基于遗传算法的弹性地基加肋板肋梁无网格优化分析

覃霞; 刘珊珊; 谌亚菁; 彭林欣

doi:10.6052/0459-1879-19-300

基于遗传算法的弹性地基加肋板肋梁无网格优化分析

覃霞^*,,
刘珊珊^*,
谌亚菁^*,
彭林欣^*†2),

^* 广西大学土木建筑工程学院, 南宁 530004
^? 广西大学广西防灾减灾与工程安全重点实验室, 工程防灾与结构安全教育部重点实验室, 南宁 530004

基金项目: 1) 国家自然科学基金资助项目(11562001);国家自然科学基金资助项目(11102044);广西科技重大专项(桂科AA18118029)

详细信息

通讯作者:
彭林欣

中图分类号: TU339
计量
- 文章访问数: 1341
- HTML全文浏览量: 227
- PDF下载量: 101
出版历程
- 收稿日期: 2019-10-29
- 刊出日期: 2020-02-09

RIB MESHLESS OPTIMIZATION OF STIFFENED PLATES RESTING ON ELASTIC FOUNDATION BASED ON GENETIC ALGORITHM

^* School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China
^? Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education, Guangxi Key Laboratory of Disaster Prevention and Engineering Safety, Guangxi University, Nanning 530004, China

摘要

摘要: 基于遗传算法及一阶剪切理论, 提出一种弹性地基上加肋板肋条位置优化的无网格方法. 首先, 通过一系列点来离散平板及肋条, 并用弹簧模拟弹性地基, 从而得到加肋板的无网格模型; 其次, 基于一阶剪切理论及移动最小二乘近似原理导出位移场, 求出弹性地基加肋板总势能; 再次, 根据哈密顿原理导出结构的弯曲控制方程, 并通过完全转换法处理边界条件; 最后, 引入遗传算法和改进遗传算法, 以肋条的位置为设计变量、弹性地基板的中心点挠度最小值为目标函数, 对肋条位置进行优化达到地基板控制点挠度最小的目的. 以不同参数、载荷布置形式的弹性地基加肋板为例, 与ABAQUS有限元结果及文献解进行比较. 研究表明, 采用所提出的无网格模型可有效求解弹性地基上加肋板弯曲问题, 结果易收敛, 同时基于遗传算法与改进混合遗传算法所提出的无网格优化方法均可有效优化弹性地基加肋板肋条位置, 后者计算效率相对较高, 只进行了三次迭代便可获得稳定的最优解, 此外在优化过程中肋条位置改变时只需要重新计算位移转换矩阵, 又避免了网格重构.
- 无网格法 /
- 弹性地基加肋板 /
- 一阶剪切理论 /
- 遗传算法 /
- 肋条位置优化
Abstract: Based on the genetic algorithm and the first-order shear deformation theory, a meshless method is proposed to optimize the position of ribs of the stiffened plate resting on elastic foundation. Firstly, the meshless model of the stiffened plate is obtained by discretizing the plate and ribs with a series of points and by simulating the elastic foundation with springs. Secondly, the displacement field is approximately obtained based on the first-order shear deformation theory and the moving-least square approximation, and the total potential energy of the stiffened plate resting on the elastic foundation is derived. Then, the boundary conditions are dealt with the full transformation method, and the governing equation of the structure is derived from the Hamilton principle. Finally, the genetic algorithm and the improved genetic algorithm are introduced with the location of ribs as the design variable and the minimal deflection of the center point of the stiffened plate as the objective function. The arrangement of ribs is optimized to achieve the minimum center point deflection of the stiffened plate resting on the elastic foundation. Taking some ribbed plates resting on elastic foundation with different parameters and load distribution as the numerical examples, the comparison with the finite element results given by ABAQUS is carried out. The results show that the proposed meshless model can effectively analyze the bending problem of stiffened plate on elastic foundation. Meanwhile, the meshless optimization method based on the genetic algorithm and the improved genetic algorithm both can effectively optimize the position of the ribs of the stiffened plate on elastic foundation, the latter is relatively efficient, and the stable optimal solution can be obtained after only three iterations. Additionally, when the position of the rib changes during the optimization process, only the displacement transformation matrix needs to be recalculated, and the mesh reconstruction is totally avoided.
- meshless method /
- elastic foundation ribbed plate /
- first-order shear deformation theory /
- genetic algorithm /
- rib position optimization

HTML全文

参考文献(1)

