Hierarchical Design of Negative Stiffness Metamaterials Using a Bayesian Network Classifier1

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Jordan Matthews ◽  
Timothy Klatt ◽  
Clinton Morris ◽  
Carolyn C. Seepersad ◽  
Michael Haberman ◽  
...  
Keyword(s):  
Bayesian Network ◽  
Hierarchical Modeling ◽  
Effective Properties ◽  
Negative Stiffness ◽  
Mechanical Stiffness ◽  
Design Problems ◽  
Length Scales ◽  
Bayesian Network Classifiers ◽  
Design Variables ◽  
Modeling Level

A set-based approach is presented for exploring multilevel design problems. The approach is applied to design negative stiffness metamaterials with mechanical stiffness and loss properties that surpass those of conventional composites. Negative stiffness metamaterials derive their properties from their internal structure, specifically by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design involves managing complex interdependencies among design variables across a range of length scales. Hierarchical material models are created for length scales ranging from the structure of the microscale negative stiffness inclusions to the effective properties of mesoscale metamaterials to the performance of an illustrative macroscale component. Bayesian network classifiers (BNCs) are used to map promising regions of the design space at each hierarchical modeling level, and the maps are intersected to identify sets of multilevel solutions that are likely to provide desirable system performance. The approach is particularly appropriate for highly efficient, top-down, performance-driven, multilevel design, as opposed to bottom-up, trial-and-error multilevel modeling.

Hierarchical Design of Composite Materials With Negative Stiffness Inclusions Using a Bayesian Network Classifier

2013 ◽  
Author(s):  
Jordan Matthews ◽  
Timothy Klatt ◽  
Carolyn C. Seepersad ◽  
Michael Haberman ◽  
David Shahan
Keyword(s):  
Composite Materials ◽  
Bayesian Network ◽  
Hierarchical Modeling ◽  
Effective Properties ◽  
Material Model ◽  
Negative Stiffness ◽  
Mechanical Stiffness ◽  
High Loss ◽  
High Stiffness ◽  
Bayesian Network Classifiers

Recent research in the field of composite materials has shown that it is theoretically possible to produce composite materials with macroscopic mechanical stiffness and loss properties that surpass those of conventional composites. This research explores the possibility of designing and fabricating these composite materials by embedding small volume fractions of negative stiffness inclusions in a continuous host material. Achieving high stiffness and loss from these materials by design, however, is a nontrivial task. This paper presents a hierarchical multiscale material model for these materials, coupled with a set-based, multilevel design approach based on Bayesian network classifiers. Bayesian network classifiers are used to map promising regions of the design space at each hierarchical modeling level, and then the maps are intersected to identify sets of multilevel or multiscale solutions that are likely to provide desirable system performance. Length scales range from the behavior of the structured microscale negative stiffness inclusions to the effective properties of mesoscale composite materials to the performance of an illustrative macroscale component — a vibrating beam coated with the high stiffness, high loss composite material.

Bayesian Network Classifiers and Design Flexibility Metrics for Set-Based, Multiscale Design With Materials Design Applications

2014 ◽  
Author(s):  
Jordan Matthews ◽  
Timothy Klatt ◽  
Carolyn C. Seepersad ◽  
Michael Haberman ◽  
David Shahan
Keyword(s):  
Composite Materials ◽  
Bayesian Network ◽  
Design Space Exploration ◽  
Design Space ◽  
Effective Properties ◽  
Materials Design ◽  
System Level ◽  
Bayesian Network Classifiers ◽  
Multi Level ◽  
Level Design

A set-based approach is presented for solving multi-scale or multi-level design problems. The approach incorporates Bayesian network classifiers (BNC) for mapping design spaces at each level and flexibility metrics for intelligently narrowing the design space as the design process progresses. The approach is applied to a hierarchical composite materials design problem, specifically, the design of composite materials with macroscopic mechanical stiffness and loss properties surpassing those of conventional composites. This macroscopic performance is achieved by embedding small volume fractions of negative stiffness (NS) inclusions in a host material. To design these materials, the set-based, multilevel design approach is coupled with a hierarchical modeling strategy that spans several scales, from the behavior of microscale NS inclusions to the effective properties of a composite material containing those inclusions and finally to the macroscopic performance of components. The approach is shown to increase the efficiency of multi-level design space exploration, and it is particularly appropriate for top-down, performance-driven design, as opposed to bottom-up, trial-and-error modeling. The design space mappings also build intuitive knowledge of the problem and promising regions of the design space, such that it is almost trivial to identify designs that yield preferred system-level performance.

