An analytical study on the bending of prismatic SMA beams

In this study, an analytical solution is presented for pure bending of shape memory alloy (SMA) beams with symmetric cross section as well as symmetric behavior in tension and compression. To this end, a three-dimensional constitutive equation is reduced to one-dimensional form and employed to study the bending response of SMA beams at high (pseudo-elasticity) and low (shape memory effect) temperatures. An analytical expression for bending stress as well as polynomial approximation for shear stress and deflection are obtained. Derived equations for bending are employed to analyze an SMA beam with rectangular cross section and results are compared with those of the finite element method. The results of this work show good agreement when compared with experimental data and finite element results. Furthermore, the existence of several zero-stress fibers during unloading of SMA beams at low temperature is demonstrated. (paper)