Rapid change of stresses in thickness direction in long orthotropic tube under internal pressure and axial load

Abstract

Exact solution for long orthotropic tube under internal pressure and axial load suggests the existence of very dangerous combinations of elastic properties. We demonstrate that such elastic properties can be thermodynamically stable. Close to a dangerous combination, stress components change very rapidly in radial direction, resulting in huge peak stresses exceeding the membrane theory predictions by several orders of magnitude, even for relatively thin-walled tubes. Another manifestation of this effect is extreme sensitivity of peak stresses to variations in elastic properties. Away from the critical condition the anomaly in stress distribution disappears and this can be the key point in the design of related structures. The rapid change of stresses in thickness direction is attributed to the auxetic property (negative Poisson’s ratio) of highly anisotropic material of the tube. As an example, we consider the filament wound tube with closed ends under internal pressure and demonstrate that, for highly anisotropic fiber-reinforced plastic, winding with angle close to 45° is potentially dangerous.