VM7

VM7
Plastic Compression of a Pipe Assembly

Overview

Reference:

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

Analysis Type(s):

Static, Plastic Analysis (ANTYPE = 0)

Element Type(s):

Plastic Straight Pipe Element (PIPE288)

4-Node Finite Strain Shell (SHELL181)

3D Structural Solid Elements (SOLID185)

Input Listing:

vm7.dat

Test Case

Two coaxial tubes, the inner one of 1020 CR steel and cross-sectional area A_s, and the outer one of 2024-T4 aluminum alloy and of area A_a, 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.

Figure 9: Pipe Assembly Problem Sketch

Figure 10: Pipe Assembly Finite Element Models

Material Properties

Geometric Properties

E_s = 26,875,000 psi

σ_(yp) _s = 86,000 psi

E_a = 11,000,000 psi

σ_(yp) _a = 55,000 psi

υ = 0.3

= 10 in

A_s = 7 in²

A_a = 12 in²

1st Load Step: δ = 0.032 in

2nd Load Step: δ = 0.050 in

3rd Load Step: δ = 0.100 in

Analysis Assumptions and Modeling Notes

The following tube dimensions, which provide the desired cross-sectional areas, are arbitrarily chosen. Inner (steel) tube: inside radius = 1.9781692 in., wall thickness = 0.5 in. Outer (aluminum) tube: inside radius = 3.5697185 in., wall thickness = 0.5 in.

The problem can be solved in three ways:

using PIPE288 - the plastic straight pipe element
using SOLID185 - the 3D structural solid element
using SHELL181 - the 4-Node Finite Strain Shell

In the SOLID185 and SHELL181 cases, since the problem is axisymmetric, only a one element Θ-sector is modeled. A small angle Θ = 6° is arbitrarily chosen to reasonably approximate the circular boundary with straight sided elements. The nodes at the boundaries have the UX (radial) degree of freedom coupled. In the SHELL181 model, the nodes at the boundaries additionally have the ROTY degree of freedom coupled.

Results Comparison

		Target	Mechanical APDL [1]	Ratio
PIPE288	Load, lb for Deflection = 0.032 in	1,024,400	1,024,400	1.00
	Load, lb for Deflection = 0.05 in	1,262,000	1,262,000	1.00
	Load, lb for Deflection = 0.1 in	1,262,000	1,262,000	1.00

From POST1 FSUM of bottom nodal forces (ΣFZ) for PIPE288 model.

		Target	Mechanical APDL [1]	Ratio
SOLID185	Load, lb for Deflection = 0.032 in	1,024,400	1,022,529	0.998
	Load, lb for Deflection = 0.05 in	1,262,000	1,259,695	0.998
	Load, lb for Deflection = 0.1 in	1,262,000	1,259,695	0.998
SHELL181	Load, lb for Deflection = 0.032 in	1,024,400	1,023,932	1.000
	Load, lb for Deflection = 0.05 in	1,262,000	1,261,654	1.000
	Load, lb for Deflection = 0.1 in	1,262,000	1,261,423	1.000

From POST1 FSUM of bottom nodal forces (ΣFZ) X 360°/6°(Identified as parameter "LOAD") for SOLID185 and SHELL181 models.