A two-dimensional inhomogeneous isotropic elastic material is considered in the arch-like region a <= r <= b, 0 <= theta <= alpha, where (r, theta) denotes plane polar coordinates. It is envisaged that three of the edges r = a, r = b, theta = alpha are traction-free, while the edge theta = 0 is subjected to an (in-plane) self-equilibrated load. An appropriate energy-like measure E(theta) of the Airy stress function phi in the region between arbitrary theta and theta = alpha 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.
On Saint-Venant’s principle for inhomogeneous curvilinear rectangle
IOVANE, Gerardo
2007-01-01
Abstract
A two-dimensional inhomogeneous isotropic elastic material is considered in the arch-like region a <= r <= b, 0 <= theta <= alpha, where (r, theta) denotes plane polar coordinates. It is envisaged that three of the edges r = a, r = b, theta = alpha are traction-free, while the edge theta = 0 is subjected to an (in-plane) self-equilibrated load. An appropriate energy-like measure E(theta) of the Airy stress function phi in the region between arbitrary theta and theta = alpha 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
