VM174

VM174
Bimetallic Beam Under Thermal Load

Overview

Reference:

B. A. Boley, J. H. Weiner, Theory of Thermal Stress, R. E. Krieger Publishing Co, Malabar, FL, 1985, pg. 429.

Analysis Type(s):

Coupled field Analysis (ANTYPE = 0)

Element Type(s):

2D Coupled-Field Solid Elements (PLANE13) (Archived)

2D 8-Node Coupled-Field Solid Elements (PLANE223)

Input Listing:

vm174.dat

Test Case

A bimetallic beam consists of two materials with different coefficients of thermal expansion, α₁ and α₂, and is initially at a reference temperature of 0°F. The beam is simply supported and a uniform temperature is applied to both surfaces. The beam is expected to undergo a large lateral deflection. Determine the midspan deflection after heating and verify the temperature T at the material interface.

Figure 252: Bimetallic Beam Problem Sketch

Material Properties

Geometric Properties

For each strip:

k₁ = k₂ = 5 Btu/hr-in-°F

For material 1:

E₁ = 10 x 10⁶ psi

α₁ = 14.5 x 10^-6 in/in°F

For material 2:

E₂ = 10 x 10⁶ psi

α₂ = 2.5 x 10^-6 in/in°F

L = 5 in

t = 0.1 in

T_top = 400.0°F

T_bot = 400.0°F

Analysis Assumptions and Modeling Notes

The problem involves a coupled thermal-stress analysis with large deflections and thus requires an iterative solution. Since the problem is symmetric, only one-half of the beam is modeled. The AZ degree of freedom is not required in this analysis and is excluded from the matrix formulation by not specifying any magnetic material properties. A convergence criteria for force is specified with a tight tolerance to converge the large deflection behavior.

Results Comparison

	Target	Mechanical APDL	Ratio
PLANE13
y, in	0.900	0.888	0.987
T, °F	400.0	400.0	1.000
PLANE223
y, in	0.900	0.889	0.987
T, °F	400.0	400.0	1.000

Figure 253: Bimetallic Beam Under Thermal Load