VM-WB-MECH-072

VM-WB-MECH-072
Thermal Stresses in a Long Cylinder

Overview

Reference:	Timoshenko, S. (1956). Strength of Material, Part II: Elementary Theory and Problems (3rd ed., p. 234, problem 1). New York, NY: D. Van Nostrand Co, Inc.
Solver(s):	Ansys Mechanical
Analysis Type(s):	Thermal Stress Analysis
Element Type(s):	2-D Thermal Solid Elements

Test Case

A long thick-walled cylinder is maintained at a temperature T_i on the inner surface and T_o on the outer surface. Determine the temperature distribution through the wall thickness. Also determine the axial stress σ_a and the tangential (hoop) stress σ_t at the inner and outer surfaces Edge sizing is used for all edges and edge behavior is defined as hard.

Figure 96: Schematic

Material Properties

Geometric Properties

E = 30 x 10⁶ psi

α = 1.435 x 10^-5/°F

ν = 0.3

k = 8.333 x 10^-4 Btu/s-in-°F

a = 0.1875 in

b = 0.625 in

T_i = -1 °F

T_o = 0 °F

Analysis Assumptions and Modeling Notes for Ansys Mechanical

Because of the symmetry in loading conditions and in the geometry, this problem is solved as an axisymmetric problem in Ansys Mechanical. The axial length is arbitrary and it is taken has 0.1 in. Nodal coupling is used in the static stress analysis. Model is used for the thermal and stress solutions.

Figure 97: Schematic in Ansys Mechanical

Results Comparison for Ansys Mechanical

Thermal Analysis	Target	Mechanical	Error (%)
T,°F (at X = 0.1875 in)	-1	-1	0
T,°F (at X = 0.2788 in)	-0.67037	-0.67057	0.0298
T,°F (at X = 0.625 in)	0	0	0

Static Analysis	Target	Mechanical	Error (%)
Stress_a, psi (at X = 0.1875 in)	420.42	416.05	-1.039
Stress_t, psi (at X = 0.1875 in)	420.42	405.43	-3.565
Stress_a, psi (at X = 0.625 in)	-194.58	-195.09	0.262
Stress_t, psi (at X = 0.625 in)	-194.58	-195.07	0.252