Cavities Identification from Partially Overdetermined Boundary Data in Linear Elasticity

[摘要] Our main interest in this work is an analysis of geometrical inverse problem related to the detection of cavities, in elasticity framework from partially overdetermined boundary data in two spatial dimensions. For the reconstruction, we have only access to the displacement field and to the normal component of the normal stress. We propose an identification method based on the Kohn-Vogelius formulation combined with the topological gradient method. An asymptotic expansion for an energy function is derived with respect to the creation of a small hole. A one-shot reconstruction algorithm based on the topological sensitivity analysis is implemented. Some numerical experiments concerning the cavities identification are finally reported, highlighting the ability of the method to identify multiple cavities.

[关键词] Geometrical inverse problems;Cavities identification;Linear elasticity;Partially overdetermined boundary data;Topological derivative;Asymptotic expansion