多场耦合系统动力学仿真方法研究进展

王国平; 陶玲; 戎保; 芮筱亭

doi:10.6052/1000-0992-22-043

多场耦合系统动力学仿真方法研究进展

doi: 10.6052/1000-0992-22-043

王国平¹,
陶玲^2, ,,
戎保¹,
芮筱亭¹

1.
南京理工大学发射动力学研究所, 南京 210094
2.
南京理工大学能源与动力工程学院, 南京 210094

基金项目: 国家自然科学基金 (11972193, 92266201) 资助项目

详细信息

作者简介:
王国平, 南京理工大学教授, 博士生导师, 发表论文160余篇, 主持国家和省部级项目10多项, 获首届国防卓越青年基金、中国青年科技奖、国家高层次人才计划、国家百千万人才工程、教育部新世纪优秀人才支持计划和江苏省“333工程”中青年领军人才等

通讯作者:
taoling@njust.edu.cn

中图分类号: O302
计量
- 文章访问数: 3720
- HTML全文浏览量: 1175
- PDF下载量: 690
- 被引次数: 0
出版历程
- 收稿日期: 2022-09-28
- 录用日期: 2022-10-21
- 网络出版日期: 2022-10-22
- 刊出日期: 2023-06-25

Review of dynamics simulation methods for multi-field coupling systems

1.
Institute of Launch Dynamics, Nanjing University of Science and Technology, Nanjing 210094, China,
2.
School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

More Information

Corresponding author: taoling@njust.edu.cn

摘要

摘要: 现代工程系统往往是以复杂结构/机械系统为主体, 融合热、流、电磁等若干子系统的多场耦合系统. 此类系统动力学建模复杂、计算难度大, 给系统动态特性高效精确评估与设计优化带来前所未有的挑战, 有关其高效精确动力学仿真方法的研究愈发受到关注. 本文详细回顾了复杂工程系统多场耦合动力学仿真方法研究成果和进展, 包括: 多场耦合动力学建模与数值求解基本策略、网格变形处理方法、耦合数据交换技术、数值计算效率等问题, 在此基础上详细讨论了单一和混合不确定性条件下多场耦合系统不确定性分析及可靠性评估方法, 以期为相关研究提供有益的借鉴和参考.
- 多场耦合 /
- 动网格 /
- 分区求解 /
- 不确定性 /
- 可靠性 /
- 耦合数据传递
Abstract: Modern engineering system is usually a multi-field coupling system with complex structure/mechanical system as the main body, which integrates thermal, electromagnetic, fluid and other subsystems. The dynamics modeling of these systems are complex and their numerical calculate are also difficult, which bring unprecedented challenges to the efficient and accurate evaluation and design optimization of the system dynamic characteristics. In this paper, the research progress of multi-field coupling dynamics simulation methods for complex engineering systems are reviewed in detail, including the basic strategies of multi-field coupling dynamics modeling and numerical solution, mesh deformation processing method, coupling data exchange technology, numerical calculation efficiency, etc. On this basis, for uncertain multi-field coupling engineering systems, their uncertainty analysis and reliability evaluation methods under single and hybrid uncertainties are discussed in detail. This review paper is expected to provide some useful references for related researchers.
- multi-field coupling /
- dynamic grid /
- partition solution /
- uncertainty /
- reliability /
- coupling data exchange

HTML全文

图 1 多物理场典型耦合关系和耦合变量示意图 (Rong et al. 2019, 王思莹等 2014, Hron & Turek 2006, Degroote et al. 2009, 宋少云 2007, Dietz et al. 2001, Fernández 2011, Erbts et al. 2015, Degroote & Vierendeels 2011)

下载: 全尺寸图片幻灯片

图 2 典型流场−结构场耦合问题分区解法示意图

下载: 全尺寸图片幻灯片

图 3 典型充液多刚体系统动力学问题分区解法示意图 (Rumold 2001)

下载: 全尺寸图片幻灯片

图 4 径向基函数和Delaunay背景图相结合的网格变形方法 (蒋波 2017)

下载: 全尺寸图片幻灯片

图 5 双翼型轨迹模拟过程网格变形/重构示意图. (a)背景网格与运动物体子网格, (b)初始位置网格, (c)网格变形, (d)大变形的网格重构 (徐琳和宋万强 2019)

下载: 全尺寸图片幻灯片

图 6 基于多体系统传递矩阵法和Van der Pol的海洋热塑性增强管流固耦合仿真. (a) 立管模型示意图, (b) 剪切流情况下立管轴向涡激振动振幅分布 (芮雪等 2020)

下载: 全尺寸图片幻灯片

图 7 基于多体系统传递矩阵法的多管火箭燃气射流−多体动力学单向耦合仿真. (a) 多管火箭发射系统动力学模型, (b) 不同时刻迎气面压强, (c) 定向管口y方向位移、角速度 (李书田 2020)

下载: 全尺寸图片幻灯片

图 8 弹炮耦合武器系统多速率协同仿真. (a) 弹丸−火炮多体系统耦合模型, (b) 多速率积分方法, (c) 后座位移和炮口位移时间历程 (Rong et al. 2013)

下载: 全尺寸图片幻灯片

图 9 不确定性刚−柔−热耦合梁系统动力学响应非侵入式自适应稀疏多项式混沌展开计算. (a) 热效应下中心刚体−梁系统, (b) 非侵入式自适应稀疏多项式混沌展开算法, (c) 梁末端横向变形标准差 (Rong et al. 2023)

下载: 全尺寸图片幻灯片

图 10 FORM-α-URA方法原理 (孟欣佳 2016)

下载: 全尺寸图片幻灯片

参考文献(209)

