Modeling of topology variations in elasticity. System modeling and optimization

Sergeï A. Nazarov , Jan Sokolowski (1)

1 IECN - Institut Élie Cartan de Nancy

Two approaches are proposed for the modelling of deformation of elastic solids with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given.

Mots clés: Shape optimization; topology optimization; asymptotic analysis; elliptic operators; singular perturbations

Domaines: Equations aux dérivées partielles [math.AP]

Sergeï A. Nazarov, Jan Sokolowski. Modeling of topology variations in elasticity. System modeling and optimization. 2005, pp.147-158. ⟨hal-00102007⟩