Development of a novel and efficient inverse method for anisotropic material identification based on a complex-variable formulation of Airy stress function is presented. The overall equilibrium and compatibility, as well as the free traction along the boundary of the internal geometric cutouts, are analytically satisfied by means of conformal mapping and analytic continuation. The inverse problem is posed as an optimization problem where the objective functional is the difference between the measured data and its counterpart evaluated using the complex-variable method. Validity of the proposed inverse method is demonstrated by identifying the elastic constants of a loaded perforated orthotropic member from measured data originated in a region adjacent to a traction-free boundary. Both simulated in-plane displacement components that are superimposed with white noise scatter and experimental strain values were used to illustrate the effectiveness of the proposed method. Numerical experiments indicate that the proposed inverse procedure is capable of accurately characterizing material with large variation of initial estimates of the elastic constants. This alleviates the problem of not knowing a priori the values of the elastic constants. The need to use only few measured data close to the hole boundary and without full-knowledge of the distant geometry and boundary conditions are some advantages of the proposed inverse procedure.

提出了一种基于艾里应力函数的复变量公式的用于各向异性材料识别的新型高效逆方法的开发。整体平衡和兼容性，以及沿着内部几何切口边界的自由牵引力，通过保角映射和解析延拓在解析上得到满足。逆问题作为优化问题提出，其中目标函数是测量数据与其使用复变量方法评估的对应数据之间的差异。通过从源自无牵引边界附近区域的测量数据中识别加载的穿孔正交各向异性构件的弹性常数，证明了所提出的逆方法的有效性。与白噪声散射叠加的模拟平面位移分量和实验应变值都用于说明所提出方法的有效性。数值实验表明，所提出的逆过程能够准确地表征弹性常数初始估计值变化很大的材料。这减轻了不知道弹性常数值的先验问题。只需要使用接近孔边界的少量测量数据，而不需要完全了解远处的几何形状和边界条件，这是所提出的逆过程的一些优点。数值实验表明，所提出的逆过程能够准确地表征弹性常数初始估计值变化很大的材料。这减轻了不知道弹性常数值的先验问题。只需要使用接近孔边界的少量测量数据，而不需要完全了解远处的几何形状和边界条件，这是所提出的逆过程的一些优点。数值实验表明，所提出的逆过程能够准确地表征弹性常数初始估计值变化很大的材料。这减轻了不知道弹性常数值的先验问题。只需要使用接近孔边界的少量测量数据，而不需要完全了解远处的几何形状和边界条件，这是所提出的逆过程的一些优点。