[1]	曹鸿钧, 段宝岩. 2005a. 多学科系统非概率可靠性分析研究. 机械科学与技术, 24: 646-649 (Cao H J, Duan B Y. 2005a. Non-probabilistic reliability analysis for multidisciplinary systems. Mechanical Science and Technology, 24: 646-649). (Cao H J, Duan B Y. 2005. Non-probabilistic reliability analysis for multidisciplinary systems. Mechanical Science and Technology 24(6): 646-649).
[2]	曹鸿钧, 段宝岩. 2005. 基于凸集模型的多学科耦合系统不确定性分析. 西安电子科技大学学报(自然科学版), 32: 335-338 (Cao H J, Duan B Y. 2005. Uncertainty analysis for multidisciplinary systems based on convexmodels. Journal of Xidian University, 32: 335-338). (Cao H J, Duan B Y. 2005. Uncertainty analysis for multidisciplinary systems based on convexmodels. Journal of XIDIAN University, 32 (3): 335-338).
[3]	陈宁, 于德介, 吕辉等. 2014. 基于有限元法的模糊参数二维声场数值分析. 工程力学, 31: 201-207 (Chen N, Yu D J, Lv H. 2014. Numerrical analysis of 2d acoustic field with fuzzy parameters based on finite element method. Engineering Mechanics, 31: 201-207). doi: 10.6052/j.issn.1000-4750.2013.06.0581 (Chen N, Yu D J, Lv H. 2014. Numerrical analysis of 2d acoustic field with fuzzy parameters based on finite element method. Engineering Mechanics, 31 (12): 201-207). doi: 10.6052/j.issn.1000-4750.2013.06.0581
[4]	陈宁. 2017. 结构-声场耦合系统的不确定数值分析与拓扑优化. [博士论文]. 长沙: 湖南大学 Chen N. 2017. Uncertain numerical analysis and topology optimization for the structural-acoustic coupled system. [PhD Thesis]. Changsha: Hunan University
[5]	程兴华. 2012. 高超声速飞行器防热壁板气动热弹性耦合建模与分析. [博士论文]. 长沙: 国防科学技术大学 Cheng X H. 2012. Coupled aerothermoelastic modeling and analysis of thermal protection panel for hypersonic vehicles. [PhD Thesis]. Changsha: National University of Defense Technology
[6]	崔鹏, 韩景龙. 2009. 一种局部形式的流固耦合界面插值方法. 振动与冲击, 28: 64-68 (Cui P, Han J L. 2009. Interface interpolation method in local forrn for fluid-structure interaction problems. Journal of Vibration and Shock, 28: 64-68). doi: 10.3969/j.issn.1000-3835.2009.10.012 (Cui P, Han J L. 2009. Interface interpolation method in local forrn for fluid-structure interaction problems. Journal of Vibration and Shock, 28(10): 64-68). doi: 10.3969/j.issn.1000-3835.2009.10.012
[7]	范锐军, 周洲. 2010. 基于Delaunay图映射的动弹网格技术及其应用. 飞行力学, 28: 95-98 (Fan R J, Zhou Z. 2010. Dynamic mesh technology based on Delaunay map and its application. Flight Dynamics, 28: 95-98). doi: 10.13645/j.cnki.f.d.2010.02.017 (Fan R J, Zhou Z. 2010. Dynamic mesh technology based on Delaunay map and its application. Flight Dynamics, 28(2): 95-98). doi: 10.13645/j.cnki.f.d.2010.02.017
[8]	高效伟, 彭海峰, 杨恺等. 2015. 高等边界元法-理论与程序. 北京: 科学出版社 Gao X W, Peng H F, Yang K, Wang J. 2015. Advanced Boundary Element Method - Theory and Procedure. Beijing: Science Press
[9]	高兴龙. 2016. 物伞流固耦合及多体系统动力学研究. [博士论文]. 长沙: 国防科学技术大学 Gao X L. 2016. Research on multibody dynamics and fluid-structure interaction of parachute-body system. [PhD Thesis]. Changsha: National University of Defense Technology
[10]	高行山, 林胜勇. 2001. 加速松池法及其在静电-力耦合问题仿真分析中的应用. 机械强度, 23: 500-502 (Gao X S, Lin S Y. 2001. Accelerated relaxation algorithm for the simulation of coupled electrostatic-mechanical systems. Journal of Mechanical Strength, 23: 500-502). (Gao X S, Lin S Y. 2001. Accelerated relaxation algorithm for the simulation of coupled electrostatic-mechanical systems. Journal of Mechanical strength, 23 (4): 500-502).
[11]	葛杨俊. 2019. 飞机结冰数值模拟中的网格重构及多物理场耦合方法研究. [硕士论文]. 合肥: 合肥工业大学 Ge Y J. 2019. Study on mesh deforming algorithm and multi-physical field coupling method in aircraft icing simulation. [Master Thesis]. Hefei: Hefei University of Technology
[12]	郭勇昌. 2016. 证据和随机混合不确定声固耦合系统的数值分析方法研究. [硕士论文], 长沙: 湖南大学 Guo Y C. 2016. Hybrid uncertain analysis for structural-acoustic problem with stochastic and evidence variables. [Master Thesis]. Changsha: Hunan University
[13]	韩旭里, 庄陈坚, 刘新儒. 2007. 基于径向基函数与B样条的散乱数据拟合方法. 计算技术与自动化, 26: 63-65 (Han X L, Zhuang C J, Liu X R. 2007. Algorithm of the scattered data approximating based on radical basis functions and b- spline. Computing Technology and Automation, 26: 63-65). (Han X L, Zhuang C J, Liu X R. 2007. Algorithm of the scattered data approximating based on radical basis functions and b- spline. Computing Technology and Automation, 26(1): 63-65).
[14]	何俐萍. 2010. 基于可能性度量的机械系统可靠性分析和评价. [博士论文]. 大连: 大连理工大学 He L P. 2010. The reliability analysis and evaluation of mechanical systems based on possibilistic measurements. [PhD Thesis]. Dalian: Dalian University of Technology
[15]	何涛. 2013. 流固耦合新算法研究及其气动弹性应用. [博士论文]. 上海: 上海交通大学 He T. 2013. Novel partitioned coupling algorithms for fluid-structure interaction with applications to aeroelasticity. [PhD Thesis]. Shanghai: Shanghai Jiao Tong University
[16]	侯艳华. 2010. 认知不确定性条件下可能性分布的构造方法研究. [硕士论文]. 成都: 电子科技大学 Hou Y H. 2010. Research on the construction method of possibility distribution under epistemic uncertainty. [Master Thesis]. Chengdu: University of Electronic Science and Technology
[17]	胡聪. 2018. 基于代理模型的多学科时变可靠性设计优化方法研究. [硕士论文]. 成都: 电子科技大学 Hu C. 2018. Study for multi-disciplinary time-dependent reliability design optimization methods based on surrogate model. [Master Thesis]. Chengdu: University of Electronic Science and Technology
[18]	黄洪钟, 田志刚. 2002. 基于广义模糊随机强度的模糊可靠性计算理论. 机械工程学报, 8: 50-53 (Huang H Z, Tian Z G. 2002. Fuzzy reliability analysis based on generalized fuzzy random strength. Chinese Journal of Mechanical Engineering, 8: 50-53). doi: 10.3321/j.issn:0577-6686.2002.03.012 (Huang H Z, Tian Z G. 2002. Fuzzy reliability analysis based on generalized fuzzy random strength. Chinese Journal of Mechanical Engineering, 8: 50-53). doi: 10.3321/j.issn:0577-6686.2002.03.012
[19]	霍霖. 2017. 高超声速飞行器体襟翼气动热弹性耦合建模与分析. [博士论文]. 长沙: 国防科学技术大学 Huo L. 2017. Coupled aerothermoelastic modeling and analysis of flap for hypersonic vehicles. [PhD Thesis]. Changsha: National University of Defense Technology
[20]	蒋波. 2017. 多场耦合信息交互及网格变形技术研究. [硕士论文]. 绵阳: 西南科技大学 Jiang B. 2017. Research on multi-field coupled information interaction and grid deformation. [Master Thesis]. Mianyang: Southwest University of Science and Technology
[21]	李世军. 2013. 非概率可靠性理论及相关算法研究. [博士论文]. 武汉: 华中科技大学 Li S J. 2013. Research on algorithms of non-probabilistic convex reliability and its theories. [PhD Thesis]. Wuhan: Huazhong University of Science and Technology
[22]	李书田. 2020. 火箭燃气射流动力学分析. [硕士论文]. 南京: 南京理工大学 Li S T. 2020. Dynamic analysis of rocket jet flow. [Master Thesis]. Nanjing: Nanjing University of Science & Technology
[23]	黎旭. 2018. 代理模型技术及其在飞行器可靠性优化中的应用研究. [博士论文]. 西安: 西北工业大学 Li X. 2018. Surrogate model technology and its application to aircraft reliability-based optimization. [PhD Thesis]. Xi’an: Northwestern University of Technology
[24]	刘安民, 高峰, 张青斌等. 2021. 基于多项式混沌展开方法的翼伞飞行不确定性. 兵工学报, 42: 1392-1399 Liu AM, Gao F, Zhang QB, et al. 2021. Application of PCE method in parafoil-flight uncertainty analysis. Acta Armamentarii, 42: 1392-1399
[25]	刘成武, 李连升, 钱林方. 2015. 随机与区间不确定下基于近似灵敏度的序列多学科可靠性设计优化. 机械工程学报, 51: 174-184 (Liu C W, Li L S, Qian L F. 2015. Sequence multidisciplinary reliability design optimization based on approximate sensitivity method under random and interval uncertainties. Journal of Mechanical Engineering, 51: 174-184). doi: 10.3901/JME.2015.21.174 (Liu C W, Li L S, Qian L F. 2015. Sequence multidisciplinary reliability design optimization based on approximate sensitivity method under random and interval uncertainties. Journal of Mechanical Engineering, 51 (21): 174-184). doi: 10.3901/JME.2015.21.174
