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

Let be a simply connected domain in the x₁-x₂ plane which lies within the strip 0<x₂, is a simple closed piecewise smooth curve. Let l= [(x₁, x₂): (x₁, x₂) and x₁>0], _l= [(x₁x₂): (x₁,x₂) and x₁>1>0].Suppose that a two-dimensional homogeneous isotropic elastic body occupies , that a self-equilibrated stress loading is applied to - l, and that l is stress-free.Knowles [2] and Flavin [6] showed that the elastic energy in _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/ may be obtained where c is a universal constant and is a characteristic dimension of , which is more appropriate than b for general non-striplike domains. In addition, an appropriate decay theorem is obtained for coil-like domains.