Shape Memory Alloy Cantilever Beam

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Shape Memory Alloy Cantilever Beam

• Mike Hilldoerfer
• Numerical Analysis for Engineers
• April 10, 2001

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Shape Memory Alloy Cantilever Beam
Background on SMAs

• Metals that possess the ability to remember
  their original size or shape
• Contain a characteristic phase transformation
  temperature dependent upon metallurgical content
• Elastic Modulus different for the 2 phases

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Shape Memory Alloy Cantilever Beam
Problem Description

• Cantilever beam composed of SMA subjected to
  temperature gradient - both phases present

F
Beam loaded at its free end Temperature gradient
crosses phase transformation temperature Results
in beam that is 1/2 Martensite, 1/2
Austenite ---Modulus varies between phases
x
L
T
Ms
Mf
l
a
Ea
Em
l
a
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Shape Memory Alloy Cantilever Beam
Mathematical Formulation
Problem separated into two functions
Function 1
Function 2
F
F
M1
L1
L2
Slope Deflection of Function 1 used as origin
for Function 2
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Shape Memory Alloy Cantilever Beam
Numerical Approaches Results

• Simpsons Method and Adaptive Quadrature Used
• Baselineisothermal, constant modulus
• SMA with temperature gradient, varied modulus

SMA with temp
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Shape Memory Alloy Cantilever Beam
Error Analysis Conclusions
SMA Exposed to Temp Gradient
All numerical solutions accurate within 0.1
Both numerical methods results the same
FEA validated solutions

• Solution makes sense
• Problem can be expanded to include plastic
  deformation and strain recovery once heated above
  transition temperature
• Beam can be developed into an actuator system