扭转轴应力集中的灰色组合模型

用应变梯度片测定构件中沿某个方向的一系列应变值，根据灰色系统建模思想对测试数据进行累加生成处理，以提高数据的确定性，建立一阶单变量灰色模型。为增加预测结果的可靠性，同时考虑孔口应变规律的经验公式，将一阶单变量灰色模型与经验公式相结合建立应力集中处应变的组合预测模型，用以预测应力集中处应变的最大值。作为应用，给出了带台肩和圆孔的扭转试件的应变电测试验和计算结果。实例表明，采用这种方法建立模型来预测应力集中处的最大值，具有所需数据少、精度高等特点，非常适合于用应变梯度片实时确定构件的应力集中系数，进而解决工程的实际问题。

A Grey Combinatorial Model Method for Stress Concentration Factors in Torsion Shafts

In the stress concentration region, a series of strain values were measured with strain gauges. According to the grey modeling method, these testing data were made 1-AGO (acumulated generating operation) to reduce their randomicity and to establish GM(1,1)model.Simultaneously,the experiential expressions of strains near the slit were considered for advancing reliability of the model. Then, a strain model about stress concentration was established by combined the GM(1,1)model and the experiential formula. As examples, the torsion shafts with a hole or a shoulder were tested by strain gauges. After modeling and calculating, the results show that the preceding method to predict the biggest strain requires fewer testing data and is of higher precision. So it is suitable for real-time ascertain of stress concentration factor when grads strain gauge is used.