基于有限测点的铝合金板残余应力场重构研究

应力函数法可基于有限测点的实测结果重构出构件的全场残余应力，但其应力函数往往难以确定，且不易通过同一应力函数同时重构出多个残余应力分量的分布. 针对上述不足，发展了一种利用通用应力函数同时重构多个残余应力分量场的方法. 该方法构造双元傅里叶函数作为艾瑞应力函数，使用判定系数确定模型阶数，并根据实测散点值优化确定应力函数中的未知参数. 最后利用模拟三点弯实验的残余应力场验证了该方法的准确性，并将其应用于真实铝合金板的残余应力场重构. 结果表明，该方法能同时重构多个应力分量，且重构残余应力场具有较高的精度. 

Study on Residual Stress Field Reconstruction of Aluminum Alloy Plate Based on Finite Measurements

The whole residual stress field of structural components can be reconstructed based on measured results from a limited number of points by the stress function method, but stress function is usually difficult to determine and it is not easy to reconstruct the distribution of several stress components through one stress function. To overcome these shortcomings, a method was developed to simultaneously reconstruct several residual stress component fields by using a general stress function. In this method, the binary Fourier function was used as the Airy stress function. The order of the model was determined by the determination coefficient, and the unknown parameters in the stress function were optimized according to measured results on some points. Finally, the accuracy of this method was verified by simulated residual stress fields of a three-point bending beam, and it was applied to the reconstruction of residual stress field of a real aluminum alloy plate. The results show that this method can simultaneously reconstruct several stress components with high accuracy.