热-机载荷下形状记忆合金梁的力学模型及其求解

Mechanical Model and Numerical Solution of Shape Memory Alloy Beam under Thermal-mechanical Load

在现有的形状记忆合金(Shape memory alloy,SMA)简化模型的基础上,结合温度与相变临界应力的关系,从应变角度出发,提出一种形式简单、物理意义更加明确且能反应SMA在热-机载荷下力学行为的分段线性模型。基于Bernoulli-Euler梁理论,利用SMA分段线性模型,建立SMA梁非线性弯曲过程中弯矩与曲率关系的力学模型。结合SMA梁力学模型,设计一套简便易行的求解流程,分别对纯弯曲和受均布载荷的简支梁进行数值求解,分析梁截面上应力分布、弯矩与挠度关系、记忆因子的变化等。结果显示建立的SMA分段线性模型能有效描述热-机载荷下SMA的力学行为,可建立简单有效的SMA结构的力学模型,更便于工程应用和理论分析。

Based on the existing piecewise linear model of shape memory alloy(SMA),combined with the relationship between temperature and critical stress of phase transition,a simple piecewise linear model of SMA with clearer physical meaning,which can reveal mechanical behavior of SMA under thermal-mechanical load,are proposed from the perspective of strain.Based on the Bernoulli-Euler beam theory,the mechanical model of the relationship between bending moment and curvature in the nonlinear bending process of SMA beams is established by using the SMA piecewise linear model.Combined with the SMA beam mechanical model,the purely curved beam and simply supported beam with uniform load are numerically solved respectively by a simple solving process.The stress distribution,bending moment and deflection,and memory factor changes are analyzed.The results show that the established SMA piecewise linear model can effectively describe the mechanical behavior of SMA under thermo-mechanical load.The simple and effective mechanical model of SMA structure can be established using the piecewise linear model,which is more convenient for engineering application and theoretical analysis.