Due to the many applications of shape memory alloys (SMAs) to make the structures more intelligent, these materials are getting great attention of researchers. Meanwhile, the nonlinear dynamic analysis of curved beams made of SMAs has not been investigated so far. Therefore, this work focuses on a nonlinear dynamic analysis of SMA curved beams under transverse impulse loading taking into account the pseudo-elastic behavior of SMAs. It is worth noting that both material and geometrical nonlinearities of the SMA curved beam are considered in this study. In order to model the nonlinear behavior of SMAs, the Lagoudas model is employed and for the mathematical modeling of the curved beam the Timoshenko beam theory under the assumption of von Karman nonlinear strains is used. Then, by employing the Hamilton principle, the governing equations of the structure are extracted, while the nonlinear kinematic equations of SMAs are coupled with the governing equations of the curved beam. To solve these coupled nonlinear equations, the numerical technique of differential quadrature method (DQM) along with Newmark's time integration scheme is employed. In this regard, the return mapping algorithm in conjunction with the Newton–Raphson method is employed to solve the nonlinear terms of equations. The quick convergence and high accuracy of the proposed formulation are achieved by the analysis of different examples. After that, some novel results are presented by investigating the influence of different types of boundary conditions, radius of curvature, angle of curvature and thickness of beam on the transient damped response, hysteresis loops and also martensite phase transformation of the SMA curved beams.

中文翻译：

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脉冲载荷作用下 SMA Timoshenko 曲梁阻尼振荡的非线性数值评估


由于形状记忆合金 （SMA） 的许多应用使结构更加智能，这些材料受到了研究人员的高度关注。同时，迄今为止尚未研究由 SMA 制成的弯曲梁的非线性动力学分析。因此，考虑到 SMA 的拟弹性行为，这项工作的重点是在横向脉冲载荷下 SMA 弯曲梁的非线性动力学分析。值得注意的是，本研究考虑了 SMA 曲梁的材料和几何非线性。为了模拟 SMA 的非线性行为，采用了 Lagoudas 模型，对于弯曲梁的数学建模，使用了 von Karman 非线性应变假设下的 Timoshenko 梁理论。然后，利用 Hamilton 原理提取结构的控制方程，同时将 SMA 的非线性运动方程与曲梁的控制方程耦合。为了求解这些耦合的非线性方程，采用了微分正交法 （DQM） 的数值技术以及 Newmark 的时间积分方案。在这方面，返回映射算法与 Newton-Raphson 方法结合使用来求解方程的非线性项。通过对不同实例的分析，实现了所提公式的快速收敛性和高精度。之后，通过研究不同类型的边界条件、曲率半径、曲率角和光束厚度对 SMA 弯曲梁的瞬态阻尼响应、磁滞回线以及马氏体相变的影响，提出了一些新颖的结果。