TY - JOUR
T1 - Adjoint-weighted variational formulation for the direct solution of plane stress inverse elasticity problems
AU - Barbone, Paul E.
AU - Rivas, Carlos E.
AU - Harari, Isaac
AU - Albocher, Uri
AU - Oberai, Assad A.
AU - Goenzen, Sevan
PY - 2008
Y1 - 2008
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=65249089663&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/135/1/012012
DO - 10.1088/1742-6596/135/1/012012
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AN - SCOPUS:65249089663
SN - 1742-6588
VL - 135
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
M1 - 012012
ER -