[26]	刘刚, 张瀚方, 池骋等. 2018. 二维电磁场-流体-温度场耦合仿真节点数据映射算法研究. 电工技术学报, 33: 148-157 (Liu G, Zhang H F, Chi C. 2018. Research on node data mapping algorithm for the 2D coupling electromagnetic-fluid-thermal fields. Transactions of China Electrotechnical Society, 33: 148-157). Liu G, Zhang H F, Chi C. 2018. Research on node data mapping algorithm for the 2D coupling electromagnetic-fluid-thermal fields. Transactions of China Electrotechnical Society, 33(1): 148-157).
[27]	刘君, 徐春光, 白晓征. 2016. 有限体积法和非结构动网格. 北京: 科学出版社 Liu J, Xu C G, Bai X Z. 2016. Finite Volume Method and Unstructric Dynamic Mesh. Beijing: Science Press
[28]	刘深深. 2014. 气动力-热-结构多场耦合数据传递方法研究 .[硕士论文]. 绵阳: 中国空气动力研究与发展中心 Liu S S. 2014. Study on the data interpolation methods of fluid-structure-thermal interaction problems .[Master Thesis]. Mianyang: China Aerodynamics Research and Development Center in Fluid Mechanics
[29]	路成. 2016. 基于耦合失效多重响应面的结构可靠性分析方法研究 .[硕士论文]. 哈尔滨: 哈尔滨理工大学 Lu C. 2016. Study of structural reliability anlysis method based on coupling failure multiple response surface .[Master Thesis]. Harbin: Harbin University of Science and Technology
[30]	孟德彪, 黄洪钟, 许焕卫等. 2011. 一种多学科系统不确定性分析方法——协同不确定性分析法的改进. 机械工程学报, 47: 129-135 (Meng D B, Huang H Z, Xu H W. 2011. An improvement method for uncertainty analysis in multidisciplinary system—modified collaborative uncertainty analysis. Journal of Mechanical Engineering, 47: 129-135). doi: 10.3901/JME.2011.19.129 (Meng D B, Huang H Z, Xu H W. 2011. An improvement method for uncertainty analysis in multidisciplinary system—modified collaborative uncertainty analysis. Journal of Mechanical Engineering, 47 (19): 129-135). doi: 10.3901/JME.2011.19.129
[31]	孟欣佳. 2016. 考虑混合不确定性的多学科可靠性设计优化方法研究 .[博士论文]. 北京: 北京理工大学 Meng X J. 2016. Research on reliability based multidisciplinary design optimization with mixed uncertainties .[PhD Thesis]. Beijing: Beijing Institute of Technology
[32]	牛明涛, 李昌盛, 陈利源. 2015. 含区间参数的结构-声耦合系统摄动分析方法. 振动与冲击, 34(10): 194-198 Niu M T, Li C S, Chen L Y. 2015. Perturbation methods for structural-acoustic coupled systems with interval parameters, Journal of Vibration and Shock, 34 (10): 194-198
[33]	屈小章, 余江鸿, 姚齐水等. 2020. 基于随机-区间混合不确定性的风机性能可靠性分析. 中国科学: 技术科学, 50(3): 299-311 Qu X Z, Yu J H, Yao Q S. 2020. Random-interval hybrid reliability analysis for fan performance in the presence of epistemic uncertainty. Scientia Sinica Technologica, 50(3): 299-311
[34]	芮筱亭, 贠来峰, 陆毓琪等. 2008. 多体系统传递矩阵法及其应用. 北京: 科学出版社 Rui X T, Yun L F, Lu Y Q. 2008. Transfer Matrix Method of Multibody System and its Applications. Beijing: Science Press
[35]	芮雪, 陈东阳, 王国平. 2020. 海洋热塑性增强管(RTP)涡激振动数值计算. 力学学报, 52: 235-246 (Rui X, Chen D Y, Wang G P. 2020. Numerical calculation of vortex-induced vibration of reinforced thermoplastic pipe. Chinese Journal of Theoretical and Applied Mechanics, 52: 235-246). doi: 10.6052/0459-1879-19-312 (Rui X, Chen D Y, Wang G P. 2020. Numerical calculation of vortex-induced vibration of reinforced thermoplastic pipe. Chinese Journal of Theoretical and Applied Mechanics, 52(1): 235-246). doi: 10.6052/0459-1879-19-312
[36]	芮延年, 傅戈雁. 2007. 现代可靠性设计. 北京: 国防工业出版社 Rui Y N, Fu G Y. 2007. Modern Reliability Design. Beijing: National Defense Industry Press
[37]	石磊, 闫溟, 杨云军等. 2013. 网格变形在俯仰振荡翼型中的应用. 航空计算技术, 43: 69-71 (Shi L, Yan M, Yang Y J. 2013. A CFD method of containing structure deformation. Aeronautical Computing Technology, 43: 69-71). doi: 10.3969/j.issn.1671-654X.2013.06.018 (Shi L, Yan M, Yang Y J. 2013. A CFD method of containing structure deformation. Aeronautical Computing Technology, 43 (6): 69-71). doi: 10.3969/j.issn.1671-654X.2013.06.018
[38]	宋少云. 2007. 多场耦合问题的协同求解方法研究与应用 .[博士论文]. 武汉: 华中科技大学 Song S Y. 2007. Research and application of collaborative solution method for multiphysics problems .[PhD Thesis]. Wuhan: Huazhong University of Science and Technology
[39]	宋少云, 李世其. 2006. 耦合场协同仿真中节点载荷插值的混合法. 计算机仿真, 23(8): 73-75 Song S Y, Li S Q. 2006. Mixed method of node load interpolation in collaborative simulation of coupled problem. Computer Simulation, 23(8): 73-75
[40]	孙鹏, 陈晨, 程涵. 2017. 基于有限元网格重构的降落伞工作过程数值研究. 科学技术与工程, 17: 139-144 (Sun P, Cheng C, Chen H. 2017. Numerical simulation of parachute working process based on finite element mesh reconstruction. Science Technology and Engineering, 17: 139-144). doi: 10.3969/j.issn.1671-1815.2017.25.022 (Sun P, Cheng C, Chen H. 2017. Numerical simulation of parachute working process based on finite element mesh reconstruction. Science Technology and Engineering, 17(25): 139-144). doi: 10.3969/j.issn.1671-1815.2017.25.022
[41]	孙岩, 邓小刚, 王光学等. 2013. 基于径向基函数改进的Delaunay图映射动网格方法. 航空学报, 35: 727-735 (Sun Y, Deng X G, Wang X G. 2013. Improvement on Delaunay graph mapping dynamic grid method based on radial basis functions. Acta Aeronautica et Astronautica Sinica, 35: 727-735). (Sun Y, Deng X G, Wang X G. 2013. Improvement on Delaunay graph mapping dynamic grid method based on radial basis functions. Acta Aeronautica et Astronautica Sinica, 35(3): 727-735).
[42]	孙岩, 孟德虹, 王运涛等. 2018. 径向基/超限插值结构网格运动方法中的变形一致性问题. 计算机辅助设计与图形学学报, 30: 354-359 (Sun Y, Meng D H, Wang Y T. 2018. Dynamic grid deform ation technique based on Delaunay graph mapping for aeroelastic investigation. Journal of Computer-Aided Design & Computer Graphics, 30: 354-359). (Sun Y, Meng D H, Wang Y T. 2018. Dynamic grid deform ation technique based on Delaunay graph mapping for aeroelastic investigation. Journal of Computer-Aided Design & Computer Graphics, 30(2): 354-359).
[43]	孙作振. 2014. 基于区间法的结构非概率可靠性研究 .[博士论文]. 长春: 吉林大学 Sun Z Z. 2014. Structural non-probabilistic reliabilty study based on interval method .[PhD Thesis]. Changchun: Jilin University
[44]	唐新姿, 王喆, 王效禹等. 2020. 多源不确定耦合下离心压气机叶轮气动稳健性. 航空动力学报, 35: 196-204 (Tang X Z, Wang Z, Wang X Y. 2020. Aerodynamic robustness of centrifugal compressor impellers under multi-source uncertain coupling. Journal of Aerospace Power, 35: 196-204). doi: 10.13224/j.cnki.jasp.2020.01.023 (Tang X Z, Wang Z, Wang X Y. 2020. Aerodynamic robustness of centrifugal compressor impellers under multi-source uncertain coupling. Journal of Aerospace Power, 35 (1): 196-204). doi: 10.13224/j.cnki.jasp.2020.01.023
[45]	王晗落. 2017. 基于凸模型的声固耦合系统分析与优化方法研究. [硕士论文]. 长沙: 湖南大学 Wang H L. 2017. Analysis and optimization of acoustic-structural coupled system based on convex model. [Master Thesis]. Changsha: Hunan University
[46]	王明杰. 2017. 基于代理模型的声振耦合系统不确定分析与优化方法研究. [博士论文]. 武汉: 华中科技大学 Wang M J. 2017. Research of uncertain analysis and optimization for the structural-acoustic coupled system based on the surrogate model technique. [PhD Thesis]. Wuhan: Huazhong University of Science ang Technology
[47]	王若冰, 谷良贤, 龚春林. 2016. 随机-区间混合不确定性分层序列化多学科可靠性分析方法. 西北工业大学学报, 34: 139-146 (Wang R B, Gu L X, Gong C L. 2016. A stratified sequencing multi-disciplinary reliability analysis method under random and interval uncertainty. Journal of Northwestern Polytechnical University, 34: 139-146). doi: 10.3969/j.issn.1000-2758.2016.01.021 (Wang R B, Gu L X, Gong C L. 2016. A stratified sequencing multi-disciplinary reliability analysis method under random and interval uncertainty. Journal of Northwestern Polytechnical University, 34 (1): 139-146). doi: 10.3969/j.issn.1000-2758.2016.01.021
