会计学25.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.1TheSimultaneousFormulationoftheProblem5.2TheNestedFormulationandSomeofItsProperties5.2TheNestedFormulationandSomeofItsProperties5.2.1ConvexityoftheNestedProblem5.2.2FullyStressedDesigns5.2.2FullyStressedDesigns5.2.2FullyStressedDesigns5.3NumericalSolutionoftheNestedProblemUsingMMA4.5TheMethodofMovingAsymptotes(MMA)4.5TheMethodofMovingAsymptotes(MMA)5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMA5.3NumericalSolutionoftheNestedProblemUsingMMAStep1:inputtheneededparameterandinitialguess:Thelocationofthenodes,whatnodesthatare(partially)fixed;theappliedforceF;Materialproperties:suchasYoung’smodulusE;lowerandupperbounds,xjminandxjmax;Vmax;x0,initialvaluesofthelowerasymptotes,L0j;aninitialvalueλ>0;Puttheiterationindexk=0.5.3NumericalSolutionoftheNestedProblemUsingMMAStep4:FormulateanMMAapproximationatxkStep5:Solvethekthsub-problemusingLagrangianduality5.3NumericalSolutionoftheNestedProblemUsingMMA39