matlab在数据包络分析中的应用及程序
系统的介绍了包络分析在实际中的应用，介绍了matlab进行包络分析的方法，并附有源程序供科研人员学习这是一个分式规划问题。若令则()可化为等价的线性规划问题:线性规划()的解和称为的最佳权向量,它们是使的效率值达到最大值的权向量。注意:作为线性规划的解,和不是唯一的义()若线性规划()的解满足:,则称为弱有效的;()若线性规划()的解中存在解并且则称为有效的。为了便于检验的有效性,一般考虑()的对偶模型的等式形式(带有松弛变量目具有非阿基米德无穷小)∑∑其中是项输入的松弛变量是项输出的松弛变量;是个的组合系数;;是个很小的止数(般取)。定理设线性规划(的最优解为则()若为弱有效()的;()若且则为有效()的程序由上一节知,要计算一个的相对效率值并讨论其(弱)有效性,须解一个线性规划若要计算所有的相对效率值,则须解个线性规划,其计算量比较大,一般须利用计算机进行计算。我们利用数学软件编写了解模型()和(的程序,比较方便地解决了的计算量大和计算复杂的问题是由公司用语言编写的著名的工程数学应用软件。它自牛推向市场以来,历经十几年的发展和竞争,现已成为国际认可的最优化的科技应用软件。目前,口经成为世界上诸多科技领域的基本应用软件。在国内、外的很多高等院校和科研机构已经十分普及。熟练地运用已成为晑校师生及科研人员的基本技能强大的矩阵运算能力和方便、直观的编程功能是我们选择它作为编写应用程序的原因。诚然,或是解线性规划问题的专业软件,但它们缺乏方便的编程功能和矩阵输入功能,在解一系列线性规划时,它们不如方便。此外,它们的普及程度远不如因此,我们认为是编写应用程序的最佳软件之一。所解的线性规划的标准形式是板小化问题:其中,是变量,是目标函数的系数向量,是不等式约枣的系数矩阵,是等式约束的系数矩阵,和分别是变量的下界和上界解线性规划()的语句为如果要解极大化问题,只须解极小化问题卜面,我们给出模型和(的程序。程序模型的程序)用户输入多指标输入矩阵用户输入多指标输出矩阵解线性规划,得的最佳权向量求出的相对效率值输出最佳权向量输出相对效率值输出投入权向量输出产出权向量程序模型(的程序)用户输入多指标输入矩阵用户输入多指标输出矩阵定义非阿基米德无穷小解线性规划,得的最佳权向量输出最佳权向量输出输出输出输出以上两个程序十分便于使用。用户只须输入多指标输入矩阵和输出矩阵,目可得到所需的结果。程序的应用设有某大学的同类型的五个系在一学年内的投入和产出的数据如下投教职工(人)教职工工资(万元)入运转经费(万元)毕业的本科生:(人)毕业的研究生(人)出发表的论文(篇)完成的科研项目(项)其中,运转经费指一学年內维持该系正常运转的各和费用,如行政小公费、图书资料费、差旅费等等。由程序,得到各系的相对效率值:以及各项投入和产出的权向量中定义,和至少是弱有效的和是非弱有效的。为了确认和的有效性并分析和非有效的原因,须利用模型(。由程序,得本问题的解:由以上解可看出:和的解中且松弛变量故由定理知,这几个系是相对有效的。和的非有效性也可以在以上解中看得一清二楚。以为例,根据有效性的经济意义,在不减少各项输出的前提下,构造一个新的投入的投入按比例减少到原投入的)倍,)并且(由非零的松弛变量可知)还可以进一步减少教职工工资万元、减少运转费用万元、多培养本科生人多完成项科研项目。对的非有效性可作类似的经济解释。结束语本文利用数学软件编写了便于使用的的计算程序,使计算量大和计算复杂的问题得到较好的解决。本文只对的模型进行了讨论。对于的另一个重要模型一模型,只须在模型(。中增加约東条件∑A,程序作相应的修攻即可。本文的程序为的理论研究和实际应用提供了方便、快捷的计算工具。参考文献:魏权龄评价相对有效性的方法北京:中国人民大学出版社盛旧瀚等里论、方法与应用北京:科学出版社,许波,刘征工程数学应用北京:清华大学出版社,
- 2020-12-11下载
- 积分：1
MSC.Marc 2013.1理论手册
MSC.MARC是功能齐全的高级非线性有限元软件，具有极强的结构分析能力。可以处理各种线性和非线性结构分析包括：线性/非线性静力分析、模态分析、简谐响应分析、频谱分析、随机振动分析、动力响应分析、自动的静/动力接触、屈曲/失稳、失效和破坏分析等ContentsMarc Volume A: Theory and User InformationrefaceAbout this manual■■■■20Purpose of volume A20Contents of volume a20How to Use this manual211 The Marc SystemMarc Programs............■■23Marc for Analysis23Mentat or patran for gul24Structure of marc24Procedure Library24Material Library24Element Library25Program Function Library25Features and benefits of marc252 Program InitiationMarc Host Systems27Workspace Requirements27Marc Workspace Requirements27File Units30Program Initiation.........32Examples of running marc Jobs■■■■■344 Marc Volume A: Theory and User Information3 Data EntryInput Conventions38Input of List of Items39Examples of lists41Table Driven Input■■41Table Input42Parameters46Model Definition Options46History Definition Options46REZONE Option474 Introduction to mesh definitionDirect Input49Element Connectivity Data49Nodal coordinate data53Activate/Deactivate54User Subroutine Input54MESH2D54Block definition54Merging of Nodes54Block Types55Symmetry, Weighting, and Constraints57Additional Options58Mentat58FXORD Option59Major classes of the fXoRD Option59Recommendations on Use of the FXORD Option63Incremental mesh generators■■■■■63Bandwidth Optimization64Rezoning.....64Substructure65Technical Background66Scaling Element Stiffness67Contents 5BEAM SECT Parameter■■■68Orientation of the Section in Space68Definition of the section68Error Analysis74ocal AdaptivityNumber of Elements