中文摘要：

形状记忆合金（Shape memory alloy,SMA）梁作为一种新型智能元件,在工程领域的应用日益广泛。基于实测的形状记忆合金材料应力-应变关系曲线及梁的大变形理论,同时考虑SMA材料拉压力学性能的不对称性及简支端移动等因素,建立形状记忆合金梁非线性弯曲变形的控制方程,并采用打靶法、辛普森数值积分等方法对方程进行数值求解。通过梁在不同载荷条件下的挠曲线以及最大挠度—弯矩曲线,分析材料非线性、几何非线性及简支端移动3个因素对SMA超弹性梁弯曲变形的影响规律。结果表明：梁中性层位置随弯矩变化;弯矩较小时,材料性能是线性的,几何非线性及简支端移动对梁的弯曲变形几乎不产生影响;弯矩较大时,材料性能是非线性的,几何非线性及简支端移动对梁的弯曲变形产生明显影响。

英文摘要：

As a new type of intelligent elements,the shape memory alloy（SMA） beam are applied widely in the engineering field.Based on experimental stress-strain curves of superelastic SMA and the large deformation theory of beams,considering the different properties between tension and compression and the end-moving,the nonlinear bending deformation equations of SMA beam are established.Meanwhile the shooting method and Simpson＇s numerical integral method are adopted.Through the deflection lines under different load condition and the maximum deflection-bending moment curve,the effects of material nonlinearity,geometric nonlinearity and the end-moving on bending deformation of SMA beam are investigated.The results show that the neutral layer of beam changes with bending moment.If the bending moment is small,the material property is linear,the geometry nonlinear and the end-moving almost have no effect on deflection deformation of beam.If the bending moment is higher,the material property is nonlinear,the geometry nonlinear and the end-moving have noticeable effect on deflection deformation of beam.