VM27

VM27
Thermal Expansion to Close a Gap

Overview

Reference:

C. O. Harris, Introduction to Stress Analysis, The Macmillan Co., New York, NY, 1959, pg. 58, problem 8.

Analysis Type(s):

Static, Thermal-stress Analysis (ANTYPE = 0)

Element Type(s):

3D Spar (or Truss) Elements (LINK180)

3D Node-to-Node Contact Elements (CONTA178)

Input Listing:

vm27.dat

Test Case

An aluminum-alloy bar is fixed at one end and has a gap δ between its other end and a rigid wall when at ambient temperature T_a. Calculate the stress σ, and the thermal strain ε_Thermal in the bar after it has been heated to temperature T.

Figure 35: Gap Problem Sketch

Material Properties

Geometric Properties

E = 10.5 x 10⁶ psi

α = 12.5 x 10^-6 in/in-°F

= 3 in

δ = 0.002 in

T_a = 70°F

T = 170°F

Analysis Assumptions and Modeling Notes

The problem is solved in 3D using LINK180 and CONTA178 elements. Models are created at arbitrary angles. The gap stiffness is arbitrarily selected at a high value (10 x 10¹⁰ psi) to approximate the rigid wall. The automatic load stepping procedure (AUTOTS,ON) is used.

Results Comparison

		Target	Mechanical APDL	Ratio
3D Analysis	Stress, psi	-6125.	-6124.785	1.000
3D Analysis	Strain_Thermal	0.00125	0.00125	1.000