Richard J. Malak

Origami-inspired active structures: a synthesis and review

Origami, the ancient art of paper folding, has inspired the design of engineering devices and structures for decades. The underlying principles of origami are very general, which has led to applications ranging from cardboard containers to deployable space structures. More recently, researchers have become interested in the use of active materials (i.e., those that convert various forms of energy into mechanical work) to effect the desired folding behavior. When used in a suitable geometry, active materials allow engineers to create self-folding structures. Such structures are capable of performing folding and/or unfolding operations without being kinematically manipulated by external forces or moments. This is advantageous for many applications including space systems, underwater robotics, small scale devices, and self-assembling systems. This article is a survey and analysis of prior work on active self-folding structures as well as methods and tools available for the design of folding structures in general and self-folding structures in particular. The goal is to provide researchers and practitioners with a systematic view of the state-of-the-art in this important and evolving area. Unifying structural principles for active self-folding structures are identified and used as a basis for a quantitative and qualitative comparison of numerous classes of active materials. Design considerations specific to folded structures are examined, including the issues of crease pattern identification and fold kinematics. Although few tools have been created with active materials in mind, many of them are useful in the overall design process for active self-folding structures. Finally, the article concludes with a discussion of open questions for the field of origami-inspired engineering.

Multi-attribute utility analysis in set-based conceptual design

During conceptual design, engineers deal with incomplete product descriptions called design concepts. Engineers must compare these concepts in order to move towards the more desirable designs. However, comparisons are difficult because a single concept associates with numerous possible final design specifications, and any meaningful comparison of concepts must consider this range of possibilities. Consequently, the performance of a concept can only be characterized imprecisely. While standard multi-attribute utility theory is an accepted framework for making preference-based decisions between precisely characterized alternatives, it does not directly accommodate the analysis of imprecisely characterized alternatives. By extending uncertainty representations to model imprecision explicitly, it is possible to apply the principles of utility theory to such problems. However, this can lead to situations of indeterminacy, meaning that the decision maker is unable to identify a single concept as the most preferred. Under a set-based perspective and approach to design, a designer can work towards a single solution systematically despite indecision arising from imprecise characterizations of design concepts. Existing work in set-based design primarily focuses on feasibility conditions and single-attribute objectives, which are insufficient for most design problems. In this article, we combine the framework of multi-attribute utility theory, the perspective of set-based design, and the explicit mathematical representation of imprecision into a single approach to conceptual design. Each of the component theories is discussed, and their combined application developed. The approach is illustrated using the conceptual design of a fixed-ratio power transmission as an example. Additionally, important directions for future research are identified, with a particular focus on the process of modeling abstract design concepts.

A KNOWLEDGE REPOSITORY FOR BEHAVIORAL MODELS IN ENGINEERING DESIGN

Computer simulations and behavioral modeling are becoming increasingly important in product development processes. Simulations can result in better decisions in less time by providing the designers with greater understanding of the product’s behavior. However, behavior model creators (i.e. analysts) and behavior model users (i.e. designers) often do not have the same level of understanding of the model, thus limiting the reuse of a model. Our goal in this research is to develop a clean interface that reduces the knowledge gap between engineering design and analysis by facilitating reuse of behavioral models. To achieve a higher level of reuse in the product design process, we propose a meta-data representation for formally characterizing behavioral models. The meta-data representation captures the assumptions, limitations, accuracy, and context of engineering behavioral models. Based on this knowledge representation, a proof-of-concept repository is implemented for archiving and exchanging reusable behavioral models. The knowledge representation and implementation is illustrated with a simple cantilever beam example.

Design optimization and uncertainty analysis of SMA morphing structures

The continuing implementation of shape memory alloys (SMAs) as lightweight solid-state actuators in morphing structures has now motivated research into finding optimized designs for use in aerospace control systems. This work proposes methods that use iterative analysis techniques to determine optimized designs for morphing aerostructures and consider the impact of uncertainty in model variables on the solution. A combination of commercially available and custom coded tools is utilized. ModelCenter, a suite of optimization algorithms and simulation process management tools, is coupled with the Abaqus finite element analysis suite and a custom SMA constitutive model to assess morphing structure designs in an automated fashion. The chosen case study involves determining the optimized configuration of a morphing aerostructure assembly that includes SMA flexures. This is accomplished by altering design inputs representing the placement of active components to minimize a specified cost function. An uncertainty analysis is also conducted using design of experiment methods to determine the sensitivity of the solution to a set of uncertainty variables. This second study demonstrates the effective use of Monte Carlo techniques to simulate the variance of model variables representing the inherent uncertainty in component fabrication processes. This paper outlines the modeling tools used to execute each case study, details the procedures for constructing the optimization problem and uncertainty analysis, and highlights the results from both studies.

