Energy change in elastic solids due to a spherical or circular cavity, considering uncertain in put data

I. Hlavacek (1) , A.A. Novotny (2) , Jan Sokolowski (3) , Antoni Zochowski (4)

1 IM / CAS - Institute of Mathematics of the Czech Academy of Science
2 LNCC / MCT - Laboratorio Nacional de Computação Cientifica [Rio de Janeiro]
3 IECN - Institut Élie Cartan de Nancy
4 IBS PAN - Systems Research Institute [Warsaw]

In the paper we consider topological derivative of shape functionals for elasticity, which is used to derive the worst and also the maximum range scenarios for behavior of elastic body in case of uncertain material parameters and loading. It turns out that both problems are connected, because the criteria describing this behavior have form of functionals depending on topological derivative of elastic energy. Therefore in the first part we describe the methodology of computing the topological derivative with some new additional conditions for shape functionals depending on stress. For the sake of fulness of presentation the explicit formulas for stress distribution around cavities are provided.

Domaines: Equations aux dérivées partielles [math.AP]

I. Hlavacek, A.A. Novotny, Jan Sokolowski, Antoni Zochowski. Energy change in elastic solids due to a spherical or circular cavity, considering uncertain in put data. 2007. ⟨hal-00174870⟩