Cherkaev-Variational Methods For Structural Optimization

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1、ThisispageiPrinter:OpaquethisVariationalMethodsforStructuralOptimizationThisispageiiPrinter:OpaquethisThisispageiPrinter:OpaquethisVariationalMethodsforStructuralOptimizationAndrejCherkaevDepartmentofMathematicsTheUniversityofUtahSaltLakeCity,UT84112-0090ivInsertthecopyrightinformation,etc.Thi

2、sispagevPrinter:OpaquethisContentsListofFiguresxiiiPrefacexvIPreliminaries11RelaxationofOne-DimensionalVariationalProblems31.1AnOptimalDesignbyMeansofComposites........31.2StabilityofMinimizersandtheWeierstrassTest......71.2.1NecessaryandSucientConditions.........71.2.2VariationalMethods:Weie

3、rstrassTest........101.3Relaxation............................141.3.1NonconvexVariationalProblems...........141.3.2ConvexEnvelope....................161.3.3MinimalExtensionandMinimizingSequences....191.3.4Examples:SolutionstoNonconvexProblems....241.3.5Null-LagrangiansandConvexity...........27

4、1.3.6Duality.........................291.4ConclusionandProblems...................322ConductingComposites352.1ConductivityofInhomogeneousMedia............352.1.1EquationsforConductivity..............352.1.2ContinuityConditionsinInhomogeneousMaterials.392.1.3Energy,VariationalPrinciples........

5、.....422.2Composites...........................452.2.1HomogenizationandEectiveTensor.........46viContents2.2.2EectivePropertiesofLaminates...........512.2.3EectiveMediumTheory:CoatedCircles......552.3ConclusionandProblems...................573BoundsandG-Closures593.1EectiveTensors:Variatio

6、nalApproach...........593.1.1CalculationofEectiveTensors............593.1.2WienerBounds.....................613.2G-ClosureProblem.......................633.2.1G-convergence.....................633.2.2G-Closure:DenitionandProperties.........673.2.3Example:TheG-ClosureofIsotropicMaterials...73

7、3.2.4WeakG-Closure(RangeofAttainability)......753.3ConclusionandProblems...................76IIOptimizationofConductingComposites794DomainsofExtremalConductivity814.1StatementoftheProblem...................824.2RelaxationBasedontheG-Clo