Method of approximation of the weak solution of elasticity problems
Igor E. Anoufriev, L.V. Petukhov · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1999
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 gi equalsV W21/2((Gamma) ) and A(u,v) is V-elliptic bilinear form. A weak solution of the first elasticity problem is a vector- valued function.