Thick Shell

ANSYS, COSMOS, ALGOR, etc. should do this nicely. Or, you could use Roark's Formulas for Stress and Strain book.

To find the strain, you have to determine the various stresses arising.

Cylindrical shapes are subjected to Longitudinal, Hoop and Radial Stresses, where Spherical shapes are subjected to Longitudinal and Radial stresses only.

In reality, the hoop pressure stress varies thru the thickness of the pipe. This stress variation is defined by Lame's equations which apply equally for thin and thick walled tubes and spheres :

σ_hoop = (P r_i² + P r_i² r_o² / r²) / (r_o² – r_i²)

σ_longitudinal = P r_i² / (r_o² – r_i²)

σ_radial = (P r_i² - P r_i² r_o² / r²) / (r_o² – r_i²)

where, r = position through the thickness, r_i = inside radius, r_o = outside radius, P = pressure

Notes.

1. In cylindrical shells, pipes and tubes, the hope stress (circumferential stress which affecting at longitudinal joint) is the most severe stress, and used in design formulas.

2. In spherical and semi-spherical shells, the longitudinal stress (circumferential joints) is the most severe stress, and used in design formulas.