Contents

## Towards Nonlinear Multimaterial Topology Optimization using Machine Learning in addition to

Barna, Mike, General Manager has reference to this Academic Journal, PHwiki organized this Journal Towards Nonlinear Multimaterial Topology Optimization using Machine Learning in addition to Metamodel-based Optimization Kai Liu Purdue University1Andrés Tovar Indiana Univ. – Purdue Univ. IndianapolisEmily NutWell Honda R&D AmericasDuane Detwiler Honda R&D AmericasSystematic Design Optimization Approach Three Stages Design Optimization2Generalized Structural optimization problemThe resulting is a distribution of up to n materials within the structure.3Conceptual Design

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Generalized Structural optimization problemK-means clustering is a simple widely used unsupervised machine learning technique.4Design ParameterizationK-meansObjectiveGiven a set of objects, K-means clustering aims to partition the n objects into K sets so as to minimize the within-cluster sum of squares: K-means clustering5Design ParameterizationAlgorithmStep 1. Given n objects, initialize k cluster centersStep 2. Assign each object to its closest cluster centerStep 3. Update the center as long as each clusterStep 4. Repeat 2 in addition to 3 until no change in cluster centersK-means clustering6Design Parameterization

Problem statement7Parametric OptimizationThe parametric optimization problem can be posted with reduced number of variables.Metamodel-based multi-objective optimization8Parametric Optimization9ExamplesMinimum complianceMBB-BeamCompliant mechanismForce InverterCrashworthiness designS-rail tubular component

Minimum Compliance10ExamplesConceptual Designelements: 60×20 Q4objective: min compliancemass fraction: 0.5material: E = 1.0, nu = 0.3optimization problem:Minimum ComplianceExamplesDesign ParameterizationUsing Kmeans to cluster conceptual design into 2 groupsCluster Number KThe bigger value of K, the closer clustered solution to the conceptual design.11Minimum Compliance12ExamplesParametric OptimizationMinimum compliance with reduced number of design variablesOptimization problem:

Minimum ComplianceExamples13Minimum Compliance – comparison of multimaterial topology optimization solutionsExamples14IterationsObjectiveClusteredMultimaterial[1]16 Topology + 1 Kmeans + 7 SQP distinct values236 Outer + 708 Inner Topology167.35169.353986Compliant Mechanism15ExamplesConceptual Designelements: 150×75 Q4objective: max output displacementmass fraction: 0.35material: E = 1.0, nu = 0.3optimization problem:

Compliant Mechanism16ExamplesDesign ParameterizationUsing Kmeans to cluster conceptual design into 2 groupsParametric OptimizationMaximize output displacement with reduced number of design variablesMinimum ComplianceExamples17Parametric OptimizationObjective: -0.614xmin: 0.011xmax: 1.000 values: 2Conceptual DesignObjective: -1.02xmin: 0.001xmax: 1.00 values: 3027Design ParameterizationObjective: 0.133xmin: 0.042xmax: 0.940 values: 2Compliant Mechanism – comparison of multimaterial topology optimization solutions.Examples18IterationsObjectiveClusteredMultimaterial[1]153 Topology + 1 Kmeans + 2 SQP distinct values200 Outer + 600 Inner Topology-0.713-0.67433070

Conceptual DesignGeometryInitial DesignCrashworthiness Design19ExamplesConceptual DesignOptimization ProblemCrashworthiness Design20ExamplesCrashworthiness Design21ExamplesDesign ParameterizationUsing Kmeans to cluster conceptual design into 11 groups[2]

Crashworthiness Design22ExamplesParametric OptimizationMaximize crashworthinessOptimization problem specific energy absorption, peak crushing as long as ce23Pareto FrontsThree Stages Design Optimization Summary241 Conceptualstructural optimizationthous in addition to s variablesgood per as long as mance2 Param.Kmeans clusteringreduced variablesworst per as long as mance3 Optimizationmultiobjective optimizationsequential metamodel updateimproved per as long as manceimproved manufacturability123Design Cycle

25ReferencesTavakoli, R., in addition to Mohseni, S. M., 2014. Alternating active-phase algorithm as long as multimaterial topology optimization problems: A 115-line MATLAB implementation, Struct Multidisc Optim, 49(4), pp. 621642.Liu, K., Tovar, A., Nutwell, E., in addition to Detwiler, D., Thin-walled compliant mechanism component design assisted by machine learning in addition to multiple surrogates, SAE Technical Paper 2015-01-1369, 2015.Acknowledgement Honda R&D Americas supported this research ef as long as t. Any opinions, findings, conclusions, in addition to recommendations expressed in this investigation are those of the writers in addition to do not necessarily reflect the views of the sponsors.

## Barna, Mike General Manager

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