Stress Problems on Pseudo-Elastic Body. (Cylinder and Sphere)

This paper treats with the comparison of rigorous and approximate solutions of stresses on the hollow thick cylinder and sphere of cast iron under external or internal hydraulic pressure. Poisson's ratios of 0 and 1/2 for the cylinder and 0 and 1/3 for the sphere are taken into computation of the rigorous solution. The approximate solution is independent of this ratio. The former is only applicable in case of same sign of two different stresses-radial and tangential, and besides does not follow with the superposition law of stress, whereas the latter is free from such restricts. The most suitable stress expression must be adopted by preliminary numerical computations on these solutions. The final conclusion is as follows : --The effect of Poisson's ratio on stress values is practically a little and the twice superposed values of stresses by rigorous solution are not reliable for the problem, subject simultaneously to external and internal pressures. The tangential stress by approximate solution gives generally an inferior result, nevertheless the radial one a good result.