This paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

本文重点研究了轴向功能梯度形状记忆合金（AFG SMA）梁的力学和马氏体转变行为。考虑到诸如奥氏体弹性模量，马氏体弹性模量，临界相变应力和最大相变应变之类的材料性质沿纵向连续变化。根据简化的线性SMA本构方程和Bernoulli-Euler梁理论，推导了应力，应变，马氏体体积分数以及变形层的变形，高度和长度的控制方程式。采用加勒金加权残差法，求解了挠度的控制微分方程。举个例子，利用所建立的模型，对AFG SMA悬臂梁在末端集中载荷作用下的弯曲行为进行了数值分析。结果表明，SMA发生马氏体相变后，AFG SMA梁的力学和马氏体相变行为很复杂。FG参数对变换区域的力学行为和几何形状的影响是显而易见的，在相关区域的AFG SMA梁的设计和分析中应考虑这些因素。