Thick Walled Cylinders University of Washington（厚壁圆筒华盛顿大学）.pdf

Thick Walled Cylinders Consider a thick walled cylinder with open ends as shown above. It is loaded by internal pressure Pi and external pressure Po as seen below. It has inner radius ri and outer radius r . o P o r o P i r i σθ σ + dσ r r σ σ θ r dr rdθ r Now consider and element at radius r and defined by an angle increment dθand a radial increment dr. By circular symmetry, the stresses σ and σ are functions θ r of r only, not θ and the shear stress on the element must be zero. For an element of unit thickness, radial force equilibrium gives: ( )( ) σ +dσ r +dr dθ σ rdθ+σ dθdr r r r θ Ignoring second order terms gives: σ σ σ