An iterative method for the Cauchy problem in linear elasticity with fading regularization effect

作者：Delvare Franck^*; Cimetiere Alain; Hanus Jean Luc; Bailly Patrice

来源：Computer Methods in Applied Mechanics and Engineering, 2010, 199(49-52): 3336-3344.

DOI：10.1016/j.cma.2010.07.004

• Cauchy problem
• Inverse problem
• Data completion
• Linear elasticity
• Regularization
• Boundary conditions

In this paper, an iterative method for solving the Cauchy problem in linear elasticity is introduced. This problem consists in recovering missing data (displacements and forces) on some parts of a domain boundary from the knowledge of overspecified data (displacements and forces) on the remaining parts. The algorithm reads as a least square fitting of the given data, with a regularization term whose effect fades as the iterations go on. So the algorithm converges to the solution of the Cauchy problem. Numerical simulations using the finite element method highlight the algorithm's efficiency, accuracy, robustness to noisy data as well as its ability to deblur noisy data.

• 出版日期2010