[48]	王思莹, 陈明, 尹协振. 2014. 柔性体与运动流体耦合问题研究进展综述. 力学与实践, 36: 566-573 (Wang S Y, Chen M, Yin X Z. 2014. The interaction between flexible bodies and moving fluid. Mechanics in Engineering, 36: 566-573). doi: 10.6052/1000-0879-13-510 (Wang S Y, Chen M, Yin X Z. 2014. The interaction between flexible bodies and moving fluid. Mechanics in Engineering, 36(5): 566-573). doi: 10.6052/1000-0879-13-510
[49]	汪学锋, 李锋, 周炜等. 2009. 流固耦合网格插值方法研究. 船舶力学, 13: 571-578 (Wang X F, Li F, Zhou W. 2009. Research on grid interpolation method of fluid-structure coupling. Journal of Ship Mechanics, 13: 571-578). doi: 10.3969/j.issn.1007-7294.2009.04.009 (Wang X F, Li F, Zhou W. 2009. Research on grid interpolation method of fluid-structure coupling. Journal of Ship Mechanics, 13 (4): 571-578). doi: 10.3969/j.issn.1007-7294.2009.04.009
[50]	吴帆. 2016. CO₂地质封存中热—流—固多场耦合并行数值模拟研究. [硕士论文]. 长春: 吉林大学 Wu F. 2016. Research on parallel numerical simulation of THM multi-physical coupling based on CO₂ geologic storage. [Master Thesis]. Changchun: Jilin University.
[51]	吴景铼. 2013. 基于Chebyshev多项式的动力学不确定性区间算法研究. [博士论文]. 武汉: 华中科技大学 Wu J L. 2013. Dynamics uncertainty research based on interval arithmetic using Chebyshev polynomials. [PhD Thesis]. Wuhan: Huazhong University of Science ang Technology
[52]	吴晓, 罗佑新, 文会军等. 2003. 非确定结构系统区间分析的泛灰求解方法. 计算力学学报, 20: 329-334 (Wu X, Luo Y X, Wen H J. 2003. Interval analysis method of uncertain structural systems using universal grey number. Chinese Journal of Computational Mechanics, 20: 329-334). doi: 10.3969/j.issn.1007-4708.2003.03.014 (Wu X, Luo Y X, Wen H J. 2003. Interval analysis method of uncertain structural systems using universal grey number. Chinese Journal of Computational Mechanics, 20 (3): 329-334). doi: 10.3969/j.issn.1007-4708.2003.03.014
[53]	吴宗敏. 2007. 散乱数据拟合的模型、方法和理论. 北京: 科学出版社 Wu Z M. 2007. Models, Methods, and Theories for the Fitting of Scattered Data. Beijing: Science Press
[54]	熊彦铭, 杨战平. 2012. 基于证据理论的系统非概率可靠性分析. 信息与电子工程, 10: 169-172 (Xiong Y M, Yang Z P. 2012. Non-probability system reliability analysis based on evidence theory. Information and Electronic Engineering, 10: 169-172). doi: 10.3969/j.issn.1672-2892.2012.02.010 (Xiong Y M, Yang Z P. 2012. Non-probability system reliability analysis based on evidence theory. Information and Electronic Engineering, 10 (2): 169-172). doi: 10.3969/j.issn.1672-2892.2012.02.010
[55]	徐琳, 宋万强. 2019. 基于动态网格的多体分离计算技术研究. 航空科学技术, 30: 7-13 (Xu L, Song W Q. 2019. Research on numerical simulation technology of multi-body separation based on dynamic grid. Aeronautical Science and Technology, 30: 7-13). doi: 10.19452/j.issn1007-5453.2019.02.002 Xu L, Song W Q, 2019. Research on numerical simulation technology of multi-body separation based on dynamic grid. Aeronautical Science and Technology, 30(2): 7-13). doi: 10.19452/j.issn1007-5453.2019.02.002
[56]	徐敏, 陈士橹. 2004. CFD/CSD耦合计算研究. 应用力学学报, 21: 33-36 (Xu M, Chen S L. 2004. Study of date exchange metod for coupling computational CFD/CSD. Chinese Journal of Applied Mechanics, 21: 33-36). doi: 10.3969/j.issn.1000-4939.2004.02.006 (Xu M, Chen S L. 2004. Study of date exchange metod for coupling computational CFD/CSD. Chinese Journal of Applied Mechanics, 21(2): 33-36). doi: 10.3969/j.issn.1000-4939.2004.02.006
[57]	夏百战. 2015. 不确定声固耦合系统的数值分析与优化方法研究. [博士论文]. 长沙: 湖南大学 Xia B Z. 2015. A research on the numerical analysis and optimization method for the nondeterministic acoustic-structural coupled system. [PhD Thesis]. Changsha: Hunan University
[58]	杨敏, 王福军, 戚兰英等. 2011. 流固耦合界面模型及其在水力机械动力学分析中的应用. 水利学报, 7: 819-825 (Yang M, Wang F J, Qi L Y. 2011. Fluid-structure coupling interface model and its application in dynamic analysis of hydraulic machinery. ShuiLi XueBao, 7: 819-825). doi: 10.13243/j.cnki.slxb.2011.07.018 (Yang M, Wang F J, Qi L Y. 2011. Fluid-structure coupling interface model and its application in dynamic analysis of hydraulic machinery. ShuiLi XueBao, 7: 819-825). doi: 10.13243/j.cnki.slxb.2011.07.018
[59]	杨瑞. 2015. 基于ALE有限元法的飞机整体油箱燃油晃动特性研究. [硕士论文]. 哈尔滨: 哈尔滨工业大学 Yang R. 2015. Research of fuel sloshing in aircraft integral tanks by the ale finite element method. [Master Thesis]. Harbin: Harbin University of Technology
[60]	尹果. 2014. 基于RBF插值的流固耦合数据传递研究. [硕士论文]. 湘潭: 湘潭大学 Yin G. 2014. Study on radial basis function interpolation in data exchange for fluid-structure interaction. [Master Thesis]. Xiangtan: Xiangtan University
[61]	游检卫. 2016. 高性能多物理场数值算法研究及其应用. [博士论文]. 南京: 东南大学 You J W. 2016. High-performance numerical method of multi-physics and its applications. [PhD Thesis]. Nanjing: Southeast University
[62]	云永琥, 陈建军, 曹鸿钧. 2016. 改进Kriging的热结构耦合梁共振非概率可靠性分析. 哈尔滨工业大学学报, 48: 131-136 (Yun Y H, Chen J J, Cao H J. 2016. Non-probabilistic reliability analysis on resonance of thermal-structural coupling of a beam based on improved Kriging. Journal of Harbin University of Technology, 48: 131-136). (Yun Y H, Chen J J, Cao H J. 2016. Non-probabilistic reliability analysis on resonance of thermal-structural coupling of a beam based on improved Kriging. Journal of Harbin University of Technology, 48(10): 131-136).
[63]	云永琥, 陈建军, 赵宽. 2014. 区间参数梁结构热弹耦合效应分析. 西安电子科技大学学报(自然科学版), 41: 64-70 (Yun Y H, Chen J J, Zhao K. 2014. Analysis of thermo-elastic coupling effects of the beam structure with interval parameters. Journal of Xidian University, 41: 64-70). (Yun Y H, Chen J J, Zhao K. 2014. Analysis of thermo-elastic coupling effects of the beam structure with interval parameters. Journal of XIDIAN University).
[64]	张斌, 丰志伟, 杨涛等. 2018. 几何约束的改进弹性体网格变形方法研究及应用. 国防科技大学学报, 40: 23-29 (Zhang B, Feng Z W, Yang T. 2018. Research and application of improved elasticity-based mesh deformation method based on geometry constraints. Journal of National University of Defense Technology, 40: 23-29). Zhang B, Feng Z W, Yang T. 2018. Research and application of improved elasticity-based mesh deformation method based on geometry constraints Journal of National University of Defense Technology, 40(6): 23-29.
[65]	张兵. 2011. 高超声速多场耦合及其GPU计算. [博士论文]. 南京: 南京航空航天大学 Zhang B. 2011. Studies on hypersonic multi-field coupled computation and its acceleration using GPU. [PhD Thesis]. Nanjing: Nanjing University of Aeronautics and Astronautics
[66]	张福才. 2015. 红外高温温度场中非完全温度点重建方法与预测精度的研究. 红外与激光工程, 44: 2598-2602 (Zhang F C. 2015. Research on temperature reconstruction method and the precision by non-complete temperature point in infrared high temperature field. Infrared and Laser Engineering, 44: 2598-2602). doi: 10.3969/j.issn.1007-2276.2015.09.010 (Zhang F C. 2015. Research on temperature reconstruction method and the precision by non-complete temperature point in infrared high temperature field. Infrared and Laser Engineering, 44(9): 2598-2602). doi: 10.3969/j.issn.1007-2276.2015.09.010
[67]	张来平, 邓小刚, 张涵信. 2010. 动网格生成技术及非定常计算方法进展综述. 力学进展, 40: 424-447 (Zhang L P, Deng X G, Zhang H X. 2010. Reviews of moving grid generation techniques and numerical methods for unsteady flow. Advances in Mechanics, 40: 424-447). doi: 10.6052/1000-0992-2010-4-J2009-123 (Zhang L P, Deng X G, Zhang H X. 2010. Reviews of moving grid generation techniques and numerical methods for unsteady flow. Advances in Mechanics, 40(4): 424-447). doi: 10.6052/1000-0992-2010-4-J2009-123
[68]	张雄, 刘岩. 2004. 无网格法. 北京: 清华大学出版社/Springer出版社 Zhang X, Liu Y. 2004. Meshloss Methods. Beijing: Tsinghua University Press/Springer Press