Design Exploration of Reliably Manufacturable Materials and Structures With Applications to a Microstereolithography System

2018 ◽  
Author(s):  
Clinton Morris ◽  
Carolyn C. Seepersad
Keyword(s):  
Material Properties ◽  
Probability Distributions ◽  
Matrix Material ◽  
Joint Probability ◽  
Negative Stiffness ◽  
Mechanical Stiffness ◽  
Design Exploration ◽  
Exploration Process ◽  
Performance Targets ◽  
Bayesian Network Classifiers

One of the challenges in designing for additive manufacturing (AM) is accounting for the differences between as-designed and as-built geometries and material properties. From a designer’s perspective, these differences can lead to degradation of part performance, which is especially difficult to accommodate in small-lot or one-of-a-kind production. In this context, each part is unique, and therefore, extensive iteration is costly. Designers need a means of exploring the design space while simultaneously considering the reliability of additively manufacturing particular candidate designs. In this work, a design exploration approach, based on Bayesian network classifiers (BNC), is extended to incorporate manufacturability explicitly into the design exploration process. The example application is the design of negative stiffness (NS) metamaterials, in which small volume fractions of negative stiffness (NS) inclusions are embedded within a host material. The resulting metamaterial or composite exhibits macroscopic mechanical stiffness and loss properties that exceed those of the base matrix material. The inclusions are fabricated with microstereolithography with features on the scale of tens of microns, but variability is observed in material properties and dimensions from specimen to specimen. In this work, the manufacturing variability of critical features of a NS inclusion fabricated via microstereolithography are characterized experimentally and modelled mathematically. Specifically, the variation in the geometry of the NS inclusions and the Young’s modulus of the photopolymer are measured and modeled by both nonparametric and parametric joint probability distributions. Finally, the quantified manufacturing variability is incorporated into the BNC approach as a manufacturability classifier to identify candidate designs that achieve performance targets reliably, even when manufacturing variability is taken into account.

Sequential Sampling With Kernel-Based Bayesian Network Classifiers

2011 ◽  
Author(s):  
David Shahan ◽  
Carolyn C. Seepersad
Keyword(s):  
Bayesian Network ◽  
Collaborative Design ◽  
Design Space ◽  
Sequential Sampling ◽  
Space Filling ◽  
Training Set ◽  
Design Problems ◽  
Sampling Schemes ◽  
Domain Specific ◽  
Bayesian Network Classifiers

Complex design problems are typically decomposed into smaller design problems that are solved by domain-specific experts who must then coordinate their solutions into a satisfactory system-wide solution. In set-based collaborative design, collaborating engineers coordinate themselves by communicating multiple design alternatives at each step of the design process. Previous research has demonstrated that classifiers can be a communication medium for facilitating set-based collaborative design because of their ability to divide a design space into satisfactory and unsatisfactory regions. The proposed kernel-based Bayesian network (KBN) classifier uses a set of example designs of known acceptability, called the training set, to create a map of the satisfactory region of the design space. However, previous implementations used deterministic space-filling sampling sequences to choose the training set of designs. The shortcoming of deterministic space-filling sampling schemes is that they do not adapt to focus the samples on regions of interest to the design team (exploitation) or, alternatively, on regions in which little information is known (exploration). In this paper, we introduce the use of KBN classifiers as the basis for sequential sampling strategies that can be exploitive, exploratory, or any combination thereof.

A Set-Based Method for Multilevel Design of Materials and Structures With Manufacturing Uncertainty

2016 ◽  
Author(s):  
Clinton Morris ◽  
Carolyn C. Seepersad ◽  
Michael R. Haberman
Keyword(s):  
High Performance ◽  
Design Space ◽  
Probability Distributions ◽  
Joint Probability ◽  
Mechanical Stiffness ◽  
Design Problems ◽  
Paper Manufacturing ◽  
Bayesian Network Classifiers ◽  
Multi Level ◽  
Joint Probability Distributions

Recent research has indicated that embedding small volume fractions of negative stiffness (NS) inclusions within a host material can create composites with macroscopic mechanical stiffness and loss properties that exceed conventional composites. To design these composites, a multi-level, set-based approach that employs Bayesian network classifiers was developed to identify sets of satisfactory designs at each level of the multilevel design space. In this paper, manufacturing uncertainties are incorporated to further refine the design space mappings created by the set-based approach. Manufacturing uncertainty refers to the random deviations in dimensions and other properties that often arise when fabricating a specimen. Joint probability distributions are used to model this manufacturing uncertainty. The joint probability distributions are formulated as kernel density estimates that can be based on manufacturing data. The joint probability distributions are incorporated within the set-based approach to identify sets of designs that not only yield satisfactory performance but also offer robustness to manufacturing uncertainty. The approach is demonstrated in the context of hierarchical composite materials, but it can be applied to other multi-level design problems to efficiently yield sets of robustly manufacturable, high performance designs.

