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.

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.

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.

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.

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.

scholarly journals A Consistent Track-to-Track Fusion Method Based on Copula Theory

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Kelin Lu ◽  
K. C. Chang ◽  
Rui Zhou
Keyword(s):  
Probability Distributions ◽  
A Priori ◽  
Joint Probability ◽  
Network Connectivity ◽  
Consistent Estimate ◽  
Fusion Algorithm ◽  
Copula Theory ◽  
Wide Range ◽  
Primary Advantage ◽  
Joint Probability Distributions

This paper addresses the problem of distributed fusion when the conditional independence assumptions on sensor measurements or local estimates are not met. A new data fusion algorithm called Copula fusion is presented. The proposed method is grounded on Copula statistical modeling and Bayesian analysis. The primary advantage of the Copula-based methodology is that it could reveal the unknown correlation that allows one to build joint probability distributions with potentially arbitrary underlying marginals and a desired intermodal dependence. The proposed fusion algorithm requires no a priori knowledge of communications patterns or network connectivity. The simulation results show that the Copula fusion brings a consistent estimate for a wide range of process noises.

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