EI、Scopus 收录
中文核心期刊

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

随机桁架结构几何非线性问题的混合摄动-伽辽金法求解

黄斌 贺志赟 张衡

黄斌, 贺志赟, 张衡. 随机桁架结构几何非线性问题的混合摄动-伽辽金法求解[J]. 力学学报, 2019, 51(5): 1424-1436. doi: 10.6052/0459-1879-19-099
引用本文: 黄斌, 贺志赟, 张衡. 随机桁架结构几何非线性问题的混合摄动-伽辽金法求解[J]. 力学学报, 2019, 51(5): 1424-1436. doi: 10.6052/0459-1879-19-099
Huang Bin, He Zhiyun, Zhang Heng. HYBRID PERTURBATION-GALERKIN METHOD FOR GEOMETRICAL NONLINEAR ANALYSIS OF TRUSS STRUCTURES WITH RANDOM PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1424-1436. doi: 10.6052/0459-1879-19-099
Citation: Huang Bin, He Zhiyun, Zhang Heng. HYBRID PERTURBATION-GALERKIN METHOD FOR GEOMETRICAL NONLINEAR ANALYSIS OF TRUSS STRUCTURES WITH RANDOM PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(5): 1424-1436. doi: 10.6052/0459-1879-19-099

随机桁架结构几何非线性问题的混合摄动-伽辽金法求解

doi: 10.6052/0459-1879-19-099
基金项目: 1)国家自然科学基金资助项目(51578431)
详细信息
    通讯作者:

    黄斌

  • 中图分类号: O342,TU32

HYBRID PERTURBATION-GALERKIN METHOD FOR GEOMETRICAL NONLINEAR ANALYSIS OF TRUSS STRUCTURES WITH RANDOM PARAMETERS

  • 摘要: 提出应用混合摄动$\!$-$\!$-$\!$伽辽金法求解随机桁架结构的几何非线性问题.将含位移项的随机割线弹性模量以及随机响应表示为幂多项式展开,利用高阶摄动方法确定随机结构几何非线性响应的幂多项式展开的各项系数.将随机响应的各阶摄动项假定为伽辽金试函数,运用伽辽金投影对试函数系数进行求解,从而得到随机桁架结构几何非线性响应的显式表达式.同已有的随机伽辽金法相比,本文所给的试函数由摄动解的线性组合而成,在求解非线性问题时,试函数的获取具有自适应性.数值算例结果表明,对于具有不同概率分布的多随机变量问题,本文方法无需对随机变量的概率分布形式进行转换,避免了转换误差,因而比同阶的广义正交多项式方法(generalizedpolynomial chaos, GPC)计算精度高.同时,在结果精度相当时,和GPC方法相比,本文方法得到的试函数系数的非线性方程维度不大,方程的求解工作量小且更易求解.当随机量涨落较大时,混合摄动$\!$-$\!$-$\!$伽辽金法计算所得的结构响应的各阶统计矩比高阶摄动法所得结果更逼近于蒙特卡洛模拟结果,显示了该方法对几何非线性随机问题求解的有效性.

     

