VM20

VM20
Cylindrical Membrane Under Pressure

Overview

Reference:

S. Timoshenko, Strength of Material, Part II, Elementary Theory and Problems, 3rd Edition, D. Van Nostrand Co., Inc., New York, NY, 1956, pg. 121, article 25.

Analysis Type(s):

Static Analysis (ANTYPE = 0)

Element Type(s):

4-Node Finite Strain Shell Elements (SHELL181)

Input Listing:

vm20.dat

Test Case

A long cylindrical membrane container of diameter d and wall thickness t is subjected to a uniform internal pressure P. Determine the axial stress σ₁ and the hoop stress σ₂ in the container. See VM13 for the problem sketch.

Figure 26: Cylindrical Membrane Problem Sketch

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

υ = 0.3

d = 120 in

t = 1 in

P = 500 psi

Analysis Assumptions and Modeling Notes

An arbitrary axial length is selected. Since the problem is axisymmetric, only a one element sector is needed. A small angle Θ = 10° is used for approximating the circular boundary with a straight-sided element. Nodal coupling is used at the boundaries. An axial traction of 15,000 psi is applied to the edge of the element to simulate the closed-end effect. The internal pressure is applied as an equivalent negative pressure on the exterior (face 1) of the element.

Results Comparison

	Target	Mechanical APDL	Ratio
Stress₁ , psi	15,000	15,000	1.000
Stress₂ , psi	29,749	29,886	1.005