优化理论及ANSYS程序在桥梁优化设计中的应用研究_邓杨芳

摘要结构优化设计是以现代数学、现代力学理论与数值方法为基础，以计算机为工具，研究结构设计优化的理论与方法。近年来，随着ANSYS程序的普及，优化理论在桥梁工程中的截面优化、索力优化等方面的应用越来越多，但有关ANSYS优化方法的数学理论还研究的不多。文中较为详细地介绍了当前优化算法中常用的几种算法原理，包括优化设计的概念、线性规划法和非线性规划法，给出了各自的算法流程，用混合罚函数法建立矩形截面钢筋混凝土简支梁数学模型，开展了截面优化分析，得到以造价最低为优化目标的截面尺寸与配筋。在此基础上，针对ANSYS优化设计中的零阶优化法和一阶优化法，给出了各自优化方法的详尽数学原理。最后以大宁河特大桥斜拉扣挂施工的扣索索力优化为例，基于一次扣索张拉法，在给定扣塔水平偏位、拱肋相邻节段高程差等约束条件下，应用ANSYS的零阶优化法，开展了斜拉扣索索力的前进迭代优化分析，得到了既能确保结构受力状态又能保证拱肋线形符合设计期望的索力。关键词：优化理论；混合罚函数法；ANSYS优化算法；零阶优化；一阶优化；索力优化ABSTRACTStructuralOptimalDesignisbasedonmodernmathematical,mechanicaltheoryandnumericalmethod,makesastudyofstructuraldesignoptimizationandautomatization.Inrecentyears,withthepopularityofANSYSprogram,theOptimizationTheoryappliedincross-sectionoptimizationofbridgeengineeringandcableforceoptimizationetcmoreandmore,butthemathematicaltheoryoftheANSYSoptimizationmethodalsostudiedless.Inthispaper,Introducesseveralalgorithmtheoryofcurrentoptimizationalgorithmindetail.Includingtheconceptofoptimaldesign,linearprogrammingandnonlinearprogrammingmethod,Givestheirrespectivealgorithmflow,establishsmathematicalmodeloftherectanglesectionreinforcedconcretesimple-supportedbeamandoptimazingusedthemixedpenaltyfunctionmethod,carriesouttheoptimizecross-sectionanalysis,toabtainthesectionsizeandreinforcementinthecaseofthelowestconstructioncost.Onthisbasis,aimingatSubproblemApproximationMethodandtheFirst-orderOptimizationMethodofANSYSoptimization,givestheiroptimizationmethodanddetailedmathematicalprinciples.Finally,AsanexampletoDaningRiversuperlargebridgeoptimizationofstayed-buckle-cableforcesofConstructedbySlantingPullandBuckleTechniqueasanexample,basedonasingletensionmethod,atagivenlevelofasymmetryofcabletower,andarchribadjacentsegmentelevationdifferenceetcconstraintcondition,appliedthezero-orderoptimizationmethodofANSYS,Carriedoutforwarditerativeoptimizationanalysisofstayed-buckle-cableforces,hasbeenabletoensurethatthestructureofstatusbyforcebutalsoensureslineararchribwiththedesignexpectationsofthecableforce.KEYWORDS:optimizationtheory；mixedpenaltyfunctionmethod；ANSYSoptimizationalgorithm；SubproblemApproximation’Method；FirstOrderOptimizationMethod；目录第一章绪论..............................................................................................................11.1引言.........................................................................................................................11.2结构优化设计的发展历史.....................................................................................11.2.1结构优化设计的概念以及优点......................................................................21.2.2国内外结构优化设计的发展..........................................................................31.3结构优化几个主要问题的现状与发展.................................................................41.3.1离散变量问题..................................................................................................41.3.2多目标优化......................................................................................................51.3.3优化建模..........................................................................................................51.3.4优化算法..........................................................................................................61.3.5形状优化与拓扑优化......................................................................................71.4结构优化软件开发和应用现状.............................................................................81.5优化算法在桥梁中的应用和研究现状.................................................................91.5.1桥梁优化特点................................................................................................101.6课题来源及工程背景...........................................................................................101.7本文的主要研究内容............................................................................................11第二章结构优化设计的基本理论............................................................................132.1引言.......................................................................................................................132.2结构优化设计的一般数学模型...........................................................................132.2.1结构优化的数学模型....................................................................................132.2.2优化设计的三大变量....................................................................................142.3结构优化设计的方法分类...................................................................................152.3.1按照目标函数或约束条件的数学特征区分................................................152.3.2按照优化方法的特征区分............................................................................152.4牛顿法和拟牛顿法...............................................................................................162.5共轭方向法...........................................................................................................192.5.1共轭方向的性质............................................................................................192.5.2利用共轭方向的性质构造共轭方向............................................................202.5.3共轭方向法步骤流程图....................