复合材料层合板可靠性分析的发生函数法
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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。
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.
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.
引文
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[13]王千,王成,冯振元,等.K-means聚类算法研究综述[J].电子设计工程,2012,20(7):21-24.WANG Qian,WANG Cheng,FENG Zhenyuan,et al.Review of k-means clustering algorithm[J].Electronic Design Engineering,2012,20(7):21-24.
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[16]金峰.结构可靠度计算[M].北京:科学出版社,2015.JIN Feng.Calculation of structural reliability[M].Beijing:Science Press,2015.
[17]李朴义,周金宇,马元节.结构可靠度计算的非均匀离散化发生函数法[J].机械科学与技术,2016,35(8):1207-1212.LI Puyi,ZHOU Jinyu,MA Yuanjie.Calculating structural reliability with generation function method based on non-uniform discretization[J].Journal of Mechanical Science and Technology,2016,35(8):1207-1212.
[2]LISNIANSKI A,LEVITIN G.Multi-state system reliability[M].New Jersey:World Scientific,2003.
[3]周金宇,谢里阳.多状态系统共因失效机理与定量分析[J].机械工程学报,2008,44(10):77-82.ZHOU Jinyu,XIE Liyang.Common cause failure mechanism and risk probability quantitative estimation of multi-state systems[J].Journal of Mechanical Engineering,2008,44(10):77-82.
[4]周金宇,谢里阳.结构系统可靠性分析的发生函数法[J].中国科学:技术科学,2010,40(2):177-185.ZHOU Jinyu,XIE Liyang.Generating function approach to reliability analysis of structural systems[J].Science China:Technology Science,2010,40(2):177-185.
[5]高鹏,谢里阳.基于改进发生函数方法的多状态系统可靠性分析[J].航空学报,2010,31(5):934-939.GAO Peng,XIE Liyang.Reliability analysis of multi-state systems based on improved universal generating function[J].Journal of Aviation,2010,31(5):934-939.
[6]郭惠昕,戴娟,程立志,等.应力-强度干涉的直方图模型及可靠度计算的发生函数法[J].中国机械工程,2013,24(15):2041-2047.GUO Huixin,DAI Juan,CHENG Lizhi,et al.Histogram-based stress-strength interference model and approach to reliability calculation by using universal generating function[J].China Mechanical Engineering,2013,24(15):2041-2047.
[7]MI J,LI Y F,LIU Y,et al.Belief universal generating function analysis of multi-state systems under epistemic uncertainty and common cause failures[J].IEEETransactions on Reliability,2015,64(4):1300-1309.
[8]JAFARY B,FIONDELLA L.A universal generating function-based multi-state system performance model subject to correlated failures[J].Reliability Engineering&System Safety,2016,152(1):16-27.
[9]SRIRAMULA S,CHRYSSANTHOPOULOS M K.Quantification of uncertainty modelling in stochastic analysis of FRP composites[J].Composites Part A Applied Science&Manufacturing,2009,40(11):1673-1684.
[10]沈观林,胡更开,刘彬.复合材料力学[M].2版.北京:清华大学出版社,2013,62-113.SHEN Guanlin,HU Gengkai,LIU Bin.Second edition of mechanics of composite materials[M].2rd ed.Beijing:Tsinghua University Press,2013,62-113.
[11]CHIACHIO M,CHIACHIO J,RUS G.Reliability in composites-A selective review and survey of current development[J].Composites Part B,2012,43(3):902-913.
[12]LEVITIN G.A universal generating function approach for the analysis of multi-state systems with dependent elements[J].Reliability Engineering&System Safety,2004,84(3):285-292.
[13]王千,王成,冯振元,等.K-means聚类算法研究综述[J].电子设计工程,2012,20(7):21-24.WANG Qian,WANG Cheng,FENG Zhenyuan,et al.Review of k-means clustering algorithm[J].Electronic Design Engineering,2012,20(7):21-24.
[14]LEVITIN G.The universal generating function in reliability analysis and optimization[M].London:Springer,2005.
[15]ASHUTOSH,GUPTA,JAIN,et al.A novel approach for part family formation using K-means algorithm[J].Advances in Manufacturing,2013,1(3):241-250.
[16]金峰.结构可靠度计算[M].北京:科学出版社,2015.JIN Feng.Calculation of structural reliability[M].Beijing:Science Press,2015.
[17]李朴义,周金宇,马元节.结构可靠度计算的非均匀离散化发生函数法[J].机械科学与技术,2016,35(8):1207-1212.LI Puyi,ZHOU Jinyu,MA Yuanjie.Calculating structural reliability with generation function method based on non-uniform discretization[J].Journal of Mechanical Science and Technology,2016,35(8):1207-1212.