功能梯度材料动力学问题的POD模型降阶分析

郑保敬; 梁钰; 高效伟; 朱强华; 吴泽艳

doi:10.6052/0459-1879-18-069

功能梯度材料动力学问题的POD模型降阶分析

doi: 10.6052/0459-1879-18-069

1三峡大学水利与环境学院, 湖北宜昌 443002
2大连理工大学航空航天学院工业装备结构分析国家重点实验室, 大连 116024);

基金项目: 国家自然科学基金资助项目(11602129, 11672061).

详细信息

作者简介:
^*郑保敬, 讲师, 主要研究方向: 计算固体力学 . E-mail: zheng _-bj@126. com

通讯作者:
郑保敬

中图分类号: O321;
计量
- 文章访问数: 1364
- HTML全文浏览量: 50
- PDF下载量: 370
- 被引次数: 0
出版历程
- 刊出日期: 2018-07-18

ANALYSIS FOR DYNAMIC RESPONSE OF FUNCTIONALLY GRADED MATERIALS USING POD BASED REDUCED ORDER MODEL $N$

1College of Hydraulic and Environmental Engineering, China Three Gorges University, Yichang 443002, Hubei, China

摘要

摘要: 为了快速分析非均质材料结构在复杂载荷作用下的动态响应, 提出一种模型降阶方法, 只需计算结构在简单均质材料情况下的动力学问题, 进而用其计算结果对非均质材料结构进行分析. 首先, 采用结构内部任意一点处的材料参数值作为整个结构的材料参数, 利用有限元分析软件计算该均质材料结构在动态载荷作用下的位移场建立数据库, 该数据库包含计算模型各个节点(自由度为 $L$ )在某时间段内 $L$ 个时刻的位移; 其次, 对数据库中的信息按照时间离散的特定方式组集成瞬像矩阵, 并利用特征正交分解方法对其进行分解, 得到该模型的 $H$ 个特征正交基底, 选取其中能反应模型主要特征的 $H < L ? N$ 个(其中 $~$ )作为一组最优基底, 通过这组基底建立模型的低阶离散控制方程; 最后, 求解低阶离散微分方程组, 得到功能梯度材料结构在复杂载荷作用下的位移场. 文中分别给出二维和三维算例, 比较了降阶模型和全阶模型计算结果, 验证了该方法的有效性, 并且计算效率能提高1 $1)$ 2个数量级.
- 特征正交分解 /
- 模型降阶 /
- 动力响应 /
- 功能梯度材料
Abstract: In order to quickly analysis the response of heterogeneous materials under dynamic loads, a reduced order method was presented in this paper which only needed to compute dynamic characteristics of homogeneous material under sudden load and got the results for analysis complex non-homogeneous material. Firstly, we used the finite element method to compute the displacement field of homogeneous materials under sudden load, and then discretized data samples was obtained to establish a database which including every moment displacement information of all degrees of freedom (order of $L$ ) during a period of time. Secondly, dealing with database by specific way of time discretization, a snapshot matrix was formed. The matrix was decomposed into $H$ orthogonal basis by proper orthogonal decomposition method and we picked up the major $H < L ? N$ basis from that. Till now we achieved the goal that reducing the model ( $H$ ). Finally, the $[4 - 5]$ basis were used to obtain order-reduced governing dynamic equation. Different dynamic loads of time dependent were applied to the model, and the dynamic response of non-homogeneous material would be achieved by solving order-reduced governing dynamic equations. The displacement fields of traditional FEM and proposed ROM were compared. 2D and 3D examples showed that the computing scales reduced one or two orders of magnitude.
- proper orthogonal decomposition /
- reduced order method /
- dynamic response /
- functionally graded materials

HTML全文

参考文献(1)

