A Nonlinear Analysis of the Mechanical Behavior of Functionally Graded Shape-Memory Alloy Beams

The nonlinear mechanical behavior of functionally graded shape-memory alloy beams under impure bending conditions is analyzed using the beam bending theory and the stress–strain relationship of shape memory alloy materials. The volume fraction of the alloy is assumed to vary in the beam thickness direction according to a power function. The stress distribution in its cross-section, in each phase transformation stage, is derived by introducing a tension-compression asymmetry coefficient, which expresses this asymmetry on the tensioncompression sides of the beams. The displacement of their neutral axis, the curvature of cross-section, and the variation of the phase boundary along their axial direction were calculated by solving the equilibrium equation. Results showed that the influence of a change in the power index on the tension-compression asymmetry was much greater than an alteration of the tension-compression asymmetry coefficient. The displacement of neutral axis and the curvature were nonlinearly negatively related to the power index. With increasing power index, the phase transformation boundary moved closer to the mid-span section. The displacement of neutral axis of the same cross-section was nonlinearly positively related to the tension-compression asymmetry coefficient, but the curvature was nonlinearly negatively related to it. The phase boundary on compressive side moved closer to the mid-span section as the tension-compression asymmetry coefficient increased. The analysis of computation results can be used as a reference in the design and application of such materials.