Created7474Boundary Conditions75Location of new nodes76Adaptive Criteria77Automatic Global remeshing80Remeshing criteria84Remeshing TechniquesPatran Tetrahedral mesher885 Structural Procedure LibraryLinear Analysis99Accuracy100Error estimates100Adaptive meshing101Fourier Analysis101Nonlinear Analysis104Geometric nonlinearities108Eulerian FormulationArbitrary Eulerian-Lagrangian(AEL) Formulation118Nonlinear Boundary Conditions118Buckling Analysis120Perturbation Analysis121Computational Procedures for Elastic-Plastic Analysis126Creep138Viscoelasticity142Viscoplasticity143Fracture Mechanics144Linear fracture mechanics144Nonlinear fracture mechanics147Numerical Evaluation of the J-integral148Numerical Evaluation of the Energy Release Rate with the VCCT Method150Automatic Crack PropagationDynamic Fracture Methodology1626 Marc Volume A: Theory and User InformationDynamic crack Propagation..162Crack Initiation163Mesh Splitting165Mesh Splitting Along Edges or Faces165Mesh Cutting167Dynamics...168Modal(Eigenvalue) Analysis.168Harmonic Response172Spectrum Response75Transient Analysis179Inertia relief191Rigid Body Mode Evaluation.191Rigid-Plastic Flow195Steady State Analysis95Transient Analysis196Technical background..196Superplasticity197Soil Analysis199Technical formulation200Mechanical Wear.,,,,,,,,203Design Sensitivity Analysis........■■205Theoretical considerations207Design Optimization208Approximation of Response Functions Over the Design Space..209Improvement of the Approximation211The Optimization algorithmMarc User Interface for Sensitivity Analysis and Optimization212Define Initial State with Results from a Previous Analysis215Pre state215Model sections217Steady State Rolling Analysis219Kinematics219lnetⅰaE仟fect...221Rolling Contact221Steady state rolling with marc221ContentsStructural Zooming Analysis.222Element Types Supported223Uncoupled Thermal Stress Analysis223Cure-Thermal-Mechanically Coupled Analysis224Cure Kinetics225Cure Shrinkage Strain228References,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,2296 Nonstructural Procedure LibraryHeat Transfer234Thermal Contact235Convergence Controls235Steady state Analysis236Transient Analysisemperature Effects238Initial Conditions239Boundary Conditions239Surface Energy243Thermochemical Ablation and Surface Energy Balance244Mathematical Presentation244Mechanical Erosion251Mechanical Erosion by Other Actions251pyrolySis251Coking255Monitoring Thermal Degradation258Presentation of the Energy Equation260Ablation262Welding27Radiation278Conrad Gap292Channel293Output294Diffusion295Technical Background296Hydrodynamic Bearing300Technical Background3028 Marc Volume A: Theory and User InformationElectrostatic Analysis304Technical Background305Magnetostatic Analysis308Technical background..309Magnetodynamic Analysis∴∴320Technical Background322Piezoelectric Analysis325Technical Background326Strain Based Piezoelectric Coupling..328Acoustic Analysis328Rigid Cavity Acoustic Analysis328Technical Background329Fluid mechanics330Finite element formulation333Penalty Method335Steady State Analysis336Transient Analysis336Solid Analysis336Solution of Coupled Problems in Fluids..336Degrees of Freedom337Element Types.337Coupled Analyses∴..