Voids identification from partially overspecified boundary data

Abstract

This work is devoted to some geometric inverse problems in linear elasticity. The problem considered is the cavities identification in mechanical structures from the knowledge of partially overdetermined boundary data, namely the displacement field and the normal component of the normal stress. We state a uniqueness result from a single pair of data under some geometrical assumptions. We propose an iterative method based on the coupling of the data completion process through the Steklov-Poincaré operator to reconstruct the shear stress and of the shape gradient method combined with the level set method to identify cavities. Numerical simulations highlight the algorithm efficiency.

Topological sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity

“…Remark 3. The energy-like error functional has been used with considerable success in wide geometric inverse problems [3,5,6,8,9,[11][12][13]18]. This function can be interpreted as an energetic least-squares one based on fields computed from the measured data and the prescribed loads on the exterior boundary.…”