Free vibration analysis and design optimization of SMA/Graphite/Epoxy composite shells in thermal environments

Abstract Composite shells, which are being widely used in engineering applications, are often under thermal loads. Thermal loads usually bring thermal stresses in the structure which can significantly affect its static and dynamic behaviors. One of the possible solutions for this matter is embedding Shape Memory Alloy (SMA) wires into the structure. In the present study, thermal buckling and free vibration of laminated composite cylindrical shells reinforced by SMA wires are analyzed. Brinson model is implemented to predict the thermo-mechanical behavior of SMA wires. The natural frequencies and buckling temperatures of the structure are obtained by employing Generalized Differential Quadrature (GDQ) method. GDQ is a powerful numerical approach which can solve partial differential equations. A comparative study is carried out to show the accuracy and efficiency of the applied numerical method for both free vibration and buckling analysis of composite shells in thermal environment. A parametric study is also provided to indicate the effects of like SMA volume fraction, dependency of material properties on temperature, lay-up orientation, and pre-strain of SMA wires on the natural frequency and buckling of Shape Memory Alloy Hybrid Composite (SMAHC) cylindrical shells. Results represent the fact that SMAs can play a significant role in thermal vibration of composite shells. The second goal of present work is optimization of SMAHC cylindrical shells in order to maximize the fundamental frequency parameter at a certain temperature. To this end, an eight-layer composite shell with four SMA-reinforced layers is considered for optimization. The primary optimization variables are the values of SMA angles in the four layers. Since the optimization process is complicated and time consuming, Genetic Algorithm (GA) is performed to obtain the orientations of SMA layers to maximize the first natural frequency of structure. The optimization results show that using an optimum stacking sequence for SMAHC shells can increase the fundamental frequency of the structure by a considerable amount.

摘要：复合壳体在工程应用中被广泛采用，且常承受热载荷作用。热载荷通常会在结构内部产生热应力，显著影响其静动态力学性能。针对该问题的可行解决方案之一，是在结构中嵌入形状记忆合金（Shape Memory Alloy，SMA）丝。本研究针对SMA丝增强层合复合圆柱壳体的热屈曲与自由振动开展分析：采用布里森模型（Brinson model）预测SMA丝的热机械性能，通过广义微分求积法（Generalized Differential Quadrature，GDQ）求解得到结构的固有频率与屈曲温度——GDQ是一种可求解偏微分方程的高效数值方法。本文通过对比研究验证了该数值方法在热环境下复合壳体自由振动与屈曲分析中的准确性与高效性；同时开展参数化研究，考察了SMA体积分数、材料性能随温度的变化规律、铺层角度以及SMA丝预应变等因素对形状记忆合金混杂复合圆柱壳体（Shape Memory Alloy Hybrid Composite，SMAHC）固有频率与屈曲行为的影响。研究结果表明，SMA对复合壳体的热振动特性具有显著调控作用。本研究的第二项目标是对SMAHC圆柱壳体进行优化，以实现特定温度下基频参数的最大化。为此，本文选取含四层SMA增强层的八层层合复合壳体作为优化对象，以四层SMA铺层的角度作为主要优化变量。鉴于优化过程复杂且耗时，本文采用遗传算法（Genetic Algorithm，GA）求解最优SMA铺层角度，以最大化结构的一阶固有频率。优化结果显示，为SMAHC壳体采用最优铺层顺序，可显著提升结构的基频。