• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2019, Vol. 55 ›› Issue (4): 67-74.doi: 10.3901/JME.2019.04.067

• 材料科学与技术 • 上一篇    下一篇

复合材料层合板可靠性分析的发生函数法

刘成龙1,2, 周金宇1, 邱睿1   

  1. 1. 江苏理工学院“结构/材料多尺度协同设计与制造”江苏省高校优秀科技创新团队 常州 213000;
    2. 机械科学研究总院江苏分院有限公司 常州 213000
  • 收稿日期:2018-05-02 修回日期:2018-09-01 出版日期:2019-02-20 发布日期:2019-02-20
  • 通讯作者: 周金宇(通信作者),男,1973年出生,博士,教授,硕士研究生导师。研究方向为机械可靠性、现代设计方法。E-mail:yuhangyuan888@sina.com
  • 作者简介:刘成龙,男,1993年出生。主要研究方向为装备轻量化设计与制造。E-mail:15861171751@163.com;邱睿,女,1984年出生,博士。主要研究方向为复合材料疲劳性能。
  • 基金资助:
    国家自然科学基金(51275221)和江苏省高校自然科学基金重大项目(16KJA460002)资助项目

Reliability Analysis of Composite Laminates Based on Generating Function Approach

LIU Chenglong1,2, ZHOU Jinyu1, QIU Rui1   

  1. 1. Excellent Science and Technology Innovation Team:Material/Structure Multi-scale Collaborative Design and Manufacture, Universities in Jiangsu, Jiangsu University of Technology, Changzhou 213000;
    2. Jiangsu Institute, China Academy of Machinery Science & Technology, Changzhou 213000
  • Received:2018-05-02 Revised:2018-09-01 Online:2019-02-20 Published:2019-02-20

摘要: 复合材料层合板可靠性分析涉及多变量、非正态、非线性功能函数和失效相关性等问题。针对分析难题引入发生函数法,分别构造描述载荷、抗力和抗力序列等概率分布的发生函数,定义相应发生函数的复合算子。通过发生函数的复合运算,根据复合材料层合板的首/终层失效准则,结合层合单元的Tsai-Hill强度理论,建立层合板可靠性分析模型。该方法适用于含有众多随机变量(包含非正态随机变量)且功能函数为非线性的结构系统可靠性评估,考虑了层合板失效路径之间因含有共同失效元,以及失效路径内部各失效元因共享同一随机载荷源而引起的失效相关性,通过K-means聚类和同类项合并技术显著缩减了计算成本从而提高效率。结合本方法给出具体算例,分析结果表明:可靠度值与传统一次可靠度方法相比更接近蒙特卡罗法仿真结果,可为复合材料层合板强度可靠性分析提供一种新思路。

关键词: K-means聚类, 发生函数, 复合材料, 可靠性

Abstract: The reliability analysis of composite laminates involves multivariable, non-normal, non-linear performance function and failure correlation, etc. Aiming at analysis problems, generating function approach is introduced via constructing special generating functions, which are used to describe probability distribution of load, resistance and resistance sequence, by defining relevant compositional operators. By means of the compositional operation of generating functions, reliability analysis model of composite laminates is established based on first/last ply failure criteria and Tsai-Hill strength theory. This method can be applied to the reliability evaluation of structure systems with many random variables(including non-normal random variables) and the non-linear performance function. Failure correlation between failure paths of laminates due to containing common failure elements and failure correlation within each failure path due to sharing the common random load source are considered by this method. In compositional operations of generating functions, K-means clustering and like terms collecting techniques are used to reduce computational costs and the efficiency is dramatically improved. Specific examples are given based on this approach. Analysis results show that the reliability value of the proposed method is closer to the Monte Carlo simulation results than that of traditional first order reliability methods. The new method can provide a new idea for the strength reliability analysis of composite laminates.

Key words: composites, generating function, K-means clustering, reliability

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