VM-WB-MECH-047

VM-WB-MECH-047
Plastic Compression of a Pipe Assembly

Overview

Reference:

Crandall, S. H., & Dahl, N. C. (1959). An Introduction to the Mechanics of Solids (p. 180, ex. 5.1). New York, NY: McGraw-Hill Book Co., Inc.

Solver(s):

Ansys Mechanical

Analysis Type(s): Plastic Structural Analysis
Element Type(s): Axisymmetric

Test Case

Two coaxial tubes, the inner one of 1020 CR steel and cross-sectional area As, and the outer one of 2024-T4 aluminum alloy and of area Aa, are compressed between heavy, flat end plates, as shown below. Determine the load-deflection curve of the assembly as it is compressed into the plastic region by an axial displacement. Assume that the end plates are so stiff that both tubes are shortened by exactly the same amount.

This test case is also solved using LS-DYNA. See VM-LSDYNA-WB-008.

Figure 59: Schematic

Schematic

Material PropertiesGeometric PropertiesLoading
VMSIM047_CR_steel:
Es = 26,875,000 psi
σ(yp)s = 86,000 psi
VMSIM047_T4_aluminum alloy:
Ea = 11,000,000 psi
σ(yp)a = 55,000 psi
ν = 0.3
= 10 in
Steel:
Inside radius = 1.9781692 in
Wall thickness = 0.5 in
Aluminum:
Inside radius = 3.5697185 in
Wall thickness = 0.5 in
1st Load step: δ = -0.032 in
2nd Load step: δ = -0.05 in
3rd Load step: δ = -0.10 in

Analysis

Because the geometry and loading are symmetric about the y-axis, the above problem can be analyzed as an axisymmetric problem.

Results Comparison

ResultsTargetMechanicalError (%)
Load, lb for Deflection @ 0.032 in1.0244 x 106 10339000.927
Load, lb for Deflection @ 0.05 in1.262 x 106 12627000.055
Load, lb for Deflection @ 0.1 in1.262 x 106 12672000.412