[1]	Li J, Chen J, Chen X.Aerodynamic response analysis of wind turbines.Journal of Mechanical Science ＆ Technology, 2011, 25(1): 89-95
[2]	Yau JD.Dynamic response analysis of suspended beams subjected to moving vehicles and multiple support excitations.Journal of Sound ＆ Vibration, 2009, 325(4): 907-922
[3]	Larsen A, Larose GL.Dynamic wind effects on suspension and cable-stayed bridges.Journal of Sound ＆ Vibration, 2015, 334(1): 2-28
[4]	邢维巍, 张硕, 樊尚春. 动态轴向载荷下谐振梁振动响应分析. 传感技术学报, 2016, 29(9): 1372-1375
[4]	(Xing Weiwei, Zhang Shuo, Fan Shangchun.Resonant beam vibrating response under dynamic axial load analysis.Chinese Journal of Sensors and Actuators, 2016, 29(9): 1372-1375 (in Chinese))
[5]	华洪良, 廖振强, 张相炎. 轴向移动悬臂梁高效动力学建模及频率响应分析. 力学学报, 2017, 49(6): 1390-1398
[5]	(Hua Hongliang, Liao Zhenqiang, Zhang Xiangyan.An efficient dynamic modeling method of an axially moving cantilever beam and frequency Response Analysis.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(6): 1390-1398 (in Chinese))
[6]	Schulz U, Peters M, Bach F W, et al.Graded coatings for thermal, wear and corrosion barriers.Materials Science ＆ Engineering A, 2003, 362(1-2): 61-80
[7]	Sadowski T, Pietras D.Heat transfer process in jet turbine blade with functionally graded thermal barrier coating.Solid State Phenomena, 2016, 254(1): 170-175
[8]	Thomas B, Roy T.Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures.Acta Mechanica, 2016, 227(2): 581-599
[9]	夏巍, 冯浩成. 热过屈曲功能梯度壁板的气动弹性颤振. 力学学报, 2016, 48(3): 609-614
[9]	(Xia Wei, Feng Haocheng.Aeroelastic flutter of post-buckled functionally graded panels.Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(3): 609-614 (in Chinese))
[10]	许新, 李世荣. 功能梯度材料微梁的热弹性阻尼研究.力学学报, 2017, 49(2): 308-316
[10]	(Xu Xin, Li Shirong.Analysis of thermoelastic damping for functionally graded material micro-beam.Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(2): 308-316 (in Chinese))
[11]	赵磊, 胡超. 功能梯度材料应用及动力学分析.飞航导弹, 2011, 1(8): 93-96
[11]	(Zhao Lei, Hu Chao.Dynamic analysis and application of functionally graded material.Winged Missiles Journal, 2011, 1(8): 93-96 (in Chinese))
[12]	Shahba A, Rajasekaran S.Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials.Applied Mathematical Modelling, 2012, 36(7): 3094-3111
[13]	Librescu L, Sang YO, Song O.Spinning thin-walled beams made of functionally graded materials: Modeling, vibration and instability.European Journal of Mechanics - A Solids, 2004, 23(3): 499-515
[14]	Thomas B, Roy T.Vibration analysis of functionally graded carbon nanotube-reinforced composite shell structures.Acta Mechanica, 2016, 227(2): 581-599
[15]	仲政, 吴林志, 陈伟球. 功能梯度材料与结构的若干力学问题研究进展. 力学进展, 2010, 40(5): 528-541
[15]	(Zhong Zheng, Wu Linzhi, Chen Weiqiu.Progress in the study on mechanics problems of functionally graded materials and structures.Adv Mech, 2010, 40(5): 528-541 (in Chinese))
[16]	Perez R, Wang XQ, Mignolet MP.Nonlinear reduced-order models for thermoelastodynamic response of isotropic and functionally graded panels.AIAA Journal, 2009, 49(49): 630-641
[17]	Lumley JL.Coherent structures in turbulence.Transition ＆ Turbulence, 1981, 1(1): 215-242
[18]	姚伟刚, 徐敏, 叶茂. 基于特征正交分解的非定常气动力建模技术. 力学学报, 2010, 42(4): 637-637
[18]	(Yao Weigang, Xu Min,Ye Mao.Unsteady aerodynamic force modeling via proper orthogonal decomposition ROM.Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(4): 637-644 (in Chinese))
[19]	Deng S, Pan C, Wang J, et al.POD analysis of the instability mode of a low-speed streak in a laminar boundary layer.Acta Mechanica Sinica, 2017, 33(6): 981-991
[20]	Shankar KA, Pandey M.Nonlinear dynamic analysis of cracked cantilever beam using reduced order model.Procedia Engineering, 2016, 144(1): 1459-1468
[21]	Deng S, Pan C, Wang J, et al.POD analysis of the instability mode of a low-speed streak in a laminar boundary layer.Acta Mechanica Sinica, 2017, 6: 981-991.
[22]	Gao X, Hu J, Huang S.A Proper orthogonal decomposition analysis method for multimedia heat conduction problems.Journal of Heat Transfer, 2016, 138(7): 1-10
[23]	胡金秀, 郑保敬, 高效伟. 基于特征正交分解降阶模型的瞬态热传导分析. 中国科学物理学力学天文学, 2015, 45(1): 73-84
[23]	(Hu Jingxiu, Zheng Baojing, Gao Xiaowei.Reduced order model analysis method via proper orthogonal decomposition for transient heat conduction.Sci Sin-Phys Mech Astron, 2015, 45(1): 73-84 (in Chinese))
[24]	梁钰, 朱强华, 高效伟. 变工况导热问题的POD分析方法//中国航天第三专业信息网第三十八届技术交流会暨第二届空天动力联合会议. 大连, 2017
[24]	(Liang Yu, Zhu Qianghua, Gao Xiaowei.POD reduced analysis method of heat conduction problem under different loads//The 2nd JCAP and 38th APTIS Technical Conference. Dalian, 2017 (in Chinese))
[25]	王勖成. 有限单元法. 北京: 清华大学出版社, 2003
[25]	(Wang Xucheng. Finite Element Method.Beijing: Tsinghua University Press, 2003 (in Chinese))
[26]	Zhang C, Gao XW, Sladek J, et al.Fracture analysis of functionally graded materials.Composites Science ＆ Technology, 2008, 68(5): 1209-1215