A variational solution of the Cauchy problem in elastostatics
Kinko Kobayashi, Yoko Ohura, Kazuei Onishi · Kyoto University Research Information Repository (Kyoto University) · 1998
A variational solution of the Cauchy problem in elastostaticsAn inverse problem in two-dimensional elasticity is considered.The purpose is to present a variational approach to identification of the boundary conditions for resolution of the Cauchy problem governed by the Navier equations in plane elastostatics.The Cauchy problem is fea- tured by simultaneously prescribed displacement and traction on a part of the boundary of an elastic body.The boundary data may contain some noises.The problem is re-formulated as a minimization problem of a functional with constraints, then the minimization problem is recast into successive primary and dual boundary value problems with no constraints in the corresponding plane elasticity problem.Two variational formulations, $i.e$ .displacement approach and traction approach, are described.It is suggested that our variational method is convergent and the proposed rocess is stable.