[1]	乔迟, 张世联 . 大跨度加筋板架优化设计研究. 舰船科学技术, 2015,37(8):23-26
[1]	( Qiao Chi, Zhang Shilian . Research on optimization design of long span stiffened plates. Ship Science and Technology, 2015,37(8):23-26 (in Chinese))
[2]	吴红刚, 牌立芳, 赖天文等. 山区机场高填方边坡桩-锚-加筋土组合结构协同工作性能优化研究. 岩石力学与工程学报, 2019,38(7):1498-1511
[2]	( Wu Honggang, Pai Lifang, Lai Tianwen , et al. Study on cooperative performance of pile-anchor-reinforced soil combined retaining structure of high fill slopes in mountainous airports. Chinese Journal of Rock Mechanics and Engineering, 2019,38(7):1498-1511 (in Chinese))
[3]	陈炉云, 张裕芳 . 基于遗传算法的复合材料结构-声辐射优化研究. 复合材料学报, 2012,29(3):203-207
[3]	( Chen Luyun, Zhang Yufang . Research on composite structure-acoustic radiation optimization based on genetic algorithm. Journal of Composite Materials, 2012,29(3):203-207 (in Chinese))
[4]	李林远 . 基于无网格法的矩形加肋板结构优化设计. [硕士论文]. 南宁: 广西大学, 2016
[4]	( Li Linyuan . Optimization design of rectangular ribbed plate structure based on meshless method. [Master Thesis]. Nanning: Guangxi University, 2016 (in Chinese))
[5]	龚曙光, 曾维栋, 张建平 . Reissner-Mindlin 板壳无网格法的闭锁与灵敏度分析及优化的研究. 工程力学, 2011,28(4):42-48
[5]	( Gong Shuguang, Zeng Weidong, Zhang Jianping . Study on numerical locking and sensitivity analysis and optimization of Reissner-Mindlin plate and shell with meshless method. Engineering Mechanics, 2011,28(4):42-48 (in Chinese))
[6]	彭细荣, 隋允康 . 考虑破损-安全的连续体结构拓扑优化ICM方法. 力学学报, 2018,50(3):611-621
[6]	( Peng Xirong, Sui Yunkang . ICM method for fail-safe topology optimization of continuum structures. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(3):611-621 (in Chinese))
[7]	王选, 刘宏亮, 龙凯等. 基于改进的双向渐进结构优化法的应力约束拓扑优化. 力学学报, 2018,50(2):385-394
[7]	( Wang Xuan, Liu Hongliang, Long Kai , et al. Stress-constrained topology optimization based on improved bidirectional evolutionary optimization method. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(2):385-394 (in Chinese))
[8]	Belytshko T, Lu YY, Gu L . Element-free Galerkin methods. International Journal for Numerical Methods in Engineering, 1994,37(2):229-256
[9]	Liu GR. Mesh Free Methods: Moving Beyond the Finite Element Method. Boca Raton: CRC Press, 2002
[10]	张雄, 刘岩, 马上 . 无网格法的理论及应用. 力学进展, 2009,39(1):1-36
[10]	( Zhang Xiong, Liu Yan, Ma Shang . Theory and application of meshless method. Advances in Mechanics, 2009,39(1):1-36 (in Chinese))
[11]	张雄, 宋康祖, 陆明万 . 无网格法研究进展及其应用. 计算力学学报, 2003,20(6):730-742
[11]	( Zhang Xiong, Song Kangzu, Lu Mingwan . Research progress and application of meshless method. Chinese Journal of Computational Mechanics, 2003,20(6):730-742 (in Chinese))
[12]	吴宇, 覃霞, 吴天文等. 基于无网格法的弹性地基加肋斜板频率数值解. 计算力学学报, 2019,36(1):110-116
[12]	( Wu Yu, Qin Xia, Wu Tianwen , et al. Numerical solution frequencies of stiffened skew plate on elastic foundation via meshless method. Chinese Journal of Computational Mechanics, 2019,36(1):110-116 (in Chinese))
[13]	庞作会, 葛修润, 王水林 . 无网格伽辽金法(EFGM)在边坡开挖问题中的应用. 岩土力学, 1999,20(1):61-64
[13]	( Pang Zuohui, Ge Xiurun, Wang Shuilin . Application of meshless Galerkin method (EFGM) to slope excavation. Rock and Soil Mechanics, 1999,20(1):61-64 (in Chinese))
[14]	龙述尧 . 弹性力学问题的局部Petrov-Galerkin方法. 力学学报, 2001,33(4):508-518
[14]	( Long Shuyao . Local Petrov-Galerkin method for elastic mechanics problems. Chinese Journal of Theoretical and Applied Mechanics, 2001,33(4):508-518 (in Chinese))
[15]	龙述尧 . 用无网格局部Petrov-Galerkin法分析弹性地基上的梁. 湖南大学学报(自然科学版), 2001,28(5):11-15
[15]	( Long Shuyao . Analysis of beams on elastic foundations by meshless local Petrov-Galerkin method. Journal of Hunan University (Natural Science), 2001,28(5):11-15 (in Chinese))
[16]	方电新, 李卧东, 王元汉等. 用无网格法计算平板弯曲问题. 岩土力学, 2001,22(3):347-349
[16]	( Fang Dianxin, Li Wodong, Wang Yuanhan , et al. Calculation of plate bending problem using meshless method. Rock and Soil Mechanics, 2001,22(3):347-349 (in Chinese))
[17]	周瑞忠, 周小平, 缪圆冰 . 具有自适应影响半径的无单元法. 工程力学, 2001,18(6):94-99
[17]	( Zhou Ruizhong, Zhou Xiaoping, Miao Yuanbing . Element-free method with adaptive radius of influence. Engineering Mechanics, 2001,18(6):94-99 (in Chinese))
[18]	Song KZ . Meshless method based on collocation with consistent compactly supported radial basis functions. Acta Mechanica Sinica, 2004,20(5):551-557
[19]	张希, 姚振汉 . 无网格彼得洛夫伽辽金法在大变形问题中的应用. 工程力学, 2006,23(s1):16-20
[19]	( Zhang Xi, Yao Zhenhan . Application of the meshless Petrof Galerkin method in large deformation problems. Engineering Mechanics, 2006,23(s1):16-20 (in Chinese))
[20]	Liew KM, Peng LX, Kitipornchai S . Nonlinear analysis of corrugated plates using a FSDT and a meshfree method. Computer Methods in Applied Mechanics and Engineering, 2007,196(21-24):2358-2376
