Anti-plane shear deformations of anisotropic sandwich structures: End effects

Abstract

Saint-Venant decay lengths for self-equilibrated edge loads in symmetric sandwich structures are examined in the context of anti-plane shear for linear anisotropic elasticity. The most general anisotropy consistent with a state of anti-plane shear is considered. Anti-plane or longitudinal shear deformations are one of the simplest classes of deformations in solid mechanics. The resulting deformations are completely characterized by a single out-of-plane displacement that depends only on the in-plane coordinates. In linear elasticity, Saint-Venant's principle is used to show that self-equilibrated loads generate local stress effects that decay away from the loaded end of a structure. For homogeneous isotropic linear elastic materials this is well-documented. Selfequilibrated loads area class of load distributions that are statically equivalent to zero, i.e., have zero resultant force and moment. When Saint-Venant's principle is valid, pointwise boundary conditions can be replaced by more tractable resultant conditions. It is shown in the present study that material inhomogeneity and anisotropy significantly affects the practical application of SaintVenant's principle to sandwich structures.