扭转问题中界面附近的边界层

Boundary layers near interfaces under torsion

基于经典的弹性理论分析 ,在剪切载荷作用下 ,异质材料的界面处存在转角的突变。根据偶应力理论 ,这一突变将导致偶应力趋于无穷大 ,显然这是不合理的结论。利用偶应力理论分析了含有界面的圆柱体的扭转问题 ,并由摄动方法给出了位移、转角和应力场的渐近解。在此基础上 ,分析了转动梯度对异质材料界面和固定边界性质的影响。分析结果表明 ,在材料界面和固定边界附近 ,存在一组边界效应解 ,它对经典的弹性理论解有可观的修正 ,修正的大小与界面两侧材料的性质有关。

Based on the classical elastic theory, the rotation angle on an interface between two mismatched materials is discontinuous when a shear stress is applied. In the light of the couple stress theory, this discontinuity would yield an infinite couple stress. To overcome this physically illogic conclusion, the couple stress theory is used to analyze the torsion problem of a cylinder with an interface. The fields of displacements, rotation angles, stresses, and couple stresses are given by using the perturbation method. Thereby, the effects of rotation gradients on the interface of heterogeneous materials and the property of fixed boundaries are analyzed. The results show that there are a group of boundary layer solutions near the interface or the fixed boundary, which have important adjustment to the results of the classical elastic theory depending on the properties of the materials besides the interface.