单层网壳结构稳定性分析方法研究
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摘要
为了准确地分析具有初始几何缺陷的单层网壳结构整体稳定性,运用随机缺陷模态法、一致缺陷模态法和N阶特征缺陷模态法,对4个不同矢跨比的K8型单层网壳进行了近1300例弹塑性荷载-位移全过程分析,探讨不同分析方法的合理性和可行性。研究表明:随机缺陷模态法能较为科学地评估初始几何缺陷对结构稳定性的影响,但计算量较大;对稳定承载力系数样本进行统计特性分析时,空间样本数量n不应小于100;运用随机缺陷模态法确定网壳结构最终的稳定承载力系数时,建议采用"3σ"原则;采用最低阶屈曲模态模拟初始几何缺陷分布,求得的稳定承载力并非最不利,其保证率得不到有效保证;N阶特征缺陷模态法能够通过较少的计算量,得到满足"3σ"原则要求的稳定承载力,并能较为合理、安全地评估网壳结构的稳定性能;在运用N阶特征缺陷模态法时,建议N=20。
To accurately analyze the integral stability of single layer latticed shells with initial geometric imperfections, nearly 1300 elasto-plastic load-displacement analyses of K8 single layer latticed shell were carried out to investigate the accuracy and feasibility of different analysis methods. Four different rise-to-span ratios of K8 single layer latticed shell were considered, and the analysis methods employed herein were the random imperfection mode method, the consistent mode imperfection method and the N-order eigenvalue imperfection mode method. The results show that the random imperfection mode method can evaluate the influence of initial geometric imperfections on structural stability more reasonably, but the calculation cost is quite large. To obtain the statistical characteristic of the stability bearing capacity coefficient samples, the number of space samples should be no less than 100. ‘3σ' principle is suggested to determine the stability bearing capacity coefficient by using the random imperfection mode method. Utilizing the first-order buckling mode to simulate the distribution of initial geometric imperfection may fail to obtain the most unfavorable stability bearing capacity. The N-order eigenvalue imperfection mode method can generate a reasonable stability bearing capacity which meets the requirement of ‘3σ' principle with less calculation, and moreover, it can evaluate the stability performance of single layer latticed shell reasonably. The N is suggested to be 20 when using the N-order eigenvalue imperfection mode method.
To accurately analyze the integral stability of single layer latticed shells with initial geometric imperfections, nearly 1300 elasto-plastic load-displacement analyses of K8 single layer latticed shell were carried out to investigate the accuracy and feasibility of different analysis methods. Four different rise-to-span ratios of K8 single layer latticed shell were considered, and the analysis methods employed herein were the random imperfection mode method, the consistent mode imperfection method and the N-order eigenvalue imperfection mode method. The results show that the random imperfection mode method can evaluate the influence of initial geometric imperfections on structural stability more reasonably, but the calculation cost is quite large. To obtain the statistical characteristic of the stability bearing capacity coefficient samples, the number of space samples should be no less than 100. ‘3σ' principle is suggested to determine the stability bearing capacity coefficient by using the random imperfection mode method. Utilizing the first-order buckling mode to simulate the distribution of initial geometric imperfection may fail to obtain the most unfavorable stability bearing capacity. The N-order eigenvalue imperfection mode method can generate a reasonable stability bearing capacity which meets the requirement of ‘3σ' principle with less calculation, and moreover, it can evaluate the stability performance of single layer latticed shell reasonably. The N is suggested to be 20 when using the N-order eigenvalue imperfection mode method.
引文
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[12]葛家琪,张国军,王树,等.2008奥运会羽毛球馆弦支穹顶结构整体稳定性能分析研究[J].建筑结构学报,2007,28(6):22―30,44.Ge Jiaqi,Zhang Guojun,Wang Shu,et al.The overall stability analysis of the suspend-dome structure system of the badminton gymnasium for 2008 Olympic Games[J].Journal of Building Structures,2007,28(6):22―30,44.(in Chinese)
[2]Balut N,Porumb D,Gioncu V.Some aspects concerning the behavior and analysis of single-layer latticed roof structures[C].Proceedings of 3rd International Colloquium on Stability of Metal Structures,Paris,1983:133―140.
[3]See T,Mcconnel R E.Large displacement elastic buckling of space structures[J].Journal of Structural Engineering,1986,112(5):1052―1069.
[4]Kani I M,Mcconnel R E.Collapse of shallow lattice domes[J].Journal of Structural Engineering,1987,113(8):1806―1819.
[5]Borri C,Spinelli P.Buckling and post-buckling behavior of single layer reticulated shells affected by random imperfections[J].Computers&Structures,1988,30(4):937―943.
[6]沈世钊,陈昕.网壳结构稳定性[M].北京:科学出版社,1999:52―59.Shen Shizhao,Chen Xin.Stability of reticulated shells[M].Beijing:Science Press,1999:52―59.(in Chinese)
[7]Gioncu V.Buckling of reticulated shells:state-of-the-art[J].International Journal of Space Structures,1995,10(1):1―46.
[8]Ragon S A,Rdal Z,Watson L T.A comparison of three algorithms for tracing nonlinear equilibrium paths of structural systems[J].International Journal of Solids and Structures,2002,39(3):689―698.
[9]郭佳民,董石麟,袁行飞.随机缺陷模态法在弦支穹顶稳定性计算中的应用[J].工程力学,2011,28(11):178―183.Guo Jiamin,Dong Shilin,Yuan Xingfei.Application of random imperfection mode method in stability calculation of suspen-dome[J].Engineering Mechanics,2011,28(11):178―183.(in Chinese)
[10]唐敢,尹凌峰,马军,等.单层网壳结构稳定性分析的改进随机缺陷法[J].空间结构,2004,10(4):44―47.Tang Gan,Yin Lingfeng,Ma Jun,et al.Advanced stochastic imperfection method for stability analysis of single layer lattice domes[J].Spatial Structures,2004,10(4):44―47.(in Chinese)
[11]栾长福,梁满.概率论与数理统计[M].广州:华南理工大学出版社,2007:153―154.Luan Changfu,Liang Man.Probability and mathematical statistics[M].Guangzhou:South China University of Technology Press,2007:153―154.(in Chinese)
[12]葛家琪,张国军,王树,等.2008奥运会羽毛球馆弦支穹顶结构整体稳定性能分析研究[J].建筑结构学报,2007,28(6):22―30,44.Ge Jiaqi,Zhang Guojun,Wang Shu,et al.The overall stability analysis of the suspend-dome structure system of the badminton gymnasium for 2008 Olympic Games[J].Journal of Building Structures,2007,28(6):22―30,44.(in Chinese)