Approaches to accommodate noisy data in the direct solution of inverse problems in incompressible plane-strain elasticity.
We apply the adjoint weighted equation method (AWE) to the direct solution of inverse problems of incompressible plane strain elasticity. We show that based on untreated noisy displacements, the reconstruction of the shear modulus can be very poor. We link this poor performance to loss of coercivity of the weak form when treating problems with discontinuous coefficients. We demonstrate that by smoothing the displacements and appending a regularization term to the AWE formulation, a dramatic improvement in the reconstruction can be achieved. With these improvements, the advantages of the AWE method as a direct solution approach can be extended to a wider range of problems.
Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel.
U
U
Albocher
Department of Mechanical Engineering, Boston University, Boston, MA 02215, USA.
P E
PE
Barbone
Department of Surgery, School of Medicine and Dentistry, University of Rochester, Rochester, NY 14642, USA.
M S
MS
Richards
Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA.
A A
AA
Oberai
Faculty of Engineering, Tel Aviv University, 69978 Ramat Aviv, Israel.
I
I
Harari
incompressible plane strain; inverse problems; regularization; smoothing; variational methods