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

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], ℛ_l= [(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 ℛ_ldecays 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.