拓扑优化理论在拱坝优化设计中的应用
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摘要
优化设计在现代结构设计中已经占有了重要的地位,它能使工程人员从众多的方案中得较为完善或合适的最优设计,是设计和制造的重要环节,并贯穿于整个研产过程。结构拓扑优化是近年来结构优化研究领域中的前沿课题和热点问题,也是结构优化中的重点和难点。与尺寸优化和形状优化相比,结构拓扑优化需要确定的参数更多,取得的经济效益更大,对工程设计人员更具吸引力。随着拓扑优化理论的进一步发展和完善,其应用于工程实践的条件也日趋成熟。
本文在阅读大量外文文献和国内相关论文的基础上,深入研究连续体结构拓扑优化的基本理论和方法,并就其在拱坝体形优化设计中的应用,做了一些探讨和尝试。具体的研究工作如下：
(1)对连续体结构的拓扑优化方法作了较为深入地研究,对均匀化方法、变密度方法以及变厚度方法等拓扑优化方法的数学模型分别做了探讨和分析。利用结构拓扑优化方法中较为常用的均匀化方法,探讨了水工结构拓扑优化设计的具体方法,并以微结构单胞为基础,解释了均匀化方法的数学模型和有限元求解的数值迭代算式。
(2)通过对拱坝的合理空间分布形式研究。在满足拱坝约束条件下,以坝体体积最小为目标,给出了分布荷载作用下的拓扑优化过程。在ANSYS有限元分析软件基础上,开发了较为通用的拓扑优化程序,从而在技术角度方面解决了拱坝结构的拓扑优化。
(3)拱坝三维有限元应力分析存在应力集中现象,坝体端部的应力失真。利用等效应力命令流,计算坝体端部等效应力来验算坝体端部应力是否满足规范要求。
(4)利用拓扑优化理论方法对拱坝的体形优化做了尝试,对拱坝的拓扑优化进行了详细分析,得到了较为满意的结果,这表明拓扑优化方法应用于拱坝体形优化设计是可行的。
Optimal design has occupied an important position in the modern design of the structure,It can obtain a more perfect or suitable optimal design from the large number of programmers,It is a important links of a virtual design and manufacturing, throughout the development and production process. Recently, topology optimization is the most challenging and hot,as well as difficult research topic in structure optimization.It usually needs to determine many more parameters than size optiminization and shape ptiminization,however,It can be obtained more benefit so that It is more attractive for design engineers. With the development of this theory,It is being applied to engineering practice gradually.
After reading numbers of the foreign documents and domestic relative paper, the basic theory and methods of continuum structural topology optimization is deeply studied, and It is applied of arch shape optimal design.Specific study are as follows:
(1)The continuum optiminzation were deeply stduied. and methematical models of topology optimization in homogenization method, varible-density method and varible-thickness method were discussed and analyzed. The specific methods of hydor-structure-optimization are designed by homogenization method used in topology optiminzation.On basis of microstructure cell, the methematical model of homogenization method and number calculation of finite element are explained.
(2)Through the study of the arch dam form of the rational spacial distribution,Under meeting constraints of arch dam, with the object of the minimum volume, the topology optiminzation of arch dam with the distributed loading is researched.Based on the finite element analysis software of ANSYS,a univerisal topology optimization program is exploited,which realizes topology optiminzation of arch dam from the point of the view of technique.
(3)Three-dimensional finite element stress analysis of arch dam has a phenomenon of stress concentration, the distortion of the arch dam stress occurred in the edge of the arch dam. The command stream of equivalent stress calculated equivalent stress of the edge of the arch dam to checking whether the dam to meet the ends of stress specifications.
(4)By using topology optimization theory,the arch dam form optiminzation design is made.the topology optiminzation of the arch dam is accomplished, all the result are satisfied,which indicates that topology optimization method of the coninuum structure is fit for the optimization design of the arch dam.
本文在阅读大量外文文献和国内相关论文的基础上,深入研究连续体结构拓扑优化的基本理论和方法,并就其在拱坝体形优化设计中的应用,做了一些探讨和尝试。具体的研究工作如下：
(1)对连续体结构的拓扑优化方法作了较为深入地研究,对均匀化方法、变密度方法以及变厚度方法等拓扑优化方法的数学模型分别做了探讨和分析。利用结构拓扑优化方法中较为常用的均匀化方法,探讨了水工结构拓扑优化设计的具体方法,并以微结构单胞为基础,解释了均匀化方法的数学模型和有限元求解的数值迭代算式。
(2)通过对拱坝的合理空间分布形式研究。在满足拱坝约束条件下,以坝体体积最小为目标,给出了分布荷载作用下的拓扑优化过程。在ANSYS有限元分析软件基础上,开发了较为通用的拓扑优化程序,从而在技术角度方面解决了拱坝结构的拓扑优化。
(3)拱坝三维有限元应力分析存在应力集中现象,坝体端部的应力失真。利用等效应力命令流,计算坝体端部等效应力来验算坝体端部应力是否满足规范要求。
(4)利用拓扑优化理论方法对拱坝的体形优化做了尝试,对拱坝的拓扑优化进行了详细分析,得到了较为满意的结果,这表明拓扑优化方法应用于拱坝体形优化设计是可行的。
Optimal design has occupied an important position in the modern design of the structure,It can obtain a more perfect or suitable optimal design from the large number of programmers,It is a important links of a virtual design and manufacturing, throughout the development and production process. Recently, topology optimization is the most challenging and hot,as well as difficult research topic in structure optimization.It usually needs to determine many more parameters than size optiminization and shape ptiminization,however,It can be obtained more benefit so that It is more attractive for design engineers. With the development of this theory,It is being applied to engineering practice gradually.
