows to study nonsmooth arches, while the standard assumptions from the literature require W3,∞-regularity for the parametric representation. Moreover, by a duality-type argument, the deformation of the arches may be explicitly expressed by integral formulas.
As examples for the shape optimization problems under study, we mention the design of the middle curve of a clamped arch or of the thickness of a clamped plate such that, under a prescribed load, the obtained deflection satisfies certain desired properties. In all cases, no smoothness is required for the design parameters.
- SIAM J. Control Optim., 40 (2001), pp. 1107--1133