EFFECTS OF CURVILINEAR ANISOTROPY ON RADIALLY SYMMETRICAL STRESSES INANISOTROPIC LINEARLY ELASTIC SOLIDS

It has been known for some time that certain radial anisotropies in so me linear elasticity problems can give rise to stress singularities wh ich are absent in the corresponding isotropic problems. Recently relat ed issues were examined by other authors in the context of plane strai n axisymmetric deformations of a hollow circular cylindrically anisotr opic linearly elastic cylinder under uniform external pressure, an ani sotropic analog of the classic isotropic Lame problem. In the isotropi c case, as the external radius increases, the stresses rapidly approac h those for a traction-free cavity in an infinite medium under remotel y applied uniform compression. However, it has been shown that this do es nor occur when the cylinder is even slightly anisotropic. In this p aper, we provide further elaboration on these issues. For the external ly pressurized hollow cylinder (or disk), it is shown that for radiall y orthotropic materials, the maximum hoop stress occurs always on the inner boundary (as in the isotropic case) but that the stress concentr ation factor is infinite. For circumferentially orthotropic materials, if the tube is sufficiently thin, the maximum hoop stress always occu rs on the inner boundary whereas for sufficiently thick tubes, the max imum hoop stress occurs at the outer boundary. For the case of an inte rnally pressurized tube, the anisotropic problem does not give rise to such radical differences in stress behavior from the isotropic proble m. Such differences do, however, arise in the problem of an anisotropi c disk, in plane stress, rotating at a constant angular velocity about its center, as well as in the three-dimensional problem governing rad ially symmetric deformations of anisotropic externally pressurized hol low spheres. The anisotropies of concern here do arise in technologica l applications such as the processing of fiber composites as well as t he casting of metals.