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# Shape Memory Alloy Cantilever Beam

Shape Memory Alloy Cantilever Beam. Mike Hilldoerfer Numerical Analysis for Engineers April 10, 2001. Shape Memory Alloy Cantilever Beam. Background on SMAs. Metals that possess the ability to ‘remember’ their original size or shape

## Shape Memory Alloy Cantilever Beam

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1. Shape Memory Alloy Cantilever Beam Mike Hilldoerfer Numerical Analysis for Engineers April 10, 2001

2. 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

3. 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 a l Ea Em a l

4. 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

5. Shape Memory Alloy Cantilever Beam Numerical Approaches & Results • Simpson’s Method and Adaptive Quadrature Used • Baseline…isothermal, constant modulus • SMA with temperature gradient, varied modulus SMA with temp

6. Shape Memory Alloy Cantilever Beam Error Analysis & Conclusions SMA Exposed to Temp Gradient All numerical solutions accurate within 0.1% • 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 Both numerical method’s results the same FEA validated solutions

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