结构强度可靠性分析的模糊随机边界元法
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摘要
利用模糊随机变量和模糊概率特征建立模糊随机边界元代数方程,对方程作λ水平截集,得到随机区间方程,将该方程中的系数矩阵,结点位移列阵和荷载列阵在初始随机向量的均值处展开,利用区间数分解和小参数摄动理论导出求解应力统计特征、结构破坏概率指标和可靠度的计算公式,并给出算例。
An algebra equation of fuzzy stochastic boundary element is established by using fuzzy random variational and fuzzy probability characteristics.By λlevel cutset,a stochastic interval equation is obtained. Expanding the coefficient matrix, the displacement vector and loading vector existing in the interval equation at the expectation value of the initial random vector. Then using the resolution of interval numbers and perturba tion theory for small parameters, the for mulas is developed for calculating the statistical characteristicsof stress and structural destruction probability guide line and reliability. Some examples are given.
An algebra equation of fuzzy stochastic boundary element is established by using fuzzy random variational and fuzzy probability characteristics.By λlevel cutset,a stochastic interval equation is obtained. Expanding the coefficient matrix, the displacement vector and loading vector existing in the interval equation at the expectation value of the initial random vector. Then using the resolution of interval numbers and perturba tion theory for small parameters, the for mulas is developed for calculating the statistical characteristicsof stress and structural destruction probability guide line and reliability. Some examples are given.
引文
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[3] 张妃二,袁 鸿.板梁组合结构可靠性分析的随机边界元法[J].应用数学和力学,1997,18(5):451-458.(ZhangFeier,YuanHong.Stochasticboundaryelementmethodofplateandbeamscompositestructure[J].ApplicationofMathandMechanics,1997,18(5):451-458.(inChinese))
[4] 杨伦标,高英仪.模糊数学(原理及应用)[M].广州:华南理工大学出版社,1993(YangLunbiao,GaoYingyi.FuzzyMath(Theory&Application)[M].PublicationofGuangzhouSouthChinaUniversityofTechnology,1993.(inChinese))
[5] 禹智涛,吕思琳,王彩华.结构模糊有限元平衡方程的一种解法[J].重庆大学学报,1996,19(1):53-58.(YuZhitao,LuSilin,WangChaihua.Asolutionofstructurefuzzyfiniteelementbalanceequation[J].JournalofChongqingUniversity,1996,19(1):53-58.(inChinese))
[6] 陈塑寰,刘寒冰,韩万芝.形状不确定性结构动特性分析的随机边界元法[J].固体力学学报,1993,14(3):265-270.(ChenSuhuan,LiuHanbing,HanWanzhi.Probabilisticboundaryelementmethodforanalysisofdynamiccharacterofstructureswithstochasticshape[J].JournalofSolidMechanics,1993,14(3):265-270.(inChinese))
[7] 张 跃.模糊随机变量[J].哈尔滨建筑工程学院学报,1989,22(3):12-21.(ZhangYue.Fuzzyrandomvariable[J].JournalofHaerbinArchitectureEngineerCollege,1989,22(3):12-21(inChinese))
[8] 张 跃.模糊随机向量[J].哈尔滨建筑工程学院学报,1989,22(4):27-41.(ZhangYue.Fuzzyrandomvector[J].JournalofHaerbinArchitectureEngineerCollege,1989,22(4):27-41.(inChinese))
[9] 吕思琳.一种模糊随机有限元法[J].重庆大学学报,1996,19(5):68-75.(Lu¨Siling.Afuzzyrandomfiniteelementmethod[J].JournalofChongqingUniversity,1996,19(5):68-75.(inChinese))
[10]李桂青,曹 宏,等.结构动力可靠性理论及其应用[M].北京:地震出版社,1993.(LiGuiqing.ChaoHong.etal.TheoryandApplicationofStructureDynamicReliability[M].Beijing:EarthquakePublication,1993.(inChinese))
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