[69]	张屹尚, 刘永寿, 赵彬等. 2012. 基于Kriging模型的充液管道共振非概率可靠性分析. 振动工程学报, 25: 117-123 (Zhang Y S, Liu Y S, Zhao B. 2012. Non-probability reliability analysis on resonance of fluid-filled pipeline based on Kriging model. Journal of Vibration Engineering, 25: 117-123). doi: 10.3969/j.issn.1004-4523.2012.02.003 (Zhang Y S, Liu Y S, Zhao B. 2012. Non-probability reliability analysis on resonance of fluid-filled pipeline based on Kriging model. Journal of Vibration Engineering, 25 (2): 117-123). doi: 10.3969/j.issn.1004-4523.2012.02.003
[70]	张文生. 2006. 科学计算中的偏微分方程有限差分法. 北京: 高等教育出版社 Zhang W S. 2006. Finite Difference Method for Partial Differential Equations in Science Computation. Beijing: Higher Education Press
[71]	赵宽. 2014. 不确定多体系统动力学分析及可靠性预测. [博士论文]. 西安: 西安电子科技大学 Zhao K. 2014. Dynamic analysis and predicition on reliability of multi-body system with uncertainty. [PhD Thesis]. Xi’an: Xidian University
[72]	赵振. 2011. 面向电磁-机械耦合的异构仿真系统瞬态场分析技术及应用. [博士论文]. 杭州: 浙江大学 Zhao Z. 2011. Study and applications on transient field of heterogeneous simulation system for electromagnetic-mechanical coupling. [PhD Thesis]. Hangzhou: Zhejiang University
[73]	仲继泽, 徐自力, 陶磊. 2016. 基于虚拟弹性体的快速动网格方法. 西安交通大学学报, 50: 132-138 (Zhong J Z, Xu Z L, Tao L. 2016. An effcient dynamic mesh method based on pseudo elastic solid. Journal of Xi'an Jiao University, 50: 132-138). doi: 10.7652/xjtuxb201610020 (Zhong J Z, Xu Z L, Tao L. 2016. An effcient dynamic mesh method based on pseudo elastic solid. Journal of Xi'an Jiao university, 50(10): 132-138). doi: 10.7652/xjtuxb201610020
[74]	周宏, 李俊峰, 王天舒. 2008. 基于ALE有限元方法的充液刚体耦合动力学仿真. 清华大学学报(自然科学版), 48: 33-36 (Zhou H, Li J F, Wang T S. 2008. Dynamics simulation of a fluid-filled coupling system using the ALE finite element method. J Tsinghua Univ (Sci & Tech), 48: 33-36). doi: 10.3321/j.issn:1000-0054.2008.11.034 (Zhou H, Li J F, Wang T S. 2008. Dynamics simulation of a fluid-filled coupling system using the ALE finite element method. J Tsinghua Univ (Sci& Tech), 48 (11): 33-36). doi: 10.3321/j.issn:1000-0054.2008.11.034
[75]	周璇, 李水乡, 孙树立等. 2011. 非结构网格变形方法研究进展. 力学进展, 41: 71-85 (Zhou X, Li S X, Sun S L. 2011. Advances in the research on unstructured mesh deformation. Advances in Mechanics, 41: 71-85). doi: 10.6052/1000-0992-2011-5-lxjzJ2011-050 (Zhou X, Li S X, Sun S L. 2011. Advances in the research on unstructured mesh deformation. Advances in Mechanics, 41(5): 71-85). doi: 10.6052/1000-0992-2011-5-lxjzJ2011-050
[76]	Abgrall R, Dobrzynski C, Froehly A. 2014. A method for computing curved meshes via the linear elasticity analogy, application to fluid dynamics problems. International Journal for Numerical Methods in Fluids, 76: 246-266. doi: 10.1002/fld.3932
[77]	Agarwal H, Renaud J E, Preston E L, et al. 2004. Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering & System Safety, 85: 281-294.
[78]	Ahn J, Kwon J H. 2004. Sequential approach to reliability analysis of multidisciplinary analysis systems. Structural and Multidisciplinary Optimization, 28: 397-406. doi: 10.1007/s00158-004-0459-z
[79]	An X M, Xu M, Chen S L. 2009. An improved CFD/CSD coupled system design and application based on bem approach//2nd International Conference on Modelling and Simulation. Manchester, England.
[80]	Andrieu-Renaud C. Sudret B. Lemaire M. 2004. The PHI2 method: a way to compute time-variant reliability. Reliability Engineering & System Safety, 84: 75-86. doi: 10.1016/j.ress.2003.10.005
[81]	Ang G L, Ang H S, Tang W H. 1992. Optimal importance-sampling density estimator. Journal of Engineering Mechanics 118(6): 1146–1163.
[82]	Aoues Y, Chateauneuf A. 2010. Benchmark study of numerical methods for reliability-based design optimization. Structural and Multidisciplinary Optimization, 41: 277-294. doi: 10.1007/s00158-009-0412-2
[83]	Arnold M, Heckmann A. 2007. From multibody dynamics to multidisciplinary applications //García Orden J C, Goicolea J M, Cuadrado J, eds. Multibody Dynamics. Computational Methods in Applied Sciences, vol 4. Dordrecht: Springer.
[84]	Astorino M, Chouly F, Fernández M. 2009. Robin based semi-implicit coupling in fluid-structure interaction: Stability analysis and numerics. SIAM Journal on Scientific Computing, 31: 4041-4065.
[85]	Badia S, Nobile F, Vergara C. 2009. Robin–Robin preconditioned Krylov methods for fluid-structure interaction problems. Comput. Methods Appl. Mech. Eng., 198 (33–36): 2768-2784.
[86]	Beckert A, Wendland H. 2001. Multivariate interpolation for fluid–structure-interaction problems using radial basis functions. Aerospace Science and Technology, 5: 125-134. doi: 10.1016/S1270-9638(00)01087-7
[87]	Ben-Haim Y. 1994. A non-probabilistic concept of reliability. Structural Safety, 14(4): 227–245.
[88]	Ben-Haim Y, Elishakoff I. 1990. Convex Models of Uncertainty in Applied Mechanics. Amsterdam: Elsevier.
[89]	Boer A D, Zuijlen A H V, Bijl H. 2007. Review of coupling methods for non-matching meshes. Computer Methods in Applied Mechanics and Engineering, 196: 1515-1525. doi: 10.1016/j.cma.2006.03.017
[90]	Brummelen E V. 2009. Added mass effects of compressible and incompressible flows in fluid-structure interaction. J. Appl. Mech. 76(2): 021206-1–7.
[91]	Bungartz H J, Lindner F, Gatzhammer B, et al. 2016. PreCICE–a fully parallel library for multi-physics surface coupling. Computers & Fluids, 141: 250-258.
[92]	Busch M, Schweizer B. 2012. Coupled simulation of multibody and ﬁnite element systems: an efﬁcient and robust semi-implicit coupling approach. Arch Appl Mech, 82: 723-741. doi: 10.1007/s00419-011-0586-0
[93]	Cavagna L, Quaranta G, Mantegazza P. 2007. Application of Navier–Stokes simulations for aeroelastic stability assessment in transonic regime. Computers & Structures, 85: 818-832.
[94]	Chaudhuri A, Lam R, Willcox K. 2018. Multifidelity uncertainty propagation via adaptive surrogates in coupled multidisciplinary systems. AIAA Journal, 56: 235-249. doi: 10.2514/1.J055678
[95]	Degand C, Farhat C. 2002. A three-dimensional torsional spring analogy method for unstructured dynamic meshes. Computers & Structures, 80: 305-316.
[96]	Degroote J, Bathe K J, Vierendeels J. 2009. Performance of a new partitioned procedure versus a monolithic procedure in fluid-structure interaction. Computers & Structures, 87(11–12): 793-801.
[97]	Degroote J, Bruggeman P, Haelterman R, et al. 2008. Stability of a coupling technique for partitioned solvers in FSI applications. Computers and Structures, 86: 2224-2234. doi: 10.1016/j.compstruc.2008.05.005
[98]	Degroote J, Vierendeels J. 2011. Multi-solver algorithms for the partitioned simulation of fluid–structure interaction. Computer Methods in Applied Mechanics and Engineering, 200: 2195-2210. doi: 10.1016/j.cma.2011.03.015
[99]	Denimal E, Nechak L, Sinou J J, et al. 2018. A novel hybrid surrogate model and its application on a mechanical system subjected to friction-induced vibration. Journal of Sound and Vibration, 434: 456-474.
[100]	Dettmer W, Perić D. 2006. A computational framework for fluid–rigid body interaction: Finite element formulation and applications. Computer Methods, in Applied Mechanics and Engineering, 195: 1633-1666. doi: 10.1016/j.cma.2005.05.033
[101]	Dietz S, Hippmann G. , Schupp G. 2001. Interaction of vehicles and flexible tracks by cosimulation of multibody vehicle systems and finite element track models //17th Symposium Dynamics of Vehicles on Roads and Tracks IAVSD 2001, Copenhagen.
