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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

IMPACT FACTOR 2017: 0.941
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CiteScore 2017: 0.91

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Volume 8, Issue 5


Numerical solution of the Cauchy problem in plane elastostatics

K. Kobayashi
Published Online: 2013-09-07 | DOI: https://doi.org/10.1515/jiip.2000.8.5.541


- A variational approach is presented for numerical identification of the boundary conditions in solution of the Cauchy problem governed by the Navier equations in two-dimensional elasticity. The Cauchy problem in elastostatics is featured by simultaneously prescribed displacement and traction on a part of the boundary of an elastic body. The boundary data may contain some noise. The problem can be reformulated as a minimization problem of a functional with constraints, then the minimization problem is recast into successive primary and adjoint boundary value problems with no constraints in the corresponding plane elasticity problem. Two variational formulations, i. e., displacement approach and traction approach, are described. For an approximate solution of the elasticity problems, the conventional direct boundary element method is applied. Through simple examples, it is shown that our variational approaches are convergent and the proposed numerical process is stable.

About the article

Published Online: 2013-09-07

Published in Print: 2000-10-01

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 8, Issue 5, Pages 541–560, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2000.8.5.541.

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