[21]	Wang D, Wang JR, Wu JC . Superconvergent gradient smoothing meshfree collocation method. Computer Methods in Applied Mechanics and Engineering, 2018,340:728-766
[22]	Zhang Z, Liew KM, Cheng Y , et al. Analyzing 2D fracture problems with the improved element-free Galerkin method. Engineering Analysis with Boundary Elements, 2008,32(3):241-250
[23]	Liu WK, Jun S, Zhang YF . Reproducing kernel particle method. International Journal for Numerical Methods in Engineering, 1995,38(10):1655-1679
[24]	Liu WK, Chen Y, Jun S , et al. Overview and applications of the reproducing kernel particle methods. Archives of Computational Methods in Engineering, 1996,3(1):3-80
[25]	Peng LX, Liew KM, Kitipornchai S . Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method. Journal of Sound and Vibration, 2006,289(3):421-449
[26]	Peng LX, Kitipornchai S, Liew KM . Analysis of rectangular stiffened plates under uniform lateral load based on FSDT and element-free Galerkin method. International Journal of Mechanical Sciences, 2005,47(2):251-276
[27]	Peng LX, Liew KM, Kitipornchai S . Analysis of stiffened corrugated plates based on the FSDT via the mesh-free method. International Journal of Mechanical Sciences, 2007,49(3):364-378
[28]	Peng LX, Kitipornchai S, Liew KM . Bending analysis of folded plates by the FSDT meshless method. Thin-Walled Structures, 2006,44(11):1138-1160
[29]	彭林欣 . 矩形加肋板线性弯曲分析的移动最小二乘无网格法. 计算力学学报, 2012,29(2):210-216
[29]	( Peng Linxin . Moving least squares meshless method for linear bending analysis of rectangular ribbed plates. Chinese Journal of Computational Mechanics, 2012,29(2):210-216 (in Chinese))
[30]	覃霞, 刘珊珊, 吴宇等. 平行四边形加肋板自由振动分析的无网格法. 工程力学, 2019,36(3):24-32, 39
[30]	( Qin Xia, Liu Shanshan, Wu Yu , et al. The meshless method for free vibration analysis of parallelogram ribbed plates. Engineering Mechanics, 2019,36(3):24-32, 39 (in Chinese))
[31]	邓立克, 王东东, 王家睿等. 薄板分析的线性基梯度光滑伽辽金无网格法. 力学学报, 2019,51(3):690-702
[31]	( Deng Like, Wang Dongdong, Wang Jiarui, Wu Junchao . A gradient smoothing Galerkin meshfree method for thin plate analysis with linear basis function. Chinese Journal of Theoretical and Applied Mechanics, 2019,51(3):690-702 (in Chinese))
[32]	马文涛 . 二维弹性力学问题的光滑无网格伽辽金法. 力学学报, 2018,50(5):1115-1124
[32]	( Ma Wentao . A smoothed meshfree Galerkin method for 2D elasticity problem. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(5):1115-1124 (in Chinese))
[33]	宋彦琦, 周涛 . 基于S-R和分解定理的三维几何非线性无网格法. 力学学报, 2018,50(4):853-862
[33]	( Song Yanqi, Zhou Tao . Three-dimensional geometric nonlinearity element-free method based on S-R decomposition theorem. Chinese Journal of Theoretical and Applied Mechanics, 2018,50(4):853-862 (in Chinese))
[34]	Goldberg, David E . Genetic Algorithms in Search, Optimization, and Machine Learning. New York: Addison-wesley publishing company, 1989
[35]	Koza J R. Genetic Programming: On the Programming of Computers by Means of Natural Selection. Cambridge: MIT Press, 1992
[36]	杨卫波, 王万良, 张景玲等. 基于遗传模拟退火算法的矩形件优化排样. 计算机工程与应用, 2016,52(7):259-263
[36]	( Yang Weibo, Wang Wanliang, Zhang Jingling , et al. Optimized layout of rectangular parts based on genetic simulated annealing algorithm. Computer Engineering and Applications, 2016,52(7):259-263 (in Chinese))
[37]	孟凡超, 初佃辉, 李克秋等. 基于混合遗传模拟退火算法的SaaS构件优化放置. 软件学报, 2016,27(4):916-932
[37]	( Meng Fanchao, Chu Dianhui, Li Keqiu , et al. Optimal placement of SaaS components based on hybrid genetic simulated annealing algorithm. Journal of Software, 2016,27(4):916-932 (in Chinese))
[38]	周鑫, 马跃, 胡毅 . 求解车间作业调度问题的混合遗传模拟退火算法. 小型微型计算机系统, 2015,36(2):370-374
[38]	( Zhou Xin, Ma Yue, Hu Yi . Hybrid Genetic Simulated Annealing Algorithm for Job Shop Scheduling Problem. Journal of Chinese Computer Systems, 2015,36(2):370-374 (in Chinese))
[39]	Salkauskas PL . Surfaces generated by moving least squares methods. Mathematics of Computation, 1981,37(155):141-158
[40]	Reddy JN . Theory and Analysis of Elastic Plates. London: Taylor & Francis, 1999
[41]	Chen J, Pan C, Wu C , et al. Reproducing Kernel Particle Methods for large deformation analysis of non-linear structures. Computer Methods in Applied Mechanics and Engineering, 1996,139(1):195-227
[42]	陈英杰, 李志航, 付宝连 . 应用混合变量余能原理求解不同载荷作用下四边简支矩形板的弯曲. 计算力学学报, 2015,32(2):287-292
[42]	( Chen Yingjie, Li Zhihang, Fu Baolian . Apply the principles of complementary energy with mixed variables to solve the bending of the rectangular plate with simply supported on four sides under different loads. Chinese Journal of Computational Mechanics, 2015,32(2):287-292 (in Chinese))