[102]	Donea J, Huerta A, Ponthot J P, et al. 2004. Chapter 14: Arbitrary lagrangian-eulerian methods //Stein E, de Borst R, Hughes T J R, Eds. Encyclopedia of Computational Mechanics, Volume 1: Fundamentals. Chichester, West Sussex. England; Wiley, 413-438.
[103]	Dong X, Zhang Z, Tian Z, et al. , 2016. A high effective parallel method for the coupling between neutronics and thermal-hydraulic //24th International Conference on Nuclear Engineering.
[104]	Du X. 2006. Uncertainty analysis with probability and evidence theories // ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 1025-1038.
[105]	Du X, Chen W. 2000. Concurrent subsystem uncertainty analysis in multidisciplinary design // The 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization. Long Beach, CA., 1-11.
[106]	Rezaei M, Fazelzadeh S, Mazidi A, et al. 2020. Fuzzy uncertainty analysis and reliability assessment of aeroelastic aircraft wings. The Aeronautical Journal, 124: 786-811. doi: 10.1017/aer.2020.2
[107]	Du X, Chen W. 2002. Collaborative reliability analysis for multidisciplinary systems design // Proc. of the 9th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, Georgia, AIAA-2002-5474.
[108]	Duchon J. 1977. Splines minimizing rotation-invariant semi-norms in sobolev spaces//Schempp W, Zeller K, eds. Constructive Theory of Functions of Several Variables, Oberwolfach 1976, Berlin: Springer–Verlag, 85–100.
[109]	Erbts P, Hartmann S, Düster A. 2015. A partitioned solution approach for electro-thermo-mechanical problems. Archive of Applied Mechanics, 85: 1075-1101. doi: 10.1007/s00419-014-0941-z
[110]	Estruch O, Lehmkuhl O, Borrell R, et al. 2013. A parallel radial basis function interpolation method for unstructured dynamic meshes. Computers & Fluids, 80: 44-54.
[111]	Faigle B, Helmig R, Aavatsmark I, et al. 2014. Efficient multiphysics modelling with adaptive grid refinement using a MPFA method. Computational Geosciences, 18: 625-636. doi: 10.1007/s10596-014-9407-1
[112]	Felippa C A, Park K C. 2005. In engineering structures under extreme conditions: multi-physics and multi-scale computer models in non-linear analysis and optimal design // Synthesis Tools for Structural Dynamics and Partitioned Analysis of Coupled Systems. Amsterdam: IOS Press.
[113]	Fernández M A. 2011. Coupling schemes for incompressible fluid-structure interaction: implicit, semi-implicit and explicit. Boletín de la Sociedad Españ ola de Matemática Aplicada, 55: 59-108.
[114]	Fernández M A, Gerbeau J F, Grandmont C. 2007. A projection semi-implicit scheme for the coupling of an elastic structure with an incompressible fluid. International Journal for Numerical Methods in Engineering, 69: 794-821. doi: 10.1002/nme.1792
[115]	Gerstner T, Griebel M. 1998. Numerical integration using sparse grids. Numer Algorithms, 18: 209-232.
[116]	Giles, M B. 2013. Multilevel Monte Carlo methods // Dick J, Kuo F, Peters G, et al. eds. Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer Proceedings in Mathematics & Statistics, vol 65. Berlin, Heidelberg: Springer.
[117]	Goura G, Badcock K, Woodgate M, Richards B. 2001. A data exchange method for ﬂuid-structure interaction problems. The Aeronautical Journal, 105: 215-221. doi: 10.1017/S0001924000025458
[118]	Guo J, Du X P. 2010. Reliability analysis for multidisciplinary systems with random and interval variables. AIAA Journal, 48: 82-91. doi: 10.2514/1.39696
[119]	Hardy R L. 1971. Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research, 76: 1905-1915. doi: 10.1029/JB076i008p01905
[120]	Harder R L, Desmarais R N. 1972. Interpolation using surface splines. AIAA Journal, 9: 189-191.
[121]	Helenbrook B T. 2003. Mesh deformation using the biharmonic operator. International Journal for Numerical Methods in Engineering, 56: 1007-1021. doi: 10.1002/nme.595
[122]	Heres P J, Deschrijver P J, Schilders W H A, Dhaene T. 2007. Combining krylov subspace methods and identification-based methods for model order reduction. International Journal of Numerical Modelling:Electronic Networks, Devices and Fields, 20: 271-282. doi: 10.1002/jnm.644
[123]	Hron J, Turek S. 2006. A monolithic FEM/Multigrid Solver for ALE formulation of fluid structure interaction with application in biomechanics, simulation, optimisation // Bungartz H-J, Schäfer M, Eds. Fluid-structure interaction-modelling, Lecture Notes in Computational Science and Engineering, 53, 146-170.
[124]	Hu W, Tian Q, Hu H Y. 2018. Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid. Science China Physics, Mechanics & Astronomy, 61: 044711. doi: 10.1007/s11433-017-9127-3
[125]	Hu Z, Du X. 2013. A sampling approach to extreme value distribution for time-dependent reliability analysis. Journal of Mechanical Design, 135: 689-698.
[126]	Huang S, Xu Y, Zhang L, et al. 2018. A data exchange algorithm for one way fluid-structure interaction analysis and its application on high-speed train coupling interface. Journal of Applied Fluid Mechanics, 11: 519-526. doi: 10.29252/jafm.11.02.27321
[127]	Ihlenburg F. 2000. Computational experience from the solution of coupled problems in ship dynamics // Sändig A M, Schiehlen W, Wendland W L, eds. Multifield Problems. Berlin, Heidelberg: Springer.
[128]	Ihrle S, Lauxmann M, Eiber A, et al. 2013. Nonlinear modelling of the middle ear as an elastic multibody system-Applying model order reduction to acousto-structural coupled systems. Journal of Computational and Applied Mathematics, 246: 18-26. doi: 10.1016/j.cam.2012.07.010
[129]	Irons B, Tuck R C. 1969. A version of the Aitken accelerator for computer iteration. International Journal for Numerical Methods in Engineering, 1: 275-277. doi: 10.1002/nme.1620010306
[130]	Jiang G Q, Yao L Y, Wu F. 2018. A stochastic perturbation finite element-least square point interpolation method for the analysis of uncertain structural-acoustics problems with random variables. Applied Acoustics, 137: 18-26. doi: 10.1016/j.apacoust.2018.03.003
[131]	Jin X J, Yang S Q, Chen H, et al. 2018. A time-dependent uncertainty design and optimization strategy using an enhanced Kriging surrogate model. Advances in Mechanical Engineering, 10: 1687814018796322.
[132]	Joosten M M, Dettmer W G, Perić D. 2009. Analysis of the block Gauss–Seidel solution procedure for a strongly coupled model problem with reference to fluid–structure interaction. International Journal for Numerical Methods in Engineering, 78: 757-778. doi: 10.1002/nme.2503
[133]	Kansa E J. 1990. Multiquadrics-a scattered data approximation scheme with applications to computational fluid dynamics Parts I and II. Computers and Mathematics with Applications, 19: 127-161.
[134]	Kaufmann A. 1975. Introduction to the Theory of Fuzzy Subset. New York: Academic Press.
[135]	Kim Y H, Kim J E. 2005. A new hybrid interpolation method using surface tracking, fitting and smoothing function applied for aeroelasticity // 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Austin, Texas.
[136]	Kieu D T, Bergeot B, Gobert M L, et al. 2019. Stability analysis of a clutch system with uncertain parameters using sparse polynomial chaos expansions. Mechanics & Industry, 20: 104.
[137]	Küttler U, Wall W A. 2006. An approach for parallel fluid-structure interaction on unstructured meshes // Mohr B, Träff J L, Worringen J, Dongarra J, eds. Recent Advances in Parallel Virtual Machine and Message Passing Interface. EuroPVM/MPI 2006. Lecture Notes in Computer Science, vol 4192. Berlin, Heidelberg: Springer.
