Abstract: In order to grasp the phase transformation mechanical behaviour of shape memory alloy beam with variable cross section during bending deformation, based on the bending deformation theory, the non-linear control equations of shape memory alloy beam with variable cross section was derived by combined with constitutive relationship of shape memory alloy,  the phase transformation process of variable cross section beam was analysed by using a step-by-step method,  the effects of mechanical load, the tension-compression asymmetry coefficient and the variable cross section coefficients on neutral axis displacement, 
curvature and phase boundary were studied and compared them with the finite element results. The results show that the effect of the variable cross section coefficient on the phase boundary and curvature is more obvious, the larger its value, the smaller the maximum value of neutral axis displacement, and the position of each phase boundary is further away from the section edge. The effects of the tension-compression asymmetry coefficient on the maximum displacement of the neutral axis is greater than that of load and variable cross section coefficient, but it has the smallest effect on the position of the cross section where the maximum value occurs. The tension-compression asymmetry coefficient has a greater effect on the phase boundary of compression side than on the tension side. The larger the tension-compression asymmetry coefficient, the more likely the phase transformation occurs on the compression side of the cross section.

Key words: shape memory alloy, finite element method, phase boundary, variable cross section beam