Design Exploration of Reliably Manufacturable Materials and Structures With Applications to Negative Stiffness Metamaterials and Microstereolithography1

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Clinton Morris ◽  
Logan Bekker ◽  
Michael R. Haberman ◽  
Carolyn C. Seepersad
Keyword(s):  
Material Properties ◽  
Matrix Material ◽  
Negative Stiffness ◽  
Mechanical Stiffness ◽  
Design Exploration ◽  
Exploration Process ◽  
Performance Targets ◽  
Bayesian Network Classifiers ◽  
Performance Requirements ◽  
Base Matrix

One of the challenges in designing metamaterials for additive manufacturing (AM) is accounting for the differences between as-designed and as-built geometries and material properties. From a designer's perspective, these differences can lead to degradation of part and metamaterial performance, which is especially difficult to accommodate in small-lot or one-of-a-kind production. In this context, each part is unique, and therefore, extensive iteration is costly. Designers need a means of exploring the design space while simultaneously considering the reliability of additively manufacturing particular candidate designs. In this work, a design exploration approach, based on Bayesian network classifiers (BNC), is extended to incorporate manufacturing variation into the design exploration process and identify designs that reliably meet performance requirements when this variation is taken into account. The example application is the design of negative stiffness (NS) metamaterials, in which small volume fractions of NS inclusions are embedded within a host material. The resulting metamaterial or composite exhibits macroscopic mechanical stiffness and loss properties that exceed those of the base matrix material. The inclusions are fabricated with microstereolithography with features on the scale of tens of microns, but variability is observed in material properties and dimensions from specimen to specimen. This variability is measured and modeled via design, fabrication, and characterization of metrology parts. The quantified manufacturing variability is incorporated into the BNC approach as a manufacturability classifier to identify candidate designs that achieve performance targets reliably, even when manufacturing variability is taken into account.

Multi-Objective Design Problem of Tire Wear and Visualization of Its Pareto Solutions2

2006 ◽  
Vol 34 (3) ◽  
pp. 170-194 ◽  
Author(s):  
M. Koishi ◽  
Z. Shida
Keyword(s):  
Inverse Problems ◽  
Conceptual Design ◽  
Dimensional Space ◽  
Design Stage ◽  
Objective Functions ◽  
Pareto Solutions ◽  
Design Problems ◽  
Multi Objective ◽  
Design Engineers ◽  
Design Variables

Abstract Since tires carry out many functions and many of them have tradeoffs, it is important to find the combination of design variables that satisfy well-balanced performance in conceptual design stage. To find a good design of tires is to solve the multi-objective design problems, i.e., inverse problems. However, due to the lack of suitable solution techniques, such problems are converted into a single-objective optimization problem before being solved. Therefore, it is difficult to find the Pareto solutions of multi-objective design problems of tires. Recently, multi-objective evolutionary algorithms have become popular in many fields to find the Pareto solutions. In this paper, we propose a design procedure to solve multi-objective design problems as the comprehensive solver of inverse problems. At first, a multi-objective genetic algorithm (MOGA) is employed to find the Pareto solutions of tire performance, which are in multi-dimensional space of objective functions. Response surface method is also used to evaluate objective functions in the optimization process and can reduce CPU time dramatically. In addition, a self-organizing map (SOM) proposed by Kohonen is used to map Pareto solutions from high-dimensional objective space onto two-dimensional space. Using SOM, design engineers see easily the Pareto solutions of tire performance and can find suitable design plans. The SOM can be considered as an inverse function that defines the relation between Pareto solutions and design variables. To demonstrate the procedure, tire tread design is conducted. The objective of design is to improve uneven wear and wear life for both the front tire and the rear tire of a passenger car. Wear performance is evaluated by finite element analysis (FEA). Response surface is obtained by the design of experiments and FEA. Using both MOGA and SOM, we obtain a map of Pareto solutions. We can find suitable design plans that satisfy well-balanced performance on the map called “multi-performance map.” It helps tire design engineers to make their decision in conceptual design stage.

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