[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 |