[138]	Küttler U, Wall W A. 2008. Fixed-point fluid–structure interaction solvers with dynamic relaxation. Comput. Mech., 1: 61-72.
[139]	Lee S H, Chen W, Kwak B M. 2009. Robust design with arbitrary distributions using Gauss-type quadrature formula. Struct Multidiscipl Optim, 39: 227-243. doi: 10.1007/s00158-008-0328-2
[140]	Li Y, Jiang P, Gao L, et al. 2013. Sequential optimisation and reliability assessment for multidisciplinary design optimisation under hybrid uncertainty of randomness and fuzziness. Journal of Engineering Design, 24: 363-382. doi: 10.1080/09544828.2012.753995
[141]	Lü H, Shangguan W B, Yu D J. 2017. A unified approach for squeal instability analysis of disc brakes with two types of random-fuzzy uncertainties. Mechanical Systems and Signal Processing, 93: 281-298.
[142]	Lunk C, Simeon B. 2006. The reverse method of lines in flexible multibody dynamics // 14th European Conference for Mathematics in Industry, Leganes, Spain.
[143]	Lutes L D, Sarkani S. 2009. Reliability analysis of system subject to first-passage failure. NASA Technical Report no. NASA/CR-2009-215782.
[144]	Long X Y, Mao D L, Jiang C, et al. 2019. Unified uncertainty analysis under probabilistic, evidence, fuzzy and interval uncertainties. Computer Methods in Applied Mechanics and Engineering, 355: 1-26.
[145]	Man J, Zhang J J, Wu L S, et al. 2018. ANOVA-based multi-fidelity probabilistic collocation method for uncertainty quantification. Advances in Water Resources, 122: 176-186. doi: 10.1016/j.advwatres.2018.10.012
[146]	Markou G A, Mouroutis Z S, Charmpis D C, et al. 2007. The ortho-semi-torsional (OST) spring analogy method for 3D mesh moving boundary problems. Computer Methods in Applied Mechanics and Engineering, 196: 747-765. doi: 10.1016/j.cma.2006.04.009
[147]	Martowicz A, Uhl T. 2012. Reliability- and performance-based robust design optimization of MEMS structures considering technological uncertainties. Mechanical Systems and Signal Processing, 32: 44-58. doi: 10.1016/j.ymssp.2012.04.022
[148]	Massat J P, Laurent C., Bianchi J P, et al. 2014. Pantograph catenary dynamic optimisation based on advanced multibody and finite element co-simulation tools. Vehicle System Dynamics, 52: 338-354.
[149]	Michler C, Brummelen E V, Borst R D. 2005. An interface Newton–Krylov solver for fluid-structure interaction. Int. J. Numer. Methods Fluids, 47: 1189-1195.
[150]	Nannapaneni S, Mahadevan S. 2020. Probability-space surrogate modeling for fast multidisciplinary optimization under uncertainty. Reliability Engineering & System Safety, 198: 106896.
[151]	Negrut D, Tasora A, Mazhar H, et al. 2012. Leveraging parallel computing in multibody dynamics. Multibody System Dynamics, 27: 95-117. doi: 10.1007/s11044-011-9262-y
[152]	Néron D, Ladevèze P. 2010. Proper generalized decomposition for multiscale and multiphysics problems. Archives of Computational Methods in Engineering, 17: 351-372. doi: 10.1007/s11831-010-9053-2
[153]	Niesner R, Haupt M, Horst P. 2006. Transient analysis methods for hypersonic applications with thermo-mechanical fluid-structure interaction. // Motasoares C A et al. eds. III European Conference on Computational Mechanics. Springer, Dordrecht.
[154]	Ogiso, Sekitomi, Yamakawa, et al. 2010. Dynamic characteristics analysis of incremental sensor using 3-D finite element method with mesh modification method based on Laplace equation // 14th Biennial IEEE Conference on Electromagnetic Field Computation, CEFC 2010.
[155]	Padmanabhan D, Batill S. 2002. Decomposition strategies for reliability based optimization in multidisciplinary system design // Proceedings of the 9th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta.
[156]	Pan C Y, Wei W L, Zhang C Y, et al. 2015. Reliability analysis of turbine blades based on fuzzy response surface method. Journal of Intelligent & Fuzzy Systems, 29: 2467-2474.
[157]	Pidaparti R. 1992. Structural and aerodynamic data transformation using inverse isoparametric mapping. Journal of Aircraft, 29: 507-509. doi: 10.2514/3.46190
[158]	Qiu Z, Wang X. 2009. Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters. Acta Mechanica Sinica, 25: 367-379. doi: 10.1007/s10409-008-0223-5
[159]	Rahman S, Xu H. 2004. A univariate dimension-reduction method for multi-dimensional integration in stochastic mechanics. Prob. Eng. Mech., 19: 393-408. doi: 10.1016/j.probengmech.2004.04.003
[160]	Rajabi M M, Ataie-Ashtiani B, Janssen H. 2015. Efficiency enhancement of optimized Latin hypercube sampling strategies: application to Monte Carlo uncertainty analysis and meta-modeling. Adv. Water. Resour., 76: 127–139.
[161]	Rong B, Rui X T, Lao T. 2013. Discrete time transfer matrix method for launch dynamics modeling and cosimulation of self-propelled artillery system. J. Appl. Mech., 80: 011008. doi: 10.1115/1.4006869
[162]	Rong B, Rui X T, Tao L, et al. 2019. Theoretical modeling and numerical solution methods for flexible multibody system dynamics. Nonlinear Dynamics, 98: 1519-1553. doi: 10.1007/s11071-019-05191-3
[163]	Rong B, Rui X T, Tao L, et al. 2023. Efficient dynamics modeling and analysis for probabilistic uncertain beam systems with geometric nonlinearity and thermal coupling effect, Nonlinear Dynamics, 111: 39-66.
[164]	Rui XT, Zhang JS, Wang X, et al. 2022. Multibody system transfer matrix method: The past, the present, and the future. International Journal of Mechanical System Dynamics, 2: 3-26. doi: 10.1002/msd2.12037
[165]	Rumold W. 2001. Modeling and simulation of vehicles carrying liquid cargo. Multibody System Dynamics, 5: 351-374. doi: 10.1023/A:1011425305261
[166]	Ryan J. 2006. Adaptive mesh refinement and domain decomposition: a framework to study multi-physical and multi-scale phenomena. First application to reacting gas flows // Alexandrov V N, van Albada G D, Sloot P M A, Dongarra J, eds. Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3992. Berlin, Heidelberg: Springer.
[167]	Samareh J A. 2002. Application of quarternions for mesh deformation. NASA Report TM-2002-21646.
[168]	Schilders W H A, Lutowska A. 2014. A novel approach to model order reduction for coupled multiphysics problems // Quarteroni A, Rozza G, eds. Reduced order methods for modeling and computational reduction. MS & A - Modeling, Simulation and Applications, vol 9. Cham: Springer.
[169]	Shafer G. 1976. A mathematical Theory of Evidence. Princeton: Princeton University Press.
[170]	Shah H, Hosder S, Winter T. 2015. Quantification of margins and mixed uncertainties using evidence theory and stochastic expansions. Reliab Eng Syst Saf, 138: 59-72. doi: 10.1016/j.ress.2015.01.012
[171]	Shayanfar M A, Barkhordari M A, Barkhori M, et al. 2017. An adaptive line sampling method for reliability analysis. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 41: 275-282. doi: 10.1007/s40996-017-0070-3
[172]	Shepard D. 1968. A two-dimensional interpolation function for irregularly-spaced data // Proceedings of the 1968 23rd ACM National Conference, 517–524. ACM.
[173]	Smith M J, Cesnik C E S, Hodges D H. 2000. Evaluation of some data transfer algorithms for noncontiguous meshes. J. Aerospace Engineering, 13: 52-58. doi: 10.1061/(ASCE)0893-1321(2000)13:2(52)
[174]	Stein K, Benney R, Kalro V, et al. 2000. Parachute fuid-structure interactions: 3-D computation. Computer Methods in Applied Mechanics and Engineering, 190: 373-386. doi: 10.1016/S0045-7825(00)00208-5
