Overview

Test Case

A long thick-walled cylinder is subjected to an internal pressure p (with no end cap load). Determine the radial stress, σ_r, and the tangential (hoop) stress, σ_t, at locations near the inner and outer surfaces of the cylinder for a pressure, p_el, just below the yield strength of the material, a fully elastic material condition.

Figure 51: Thick-Walled Cylinder Problem Sketch

Analysis Assumptions and Modeling Notes

The theory available for this problem is based on the Tresca (maximum shear) yield criterion while Mechanical APDL uses the von Mises yield criterion. The applied p_ult pressure is calculated from the Tresca theory by using . This procedure is sufficient to calculate approximate loads but the resulting nonlinear stress components should not be compared directly.

The problem is solved first using axisymmetric solid elements (PLANE182) and then using 3D solid elements (SOLID185). Since the problem is axisymmetric, only a small sector (5°) is modeled with SOLID185. In order to ensure constant axial strain (implied by the "long" cylinder definition), nodal coupling is used with PLANE182 and SOLID185. To illustrate the use of surface effect elements, the internal pressure P is applied using 2D structural surface effect elements (SURF153) in the first analysis, whereas 3D structural surface effect elements (SURF154) are used in the second analysis. Results are obtained from the solution phase and from the element centroid data.

Results Comparison