# Saint-Venant's principle in linear two-dimensional elasticity for non-striplike domains

Research paper by Shlomo Breuer, Joseph J. Roseman

Indexed on: 01 Mar '77Published on: 01 Mar '77Published in: Archive for Rational Mechanics and Analysis

#### Abstract

Let ℛ be a simply connected domain in the x1-x2 plane which lies within the strip 0<x2<b, whose boundary, ∂ℛ, is a simple closed piecewise smooth curve. Let l= [(x1, x2): (x1, x2) ε∂ℛ and x1>0], ℛl= [(x1x2): (x1,x2) εℛ and x1>1>0].Suppose that a two-dimensional homogeneous isotropic elastic body occupies ℛ, that a self-equilibrated stress loading is applied to ∂ℛ - l, and that l is stress-free.Knowles [2] and Flavin [6] showed that the elastic energy in ℛldecays exponentially with respect to l with an exponential decay constant of the form k/b, where k is a universal constant. It is shown here that a decay constant of the form c/λ may be obtained where c is a universal constant and λ is a “characteristic dimension” of ℛ, which is more appropriate than b for general “non-striplike” domains. In addition, an appropriate decay theorem is obtained for “coil-like” domains.