END EFFECTS FOR ANTIPLANE SHEAR DEFORMATIONS OF SANDWICH STRUCTURES

The purpose of this research is to further investigate the effects of material inhomogeneity and the combined effects of material inhomogene ity and anisotropy on the decay of Saint-Venant end effects. Saint-Ven ant decay rates for self-equilibrated edge loads in symmetric sandwich structures are examined in the context of anti-plane shear for linear anisotropic elasticity. The problem is governed by a second-order, li near, elliptic, partial differential equation with discontinuous coeff icients. The most general anisotropy consistent with a state of anti-p lane shear is considered, as well as a variety of boundary conditions. Anti-plane or longitudinal shear deformations are one of the simplest classes of deformations in solid mechanics. The resulting deformation s are completely characterized by a single out-of-plane displacement w hich depends only on the in-plane coordinates. They can be thought of as complementary deformations to those of plane elasticity. While thes e deformations have received little attention compared with the plane problems of linear elasticity, they have recently been investigated fo r anisotropic and inhomogeneous linear elasticity. In the context of l inear elasticity, Saint-Venant's principle is used to show that self-e quilibrated loads generate local stress effects that quickly decay awa y from the loaded end of a structure. For homogeneous isotropic linear elastic materials this is well-documented. Self-equilibrated loads ar e a class of load distributions that are statically equivalent to zero , i.e., have zero resultant force and moment. When Saint-Venant's prin ciple is valid, pointwise boundary conditions can be replaced by more tractable resultant conditions. It is shown in the present study that material inhomogeneity significantly affects the practical application of Saint-Venant's principle to sandwich structures.