VM13

VM13
Cylindrical Shell Under Pressure

Overview

Reference:

S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1955, pg. 45, article 11.

A. C. Ugural, S. K. Fenster, Advanced Strength and Applied Elasticity, Elsevier, 1981.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

2-Node Finite Strain Axisymmetric Shell (SHELL208)

Input Listing:

vm13.dat

Test Case

A long cylindrical pressure vessel of mean diameter d and wall thickness t has closed ends and is subjected to an internal pressure P. Determine the axial stress σ_y and the hoop stress σ_z in the vessel at the midthickness of the wall.

Figure 16: Cylindrical Shell Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.3

t = 1 in

d = 120 in

P = 500 psi

Analysis Assumptions and Modeling Notes

An arbitrary axial length of 10 inches is selected. Nodal coupling is used in the radial direction. An axial force of 5654866.8 lb ((Pπd²)/4) is applied to simulate the closed-end effect.

Results Comparison

	Target[1]	Mechanical APDL	Ratio
Stress_y , psi	15,000.	15,000.[2]	1.000
Stress_z , psi	29,749.	30,000.	1.008

Axial Stress σ_y is calculated (per S. Timoshenko, Strength of Material, Part I, Elementary Theory and Problems) using thin shell theory. Since SHELL208 uses thick shell logic to determine stress variations through the thickness, the hoop stress σ_zis calculated per A. C. Ugural, S. K. Fenster, Advanced Strength and Applied Elasticity.
SX in element solution printout since element X-axis is parallel to global Y-axis.