施引文献(12)

期刊类型引用(7)

1.	陈卫，彭林欣. 加筋折叠壳静力弯曲的移动最小二乘无网格法. 计算力学学报. 2025(01): 106-114 . 百度学术
2.	彭林欣，谌亚菁，覃霞，杨健生. 弹性地基圆形加肋板静力弯曲及弯曲自由振动分析的无网格法. 振动与冲击. 2022(07): 11-22+30 . 百度学术
3.	赵崇阳. 基于遗传算法的学生在线竞赛系统研究. 自动化与仪器仪表. 2022(04): 146-150 . 百度学术
4.	李鑫冉，赵海斌. 近地小行星极短弧定轨的进化算法研究. 力学学报. 2021(03): 902-911 . 本站查看
5.	陈增涛，王发杰，王超. 广义有限差分法在含阻抗边界空腔声学分析中的应用. 力学学报. 2021(04): 1183-1195 . 本站查看
6.	李洋，桑建兵，敖日汗，马钰，魏新宇. 基于仿真和智能算法骨骼肌超弹性本构参数的反演方法研究. 力学学报. 2021(05): 1449-1456 . 本站查看
7.	殷浩，李永华，杜江. 基于随机模型的动车组制动模块稳健优化设计. 机械与电子. 2020(10): 3-7+12 . 百度学术