TY - JOUR
T1 - Pressuring, shearing, torsion and extension of a circular tube or bar of cylindrically anisotropic material
JF - Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
SP - 2397
LP - 2421
M3 - 10.1098/rspa.1996.0129
VL - 452
IS - 1954
AU -
Y1 - 1996/11/08
UR - http://rspa.royalsocietypublishing.org/content/452/1954/2397.abstract
N2 - One of the novel features of the present paper is that we have written the equation of equilibrium and the stress-strain law of an inhomogeneous anisotropic linear elastic material in a compact form for cylindrical coordinate system using matrix notation. For a two-dimensional deformation the result resembles Stroh’s sextic formalism in a rectangular coordinate system. We then consider the material to be cylindrically anisotropic. It means that the elastic stiffnesses referred to a cylindrical coordinate system are constants. The problem of a circular tube subjected to a uniform normal stress and shearing stresses at the inner and outer surfaces of the tube is studied. Also studied are the axial extension and torsion of the tube. Unlike isotropic materials for which the applied normal stress (or shear stress) induces only the normal (or shear) stress, all three displacement components and most of the six stress components are nonzero for general anisotropic materials. This is particularly interesting for the uniform axial extension of the tube. For an isotropic material the stress σ33 is the only non-zero and uniform stress inside the tube. For a cylindrically anisotropic material the stresses σrr, σθθ, and σθ3 are also non-zero. Moreover, they depend on r and are not uniform. A solid cylinder or a cylinder with a pin hole is a special case of a tube. It is shown that, for the loads mentioned above including the axial extension, the stress may be unbounded at the pinhole.
ER -