  • [1] Bielewicz E, Górski J . Shells with random geometric imperfections simulation --- based approach. International Journal of Non-Linear Mechanics, 2002,37(4):777-784
    [2] Schenk CA, Schu?ller GI . Buckling analysis of cylindrical shells with cutouts including random boundary and geometric imperfections. Computer Methods in Applied Mechanics & Engineering, 2007,196(35):3424-3434
    [3] Capiez-Lernout E, Soize C, Mignolet MP . Computational stochastic statics of an uncertain curved structure with geometrical nonlinearity in three-dimensional elasticity. Computational Mechanics, 2012,49(1):87-97
    [4] Impollonia N, Muscolino G . Static and dynamic analysis of non-linear uncertain structures. Meccanica, 2002,37(1-2):179-192
    [5] Impollonia N, Sofi A . A response surface approach for the static analysis of stochastic structures with geometrical nonlinearities. Computer Methods in Applied Mechanics & Engineering, 2003,192(37):4109-4129
    [6] 程进 . 基于响应面法的几何非线性结构概率响应分析. 同济大学学报(自然科学版), 2006,34(9):1147-1151
    [6] ( Cheng Jin . Probabilistic response analysis of geometrically nonlinear structure based on systematic response surface method. Journal of Tongji University (Natural Science), 2006,34(9):1147-1151 (in Chinese))
    [7] Contento A, Luongo A . Static and dynamic consistent perturbation analysis for nonlinear inextensible planar frames. Computers & Structures, 2013,123:79-92
    [8] Kaminski M . On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties. International Journal for Numerical Methods in Engineering, 2015,104(11):1038-1060
    [9] 黄斌, 索建臣, 毛文筠 . 随机杆系结构几何非线性分析的递推求解. 力学学报, 2007,39(6):835-842
    [9] ( Huang Bin, Suo Jianchen, Mao Wenjun . Geometrical nonlinear analysis of truss structures with random parameters utilizing recursive stochastic finite element method. Chinese Journal of Theoretical and Applied Mechanics, 2007,39(6):835-842 (in Chinese))
    [10] 廖世俊 . 超越摄动------同伦分析方法导论. 北京: 科学出版社, 2006
    [10] ( Liao Shijun. Beyond Perturbation -- Introduction to the Homotopy Analysis Method. Beijing: Science Press, 2006 (in Chinese))
    [11] 谭国强, 王朝伟 . 摄动加权残数法及其在几何非线性问题中的应用. 铁道科学与工程学报, 1985(4):28-40
    [11] ( Tan Guoqiang, Wang Chaowei . Perturbed weighted residual method and the application in nonlinear problems. Journal of Railway Science and Engineering, 1985(4):28-40 (in Chinese))
    [12] 孙博华 . 摄动权余法及在薄板大挠度问题上的应用. 固体力学学报, 1986 ( 4):50-57
    [12] ( Sun Bohua . Perturbation weighted residuals method and its application in large deflection problems of thin plates. Chinese Journal of Solid Mechanics, 1986 ( 4):50-57 (in Chinese))
    [13] Zhao Q, Ye TQ . Hybrid changeable basis galerkin technique for nonlinear analysis of structures. Applied Mathematics and Mechanics, 1995,16(7):667-674
    [14] Noor AK, Peters JM . Recent advances in reduction methods for instability analysis of structures. Computers & Structures, 1983,16(1):67-80
    [15] 孟广伟, 周立明, 李锋 等. 摄动随机局部正交无网格伽辽金法. 吉林大学学报(工学版), 2010,40(6):1556-1561
    [15] ( Meng Guangwei, Zhou Liming, Li Feng , et al. Perturbation stochastic local orthogonal element-free Galerkin method. Journal of Jilin University (Engineering and Technology Edition), 2010,40(6):1556-1561 (in Chinese))
    [16] Huang B, Li QS, Tuan AY , et al. Recursive approach for random response analysis using non-orthogonal polynomial expansion. Computational Mechanics, 2009,44(3):309-320
    [17] 黄斌 . 随机结构有限元分析的递推求解方法的改进. 计算力学学报, 2010,27(2):202-206.
    [17] ( Huang Bin . Improvement on recursive stocha-stic finite element method. Chinese Journal of Computational Mechanics, 2010,27(2):202-206 (in Chinese))
    [18] Li YJ, Huang B . Reliability analysis of structure with random parameters based on multivariate power polynomial expansion. Journal of Southeast University, 2017,33(1):59-63
    [19] Li YJ, Huang B, Li CQ . Hybrid perturbation-Galerkin methods for structural reliability analysis. Probabilistic Engineering Mechanics, 2017, ( 48):59-67
    [20] Ghanem R, Spanos PD . Polynomial chaos in stochastic finite elements. Journal of Applied Mechanics, 1990,57(1):197-202
    [21] Xiu D, Karniadakis GE . The Wiener--Askey polynomial chaos for stochastic differential equations. SIAM Journal on Scientific Computing, 2002,24:619-644
    [22] 李烨君 . 基于混合摄动$\!$-$\!$-$\!$伽辽金法的结构可靠性分析. [博士论文]. 武汉:武汉理工大学, 2017
    [22] ( Li Yejun . Structural Reliability Analysis Based on Hybrid Perturbation-Galerkin Methods. [PhD Thesis]. Wuhan: Wuhan University of Technology, 2017 (in Chinese))
    [23] Xiu D, Karniadakis GE . Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Computer Methods in Applied Mechanics & Engineering, 2002,191(43):4927-4948
    [24] Mohan PS, Nair PB, Keane AJ . Multi-element stochastic reduced basis methods. Computer Methods in Applied Mechanics and Engineering, 2008,197(17-18):1495-1506
    [25] 周春晓, 汪锐琼, 聂肇坤 等. 基于最大熵方法的水下航行体结构动力响应概率建模. 力学学报, 2018,50(1):114-123
    [25] ( Zhou Chunxiao, Wang Ruiqiong, Nie Zhaokun , et al. Probabilistic modelling of dynamic response of underwater vehicle structure via maximum entropy method. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(1):114-123 (in Chinese))
    [26] 芮珍梅, 陈建兵 . 加性非平稳激励下结构速度响应的FPK方程降维. 力学学报, 2019,51(3):922-931
    [26] ( Rui Zhenmei, Chen Jianbing . Dimension reduction of FPK equation for velocity response analysis of structures subjected to additive nonstationary excitations. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):922-931 (in Chinese))
    [27] 石晟, 杜东升, 王曙光 等. 概率密度演化方程TVD格式的自适应时间步长技术及其初值条件改进. 力学学报, 2019,51(4):1223-1234
    [27] ( Shi Sheng, Du Dongsheng, Wang Shuguang , et al. Non-uniform time step TVD scheme for probability density evolution function with improvement of initial condition. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(4):1223-1234 (in Chinese))
    [28] Zhang H, Huang B . A new homotopy-based approach for structural stochastic analysis. Probabilistic Engineering Mechanics, 2019,55:42-53
    [29] Wu D, Gao W, Tangaramvong S , et al. Robust stability analysis of structures with uncertain parameters using mathematical programming approach. International Journal for Numerical Methods in Engineering, 2014,100(10):720-745
    [30] Fan J, Zhang YP . Non-stationary random response analysis of structures with uncertain parameters. Probabilistic Engineering Mechanics, 2017,50:53-63
  • 加载中
计量
  • 文章访问数:  1180
  • HTML全文浏览量:  163
  • PDF下载量:  123
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-04-19
  • 刊出日期:  2019-09-18

目录

    /

    返回文章
    返回