[175]	Sullivan C C, Yamashita H, Sugiyama H, 2022. Reduced order modeling of deformable tire-soil interaction with proper orthogonal decomposition. Computers and Information in Engineering (IDETC-CIE) Conferences, 17(5): 051009.
[176]	Sun WJ, Gong D, Zhou JS. 2015. Study on wheel-rail coupled vibration of metro with co-simulation of finite element analysis and multi-body dynamics simulation. Applied Mechanics and Materials, 752-753: 636-41. doi: 10.4028/www.scientific.net/AMM.752-753.636
[177]	Thévenza P, Blu T, Unser M. 2009. Interpolation revisited. IEEE Trans. Med. Imaging, 19: 739-758.
[178]	Thunnissen D P. 2003. Uncertainty classification for the design and development of complex systems // 3rd Annual Predictive Methods Conference, Newport Beach, CA.
[179]	Tian Q L, Yu Z Q, Lan P, et al. 2022. Model order reduction of thermo-mechanical coupling flexible multibody dynamics via free-interface component mode synthesis method. Mechanism and Machine Theory, 172: 104786. doi: 10.1016/j.mechmachtheory.2022.104786
[180]	Tzvieli A. 1990. Possibility theory: an approach to computerized processing of uncertainty. Journal of the Association for Information Science and Technology, 41: 153-154.
[181]	Vardon P J, Banicescu I, Cleall P J, et al. 2009. Coupled thermo-hydro-mechanical modelling: a new parallel approach //IEEE International Symposium on Parallel & Distributed Processing. IEEE.
[182]	Wall W A. 2012. Computational fluid-solid-mechanics in bio-medical engineering—where to go from here?//ECCOMAS 2012 CD-ROM Proceedings.
[183]	Wang C, Qiu Z P, He Y Y. 2015. Fuzzy interval perturbation method for uncertain heat conduction problem with interval and fuzzy parameters. Int. J. Num. Meth. Eng., 104: 330-346. doi: 10.1002/nme.4932
[184]	Wang L Q, Yang G L, Sun Q Q, et al. 2019. An uncertain optimization method for overall ballistics based on stochastic programming and a neural network surrogate model. Engineering Optimization, 51: 663-679. doi: 10.1080/0305215X.2018.1484122
[185]	Wang P C, Tian H, Zhu H, et al. 2020. Multi-disciplinary design optimization with fuzzy uncertainties and its application in hybrid rocket motor powered launch vehicle. Chinese Journal of Aeronautics, 33: 1454-1467. doi: 10.1016/j.cja.2019.11.002
[186]	Wang S M, Ni Y L, Duan Y F, et al. 2021. Vector form intrinsic finite element method for stochastic analysis of train-track-bridge coupling system. International Journal of Structural Stability and Dynamics, 21: 2140012. doi: 10.1142/S0219455421400125
[187]	Wang W, Kolditz O. 2009. Sparse matrix and solver objects for parallel finite element simulation of multi-field problems// High Performance Computing and Applications, Second International Conference, HPCA 2009, Shanghai, China.
[188]	Wang Y, Qin N, Zhao N. 2018. Delaunay graph-based moving mesh method with damping functions. Chinese Journal of Aeronautics, 31: 40-50.
[189]	Xia B, Yu D. 2013. Modified interval perturbation finite element method for a structural-acoustic system with interval parameters. Journal of Applied Mechanics, 80: 041027. doi: 10.1115/1.4023021
[190]	Xie W H, Yang Y J, Meng S H, et al. 2019. Probabilistic reliability analysis of carbon/carbon composite nozzle cones with uncertain parameters. Journal of Spacecraft and Rockets, 56: 1765-1774. doi: 10.2514/1.A34392
[191]	Xu H, Rahman S. 2004. A generalized dimension-reduction method for multidimensional integration in stochastic mechanics. Int. J. Num. Methods Eng., 61: 1992-2019. doi: 10.1002/nme.1135
[192]	Yamashita H, Arora R, Kanazawa H, et al. 2019. Reduced-order thermomechanical modeling of multibody systems using floating frame of reference formulation. Journal of Multi Body Dynamics, 233: 617-630. doi: 10.1177/1464419318810886
[193]	Yang F L, Chen C H, Young D L. 2011. A novel mesh regeneration algorithm for 2D FEM simulations of flows with moving boundary. Journal of Computational Physics, 230: 3276-3301. doi: 10.1016/j.jcp.2011.01.008
[194]	Yao W, Chen X, Ouyang Q, Van Tooren M. 2013. A reliability-based multidisciplinary design optimization procedure based on combined probability and evidence theory. Structural and Multidisciplinary Optimization, 48: 339-354. doi: 10.1007/s00158-013-0901-1
[195]	Yu S, Wang Z. 2018. A novel time-variant reliability analysis method based on failure processes decomposition for dynamic uncertain structures. Journal of Mechanical Design, 140: 051401. doi: 10.1115/1.4039387
[196]	Yu S, Wang Z, Meng D. 2018. Time-variant reliability assessment for multiple failure modes and temporal parameters. Structural and Multidisciplinary Optimization, 58: 1705-1717. doi: 10.1007/s00158-018-1993-4
[197]	Youn B D, Choi K K. 2004. Selecting probabilistic approaches for reliability-based design optimization. AIAA Journal, 42: 124-131. doi: 10.2514/1.9036
[198]	Zadeh L A. 1965. Fuzzy sets. Information and Control, 8: 338-353. doi: 10.1016/S0019-9958(65)90241-X
[199]	Zayed A, Garbatov Y, Soares C G. 2013. Time variant reliability assessment of ship structures with fast integration techniques. Probabilistic Engineering Mechanics, 32: 93-102.
[200]	Zhang A M, Sun P N, Ming F R, et al. 2017. Smoothed particle hydrodynamics and its applications in fluid-structure interactions. Journal of Hydrodynamics, 29: 187-216. doi: 10.1016/S1001-6058(16)60730-8
[201]	Zhang J, Zhao Y, Zhang Y H, et al. 2013. Non-stationary random vibration of a coupled vehicle-slab track system using a parallel algorithm based on the pseudo excitation method. Journal of Rail and Rapid Transit, 227: 203-216.
[202]	Zhang M C, Yao Q, Sun S Y, et al. 2020. An efficient strategy for reliability-based multidisciplinary design optimization of twin-web disk with non-probabilistic model. Applied Mathematical Modelling, 82: 546-572. doi: 10.1016/j.apm.2020.01.066
[203]	Zhang S J, Zulli P, Feng Y Q, Dong X F, Yu A B. 2003. Effects of differencing schemes on simulation of dense gas-particle two-phase flows // Armfield S W, Morgan P, Srinivas K, eds. Computational Fluid Dynamics 2002. Heidelberg: Springer, Berlin.
[204]	Zhang X, Gao H, Huang H, Bchcra D. 2018. An equivalent method for fuzzy reliability analysis // 2018 Annual Reliability and Maintainability Symposium (RAMS), Reno, NV, USA, 1-4.
[205]	Zhang X D, Huang H Z. 2010. Sequential optimization and reliability assessment for multidisciplinary design optimization under aleatory and epistemic uncertainties. Structural and Multidisciplinary Optimization, 40: 165-175. doi: 10.1007/s00158-008-0348-y
[206]	Zhao Y, Tai J. 2002. Ahmed F. Simulation of micro flows with moving boundaries using high-order upwind FV method on unstructured grids. Computational Mechanics, 28: 66-75. doi: 10.1007/s00466-001-0271-1
[207]	Zienkiewicz O C, Paul D K, Chan A H C. 1988. Unconditionally stable staggered solution procedure for soil-pore-fluid interaction problems. International Journal for Numerical Methods in Engineering, 26: 1039-1055. doi: 10.1002/nme.1620260504
[208]	Zienkiewicz O C, Taylor R L, Zhu J Z . 2013. The Finite Element Method. London: Butterworth-Heinemann.
[209]	Zohdi T I. 2017. Modeling and simulation of laser processing of particulate-functionalized materials. Archives of Computational Methods in Engineering, 24: 89-113. doi: 10.1007/s11831-015-9160-1