Abstract
We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain.
Highlights
We study the asymptotic behavior of solutions with finite energy to the displacement problem of linear elastostatics in a three-dimensional exterior Lipschitz domain
The displacement problem of elastostatics in an exterior Lipschitz domain Ω of R3 consists of finding a solution to the equations [1]
(div C[∇u])i = ∂ j (Cijhk ∂k uh ), Lin is the space of second–order tensors and Sym, Skw are the spaces of the symmetric and skew elements of Lin respectively; if E ∈ Lin and v ∈ R3, Ev is the vector with components Eij v j
Summary
The displacement problem of elastostatics in an exterior Lipschitz domain Ω of R3 consists of finding a solution to the equations [1] (div C[∇u])i = ∂ j (Cijhk ∂k uh ), Lin is the space of second–order tensors (linear maps from R3 into itself) and Sym, Skw are the spaces of the symmetric and skew elements of Lin respectively; if E ∈ Lin and v ∈ R3 , Ev is the vector with components Eij v j . Where u is the (unknown) displacement field, û is an (assigned) boundary displacement, B is the unit ball, C ≡ [Cijhk ] is the (assigned) elasticity tensor, i.e., a map from Ω × Lin → Sym, linear on Sym and vanishing in Ω × Skw. We shall assume C to be symmetric, i.e., E · C[ L ] = L · C[ E ]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