■量■画■■■,,,,,,,,339Thermal Mechanically Coupled Analysis341Coupled Acoustic-Structural AnalysisFluid/Solid Interaction- Added Mass Approach342346Coupled Electrostatic-Structural Analysis348Coupled Magnetostatic-Structural Analysis350Coupled Thermal-Electrical Analysis (Joule Heating)352Coupled Electrical-Thermal-Mechanical Analysis355Coupled Magnetostatic-Thermal Analysis357Coupled Magnetodynamic-Thermal Analysis358Coupled Magnetodynamic-Thermal-Structural Analysis..359References∴,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,362Contents 97 Material LibraryLinear Elastic Material365Composite Material ......367Layered Materials368Classical Lamination Theory for Multi-Layered Shells371Material Preferred direction372Material Dependent Failure Criteria376Interlaminar Shear for Thick Shell, Beam, Solid shell, and 3-d Composite brick elements394Interlaminar Stresses for continuum composite elements397Progressive Composite Failure397Mixture model399Gasket403Constitutive model403Nonlinear Hypoelastic Material407Thermo-Mechanical Shape Memory Model422Transformation Induced deformation424Constitutive Theory425Phase Transformation strains425Experimental Data Fitting for Thermo-mechanical Shape Memory Alloy427Mechanical Shape Memory Model431Conversion from Thermo-Mechanical to Mechanical SMA oyExperimental Data Fitting for Mechanical Shape Memory alle434435Elastomer436Updated Lagrange formulation for nonlinear elasticity455Time-independent Inelastic Behavior456Yield Conditions458Mohr-Coulomb Material(Hydrostatic Stress Dependence)464Buyukozturk Criterion(Hydrostatic Stress Dependence)465Powder material465Obtaining Crush Curve and Shear Failure Parameters by Curve Fitting in Marc475Work or strain hardening.....,,,479Flow rule485Constitutive Relations486Time-independent Cyclic Plasticity489Time-dependent Inelastic Behavior492Creep(Maxwell Model)翻495Oak Ridge National Laboratory Laws50010 Marc Volume A: Theory and User InformationSwelling.501Viscoplasticity502Time-dependent Cyclic Plasticity502Anand solder model504Viscoelastic Material505Bergstrom-Boyce Model516Narayanaswamy Model518Frequency-dependent Material Behavior522Viscoelastic Material Behavior in the Frequency Domain522Thermo-Rheologically Simple Material Behavior in the Frequency Domain538Deformation Dependent Relaxation in the Frequency Domain539Harmonic Equations of motion541Performing viscoelastic Analysis in the Frequency Domain543Temperature Effects and Coefficient of Thermal Expansion,546Piecewise Linear Representation547Temperature-Dependent Creep548Coefficient of Thermal Expansion549Time-Temperature-Transformation549Low Tension Material552Uniaxial Cracking Data552LoW Tension Cracking552Tension Softening552Crack Closure553Crushing553Analysis554Soil model554Elastic Models554Cam-Clay Model555Evaluation of soil parameters for the critical state soil model557Damage Models565Ductile metals565Elastomers568Cohesive Zone Modeling570Nonstructural materials578Heat transfer analysis579Piezoelectric Analysis579Thermo-Electrical Analysis579Coupled Electrical-Thermal-Mechanical Analysis579Hydrodynamic Bearing AnalysisFluid/ Solid Interaction Analysis- Added Mass approach579.579
- 2020-12-04下载
- 积分：1
