1. To solve the inverse Cauchy problem in linear elasticity by a novel Lie-group integrator.
- Author
-
Liu, Chein-Shan
- Subjects
- *
INVERSE problems , *NUMERICAL solutions to the Cauchy problem , *LINEAR systems , *LIE groups , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *ALGORITHMS - Abstract
In this paper, we propose a simple, iteration free and easy-to-implement numerical algorithm for the solution of inverse Cauchy problem in linear or nonlinear elasticity. The bottom of a finite rectangular plate is imposed by overspecified boundary data, and we seek unknown data on the top side. A spring-damping transform method (SDTM) is introduced to the Navier equations, such that after a discretization by the differential quadrature method, we can apply a novel Lie-group integrator, namely the mixed group-preserving scheme (MGPS), to solve them as an initial value problem. Several numerical examples including nonlinear ones are examined to show that the MGPS can overcome the ill-posed behaviour of the inverse Cauchy problem in elasticity, which has good efficiency and stability against the noisy disturbance, even with an intensity large up toand. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF