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

2. Shape Memory Alloy Cantilever Beam 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 Background on SMAs

3. Shape Memory Alloy Cantilever Beam Cantilever beam composed of SMA subjected to temperature gradient - both phases present Problem Description F x la MsMs MfMf T la EmEm Ea L 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

4. Shape Memory Alloy Cantilever Beam Mathematical Formulation L1 F M1 L2 F Problem separated into two functions Function 1Function 2 Slope & Deflection of Function 1 used as origin for Function 2

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

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