Lamé thick cylinder in rigid casing

Stress and radial displacement distribution in a thick-walled cylinder under internal pressure with outer surface constrained along its surface normal (rigid casing, ur(b) = 0).

Tolerance:

5%

Problem statement

Geometry

Thick-walled hollow cylinder: inner radius a = 50 mm, outer radius b = 100 mm, length L = 20 mm.

Material

Structural steel: E = 200 GPa, ν = 0.3.

Boundary conditions

Internal pressure p = 10 MPa on inner surface r = a; normal constraint (n·u = 0, roller/casing) on outer surface r = b; axial plane strain (uz = 0) on both end faces z = 0 and z = L.

Measured quantity

Hoop stress σ_θθ across the cylinder wall thickness from r = a to r = b. Headline value is the outer hoop stress σ_θθ(b) = −2.2247 MPa (analytical Lamé), demonstrating stress reversal across wall thickness and zero radial displacement ur(b) = 0 (computed max 1.68e-14 m).

Results comparison

Updated: 2026-08-06 · WebCAE solver