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