铆接界面端三维奇异性应力场的研究

针对铆接结构的特点，应用特征函数扩展技术分析柱坐标下接触界面端的应力奇异性问题。建立了柱坐标下圆柱体端面接触边缘附近的三维渐近位移场和应力场渐近表达式，并根据铆钉/被铆接件接触界面端的位移和应力边界条件，建立一个非线性特征方程组。据此方程组可求解界面端邻域的应力奇异性指数、位移和应力角分布函数的数值解。通过与有限元方法计算结果相对比，验证了该方法的有效性。分析了平头、沉头以及半圆头铆钉构成的铆接结构的应力奇异性问题，考察了铆钉材料、几何形式和摩擦系数对接触界面端应力奇异性指数和应力场角分布的影响。

RESEARCH ON 3-D SINGULAR STRESS FIELDS NEAR CONTACT BOUNDARIES OF RIVETED ASSEMBLIES

Based on the structural features of rivets, an eigenfunction expansion approach is used to analyze the stress singularities in the neighborhood of contact interfaces in cylindrical coordinates. The expressions of the three-dimensional asymptotic stress and displacement fields in the vicinity of the circumferential line are established. A group of non-linear characteristic equations are established under various boundary conditions of displacement and stresses of an assembly with a rivet in a bi-layer plate, based on which the orders of stress singularity, displacement and stress angular variation functions are determined. In the benchmark example, the results show that the eigenfunction expansion approach is valid for estimating the order of stress singularity in the cylindrical coordinates by comparing with the finite element method. In the numerical examples, the stress singularities in three-dimensional contact boundaries of riveted assemblies with flat, countersunk and universal head rivets are analyzed, and the effects of rivet materials, geometrical shapes and friction coefficients on the orders of stress singularities and stress angular variations are investigated.