基于代理模型的功能梯度梁的材料特性参数反求

针对功能梯度材料参数的反求问题，提出了一种基于代理模型的反求方法。应用有限元软件建立功能梯度梁的波动响应模型，获得模型在激振力作用下的动态位移响应。通过试验设计选取合理的样本点，建立响应面模型代替有限元软件作为程序的正问题求解器，遗传算法作为反问题求解器，用添加不同噪声水平的峰值位移来模拟反求模型的实际输入作为整个算法的输入数据，最终获得材料的体积参数。以实际SiC-C功能梯度梁为算例，分析了单次正弦激振力下，有限元软件获得的动态响应，并根据获得的位移响应应用遗传算法来反求SiC-C梁的体积分数。算例验证了本方法的有效性。基于代理模型的反求方法避免了多次调用正问题求解器，提高了计算效率。 

Surrogate-based inverse technique for material characterization of functionally graded beam

A surrogate-based inverse procedure is presented for characterizing the material property of functionally graded material（FGM）. A forward model was built by the finite element software and the dynamic displacement responses excited by the load was obtained. A response surface model was established based on the responses of the sample points selected by employing design of experiment， the substitute for the finite element software as the forward operator and the genetic algorithm was employed as the inverse operator. The maximums of the displacement responses with different levels of noise were used as the inputs for the whole procedure，and the material volume fraction parameters were finally determined. The dynamic displacement responses excited by the single sin load in an actual SiC C functionally graded beam were applied to determine the volume fractions of the SiC-C beam through the genetic algorithm. The numeric example demonstrates the efficiency of the presented method. The surrogate-based inverse method improves the calculating efficiency by avoiding repetitious forward calculations.