Let ^tT be a bounded 3D domain with Lipschitz boundary (Gamma) , (sigma) equals (pi) R ² is a prescribed displacement on (Gamma) (volume forces are absent). We denote by A(u,v) equals integral_(Omega ) L(epsilon) (u) (DOT) (epsilon) (v) dx bilinear form corresponding to the first elasticity problem where L is a tensor of Hooke's law written in the tensor form (sigma) equals L(epsilon) (isotropic case will be the subject of consideration) and by V a subspace of Sobolev space W₂¹((Omega) ,R³) that is V equals {v equalsV W₂¹((Omega) ,R³) v equals 0 on (Gamma) }. We assume that g_i equalsV W₂^1/2((Gamma) ) and A(u,v) is V-elliptic bilinear form. A weak solution of the first elasticity problem is a vector- valued function.

Date Published: 5 May 1999
PDF: 4 pages
Proc. SPIE 3687, International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering, (5 May 1999); doi: 10.1117/12.347463

Published in SPIE Proceedings Vol. 3687:
International Workshop on Nondestructive Testing and Computer Simulations in Science and Engineering
Alexander I. Melker, Editor(s)