Adjoint-weighted variational formulation for the direct solution of plane stress inverse elasticity problems

Paul E. Barbone, Carlos E. Rivas, Isaac Harari, Uri Albocher, Assad A. Oberai, Sevan Goenzen

Research output: Contribution to journalArticlepeer-review

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Abstract

We describe a novel variational formulation of the inverse elasticity problem given interior data. The strong form of this problem is governed by equations of pure advective transport. To address this problem, we generalize the adjoint-weighted variational equation (AWE) formulation, originally developed for flow of a passive scalar. Here, we shall study the properties of the AWE formulation in the context of inverse plane stress elasticity imaging. We show that the solution of the AWE formulation is equivalent to that of the strong form when both are well posed. We prove that the Galerkin discretization of the AWE formulation leads to a stable, convergent numerical method, and prove optimal rates of convergence.

Original languageEnglish
Article number012012
JournalJournal of Physics: Conference Series
Volume135
DOIs
StatePublished - 2008

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