复合材料连接件钉载分配与孔周应力解析计算  

An analytical investigation on the pin-load and stress distributions in composite joints

作　　者：苏杰[1] 李亚智[1] 杨帆[1] 丁瑞香 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《应用力学学报》2015年第5期717-723,890,共7页Chinese Journal of Applied Mechanics

基　　金：航空科学基金(20120953010)

摘　　要：钉载分配与钉孔边应力集中是多钉机械连接结构设计和强度校核中十分关心的问题。本文基于经典层合板理论以及平面弹性复变方法,充分利用Faber级数工具,将多钉连接的工程问题变成解析函数边值问题。结合特定边界条件的处理方法,利用一种基于待定系数法的动态选点方式求解傅里叶系数,将计算应力函数未知系数的问题转化为非线性方程组的迭代求解,最终利用最速下降法求解了非线性方程组,得到完备的应力函数及钉载值。在此基础上计算了材料坐标系下不同铺层角的各层孔周应力,首先:进行了一列三钉连接的实例计算,得到的钉载分配结果与其他解析法已有结果比较接近,1号、2号、3号螺栓钉载分配相对误差分别为-0.008%、1.9%、-0.008%;随后又将三排三列多钉连接实例计算得到的钉载比例以及孔周应力分布与有限元法得到的对应值进行了比较,发现本文的解析法计算的结果与有限元法结果吻合良好。这表明本文方法有一定的合理性和工程应用价值。Pin-load distribution and the stresses around fastener hole are very much concerned in the design and strength evaluation of multiple fastened mechanical joints. Based on the complex method in plane elastic problem, an analytical method for transferring the analysis of multiple pin composite joint to boundary value problem for analytic functions is examined, taking full advantage of Faber series. The general solution of the problem is then converted into the iterative solution of a set of nonlinear equations, with the treatment of specified boundary conditions and the dynamic selected point manner for solving Fourier coefficients, a complete stress function and each ratio of pin-load to the external tension load are obtained by using the steepest descent method. In addition, the fastener hole stress distribution in the plies of different orientations are determined. Pin-load distribution solved by other analytical method is relatively similar to that derived from the complex analytical method. The relative errors of three bolts' pin-load are-0.008%, 1.9% and-0.008%, respectively. The solution of the present method for an example problem yields the pin-load ratios and ply stresses that are in accordance with the corresponding finite element solution. It shows that this method has some rationality and engineering value.

关 键 词：复合材料层合板 多钉机械连接 钉载分配 应力分布 解析解 

分 类 号：V214.8[航空宇航科学与技术—航空宇航推进理论与工程] O343.8[理学—固体力学]