After reading numbers of the foreign documents and domestic relative paper, the basic theory and methods of continuum structural topology optimization is deeply studied, and It is applied of arch shape optimal design.Specific study are as follows:
(1)The continuum optiminzation were deeply stduied. and methematical models of topology optimization in homogenization method, varible-density method and varible-thickness method were discussed and analyzed. The specific methods of hydor-structure-optimization are designed by homogenization method used in topology optiminzation.On basis of microstructure cell, the methematical model of homogenization method and number calculation of finite element are explained.
(2)Through the study of the arch dam form of the rational spacial distribution,Under meeting constraints of arch dam, with the object of the minimum volume, the topology optiminzation of arch dam with the distributed loading is researched.Based on the finite element analysis software of ANSYS,a univerisal topology optimization program is exploited,which realizes topology optiminzation of arch dam from the point of the view of technique.
(3)Three-dimensional finite element stress analysis of arch dam has a phenomenon of stress concentration, the distortion of the arch dam stress occurred in the edge of the arch dam. The command stream of equivalent stress calculated equivalent stress of the edge of the arch dam to checking whether the dam to meet the ends of stress specifications.
(4)By using topology optimization theory,the arch dam form optiminzation design is made.the topology optiminzation of the arch dam is accomplished, all the result are satisfied,which indicates that topology optimization method of the coninuum structure is fit for the optimization design of the arch dam.
引文
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[3]G M Michell. The limits of economy of materials in frame structures[J]. Philosophical Magazine Series,1904,8(47):589-597
[4]H L Cox. The design of structures of least weight[M]. Oxford:Pergamon,1965
[5]G A Hegeminer, W Prager. On Michell trusses[J]. International Journal of Mechanical Sciences, 1969,11(2):209-215
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[8]GIN Rozvany. Partial relaxation of orthogonality requirement for classical Miehell trusses[J]. Structucal Optimization,1997,13(4):271-274
[9]GIN Rozvany, W Gollub, M Zhou. Exact Michell layouts for various combinations of line supports-Part Ⅱ [J]. Structural Optimization,1997,14(2/3):138-149
[10]周克民,胡云昌.利用有限元构造Michell析架的一种方法[J].力学学报,2002,34(6)：935-940
[11]W S Dorn, R E Gomory, H J Greenberg. Automatic design of optimal structures [J]. J.de Mechanique,1964,3(1):25-52
[12]N W Dobbs, IP Felton. Optimization of truss geometry[J]. ASCE, J.Struct.Div,1969,95(ST10): 2105-2118.
[13]U Ringertz. A branch and bound algorithm for topology optimization of truss structures[J]. Eng.Opt,1986,10(2):111-124
[14]许素强,夏人伟.结构优化法研究综述[J].航空学报,1995,16(4)：385-396
[15]Kirsch U, topping BHV. Minimum Weight Design of Structural Topologies[J]. J. Structural Eng, 1992, (8):177-1785
[16]B Y Duan, A B Templeman, J J Chen, Entropy-based method for topological optimization of truss structures[J]. Computers and Structures,2000,75(5):539-550
[17]K Svanberg. The method of moving asymptotes-a new method for structural optimization[J]. International Journal for Numerical Methods in Engineering,1987,24:359-373
[18]蔡文学.桁架结构拓扑优化设计的模拟退火算法[J].华南理工大学学报,1998,(9)：78-84
[19]段宝岩,叶尚辉.考虑性态约束时多工况析架结构拓扑优化设计[J].力学学报,1992,24(1)：59-69
[20]孙焕纯,柴山,王跃方.离散变量结构优化设计的发展现状及展望[J].力学与实践,1997,19(4)：7-11
[21]王跃方,孙焕纯,黄丽华.离散变量结构拓扑优化设计研究[J].固体力学学报,1998,19(1)：59-63
[22]谭中富,孙焕纯.多工况作用下空间析架结构拓扑优化的修正单纯形法[J].力学学报,1994,26(1)：90-9
[23]柴山,石连栓,孙焕纯.包含两类变量的离散变量的析架结构拓扑优化设计[J].力学学报,1999,31(5)：574-583
[24]陈建军,曹一波,段宝岩.基于可靠性的析架结构拓扑优化设计[J].力学学报,1998,30(3)：277-284
[25]Zhou M. Difficultieis in truss Topology Optimization with Stress and Local. Buckling Constraints[J]. Structural Optimization,1996, (11):134-136
[26]Rozvang GIN. Difficulties in Truss Topology Optimization with Local Buckling and System Stability Constraints[J]. Structural Optimization,1996, (11):213-221
[27]M P Bendsoe, N Kikuchi. Generating optimal topologies in structural design using a homogenization menthod[J]. Comp.Meth.Appl.Mech.Engrg,1988,71(1):197-224
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