On Saint-Venant's Principle for an Inhomogeneous Curvilinear Rectangle

A two-dimensional inhomogeneous isotropic elastic material is considered in the arch-like region a ≤ r ≤ b,0 ≤ θ ≤ α, where ( r,θ) denotes plane polar coordinates. It is envisaged that three of the edges r = a, r = b, θ = α are traction-free, while the edge θ = 0 is subjected to an (in-plane) self-equilibrated load. An appropriate energy-like measure E( θ) of the Airy stress function φ in the region between arbitrary θ and θ = α is defined, and it is proved to be positive definite provided that some appropriate assumptions are satisfied by the material and geometric characteristics of the arch-like region. Then, a version of Saint-Venant's Principle for the curvilinear strip is established.