Exact Solution for Bending of Shape Memory Alloy Beams

Abstract

Bending is an attractive mode of operation and application of shape memory alloys (SMA). To date numerical methods, such as the finite element method, have been used to model the coupled thermo-mechanical behavior of these alloys. In this article, an analytical approach is developed to calculate the exact solution of SMA beams deflection due to an external force. The approach is based on the assumption of linear distribution of strain along the height of a beam cross section. The approach is validated by comparing the results with the existing plastic solution and experimental data.

Keywords:

• shape memory alloys
• bending
• nonlinear stress
• Euler–Bernoulli beam
• radius of curvature