考虑装配间隙的双搭接螺栓连接剪切刚度的解析求解方法
Analytical solution of shear stiffness for double-lap bolted joints with clearances

螺栓的连接刚度是复合材料连接设计中的重要参数，装配间隙对其有明显的影响。针对弹性基刚度kc*，引入Liu Cai-Shan的内圆接触模型，推导了考虑装配间隙的解析表达式，发现kc*随着装配间隙增加而降低。针对钉头约束系数kr，基于应力假设和应变能方法，给出了估算表达式。在获得kc*和kr基础上，建立弹性基剪切梁模型并推导了双搭接螺栓连接刚度的解析解，并采用3-D细节有限元模型对解析方法进行了验证。最后，通过有限元方法分析了间隙对连接刚度产生影响的力学机制，并用解析方法定量给出了1~300 μm的装配间隙对连接刚度影响的大小。 The joint stiffness is an important parameter in the design of composite bolted joints and is influenced largely by the bolt-hole clearance. Aiming at the elastic foundation stiffness kc*, an analytical expression was derived by introducing Liu Cai-Shan's inner cylindrical contact model. This analytical expression can take account of the bolt-hole clearance and it shows that kc* deceases with the increase of clearance. Aiming at the nail-head restraint coefficient kr, an approximate expression was obtained by the strain energy method from a reasonable stress distribution hypothesis. Based on kc* and kr, the analytical solution of the joint stiffness was derived from an elastic foundation beam model. The load-displacement curves of double-lap bolted joints predicted by the analytical method were validated by 3-D detailed FE-models. Finally, the mechanical mechanism of the clearance influence on the joint stiffness was analyzed by finite element method. Moreover, the influences of the clearances form 1-300 μm were given quantitatively by the analytic method.