Towards Nonlinear Multimaterial Topology Optimization using ...
Towards Nonlinear Multimaterial Topology Optimization using Machine Learning and Metamodel-based Optimization Kai Liu Purdue University Emily NutWell Honda R&D Americas Andrs Tovar Indiana Univ. - Purdue Univ. Indianapolis Duane Detwiler Honda R&D Americas 1 Three Stages Design Optimization Systematic Design Optimization Approach Conceptual Design Generating conceptual design using
structural optimization Continuous design distribution Design Parameterization Parameterizing conceptual design using machine learning Simple and efficient Parametric Optimization Utilizing parametric optimization with reduced number of design variables Further improves
performances and manufacturability 2 Conceptual Design Generalized Structural optimization problem The resulting is a distribution of up to n materials within the structure. 3 Design Parameterization Generalized Structural optimization problem K-means K-means clustering is a simple widely used
unsupervised machine learning technique. 4 Design Parameterization K-means clustering Objective Given 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: 5 Design Parameterization K-means clustering Algorithm Step 1. Given n objects, initialize k cluster centers
Step 2. Assign each object to its closest cluster center Step 3. Update the center for each cluster Step 4. Repeat 2 and 3 until no change in cluster centers 6 Parametric Optimization Problem statement The parametric optimization problem can be posted with reduced number of variables.
9 Examples Minimum Compliance Conceptual Design elements: 60x20 Q4 objective: min compliance mass fraction: 0.5 material: E = 1.0, nu = 0.3
optimization problem: 10 Examples Minimum Compliance Design Parameterization Using Kmeans to cluster conceptual design into 2 groups Cluster Number K The bigger value of K, the closer clustered solution to the conceptual design.
11 Examples Minimum Compliance Parametric Optimization Minimum compliance with reduced number of design variables Optimization problem: 12 Examples Minimum Compliance Conceptual Design
Compliant Mechanism Conceptual Design elements: 150x75 Q4 objective: max output displacement mass fraction: 0.35 material: E = 1.0, nu = 0.3 optimization problem: 15
Examples Compliant Mechanism Design Parameterization Using Kmeans to cluster conceptual design into 2 groups Parametric Optimization Maximize output displacement with reduced number of design variables 16 Examples Minimum Compliance Conceptual Design
reduced variables worst performance 3 24 References 1. Tavakoli, R., and Mohseni, S. M., 2014. Alternating active-phase algorithm for multimaterial topology optimization problems: A 115line MATLAB implementation, Struct Multidisc Optim, 49(4), pp. 621 642. 2. Liu, K., Tovar, A., Nutwell, E., and Detwiler, D., Thin-walled compliant mechanism component design assisted by machine learning and multiple surrogates, SAE Technical Paper 2015-01-1369, 2015. Acknowledgement
Honda R&D Americas supported this research effort. Any opinions, findings, conclusions, and recommendations expressed in this investigation are those of the writers and do not necessarily reflect the views of the sponsors. 25
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