Design and Optimization of a Shape Memory Alloy-Based Self-Folding Sheet

Origami engineering—the practice of creating useful three-dimensional structures through folding and fold-like operations on two-dimensional building-blocks—has the potential to impact several areas of design and manufacturing. In this article, we study a new concept for a self-folding system. It consists of an active, self-morphing laminate that includes two meshes of thermally-actuated shape memory alloy (SMA) wire separated by a compliant passive layer. The goal of this article is to analyze the folding behavior and examine key engineering tradeoffs associated with the proposed system. We consider the impact of several design variables including mesh wire thickness, mesh wire spacing, thickness of the insulating elastomer layer, and heating power. Response parameters of interest include effective folding angle, maximum von Mises stress in the SMA, maximum temperature in the SMA, maximum temperature in the elastomer, and radius of curvature at the fold line. We identify an optimized physical realization for maximizing folding capability under mechanical and thermal failure constraints. Furthermore, we conclude that the proposed self-folding system is capable of achieving folds of significant magnitude (as measured by the effective folding angle) as required to create useful 3D structures.

Using Support Vector Machines to Formalize the Valid Input Domain of Predictive Models in Systems Design Problems

Predictive modeling can be a valuable tool for systems designers, allowing them to capture and reuse knowledge from a set of observed data related to their system. An important challenge associated with predictive modeling is that of describing the domain over which model predictions are valid. This is necessary to avoid extrapolating beyond the original data, particularly when designers use predictive models in concert with optimizers or other computational routines that search a model’s input space automatically. The general problem of domain description is complicated by the characteristics of observational data sets, which can contain small numbers of samples, can have nonlinear associations among the variables, can be nonconvex, and can occur in disjoint clusters. Support vector machine (SVM) techniques, developed originally in the machine learning community, offer a solution to this problem. This paper is a description of a kernel-based SVM approach that yields a formal mathematical description of the valid input domain of a predictive model. The approach also provides for cluster analysis, which can lead to improved model accuracy through the decomposition of a data set into multiple subsets that designers can model independently. This paper includes a mathematical presentation of kernel-based SVM methods, an explanation of the procedure for applying the approach to predictive modeling problems, and illustrative examples for applying and using the approach in systems design.

Modeling Design Concepts under Risk and Uncertainty using Parameterized Efficient Sets

Decisions made during conceptual design can have a major impact on the success of a design project. However, the inherently imprecise nature of design is a major source of uncertainty and risk in conceptual design decisions. A single concept relates to a large set of specific design implementations, each of which has a different level of desirability based on the tradeoffs designers are willing to make. It therefore is beneficial for designers to have an understanding of the various tradeoffs they can achieve by implementing a concept. In this paper, we describe an approach to modeling design concepts under uncertainty based on a tradeoff space representation. We use the principles of decision making to develop a useful interpretation of a tradeoff space for decisions under uncertainty and to identify criteria useful for eliminating undesirable tradeoffs from consideration. We illustrate our approach to modeling and decision making on an example for the conceptual design of a gearbox.

COMPOSING TRADEOFF MODELS FOR MULTI-ATTRIBUTE SYSTEM-LEVEL DECISION MAKING

In this paper, we study the prospects for modeling a system by composing tradeoff models of its components. A tradeoff model is an abstract representation of a system in terms of a predictive relationship between its top-level attributes. Designers can use this to predict the attributes they would achieve if they implemented the system. Prior approaches to generating tradeoff information are incompatible with model composition due to their reliance on classical Pareto dominance. We show that by using a generalization of this, called parameterized Pareto dominance, designers can produce tradeoff models that they can compose validly. The focus of this paper is on analyzing the modeling approach mathematically. The main result is proof that, under mild assumptions about how component-level attributes relate to system-level attributes, the approach is mathematically sound from a decision-theoretic perspective. The paper also includes a demonstration of the approach on the design of a hydraulic log splitter system using hydraulic component tradeoff models based on data about commercially-available components.

Foundations of validating reusable behavioral models in engineering design problems

We present a conceptual framework for validating reusable behavioral models. The setting for this work is a modern product development environment in which design is performed by teams of specialists that collaborate through model reuse. The various modes of model reuse separate validation-relevant knowledge from the tasks for which it is needed. To enable efficient and effective transfer of this knowledge to the tasks for which it is needed, we propose a framework for validating reusable behavioral models based on formal representations of validation-relevant knowledge. The framework defines the abstract knowledge representation as well as an abstract process for applying this knowledge to validate reusable behavioral models. Although this framework is not a complete solution to the validation problem in design, it forms a foundation for understanding and solving the problem and represents a starting point for future investigation.

On Characterizing and Assessing the Validity of Behavioral Models and Their Predictions

We present a conceptual framework for the validation of behavioral models and the prediction information derived from them. The setting for this work is a modern product development environment in which design is performed by teams of specialists who exchange information and knowledge. This setting makes validation responsibilities ambiguous and separates users from knowledge relevant to validation. To alleviate these problems, we identify three complementary validation responsibilities—validity characterization, compatibility assessment and adequacy assessment—that together solve the validation problem. We define the responsibilities in terms of formal descriptions of models and predictions that provide accuracy assurances within a welldefined context. Because behavioral models are similar to scientific theories and are a form of knowledge, it is possible to draw upon the philosophy literature to gain insight into validation. We review the relevant epistemology and the philosophy of science literature and identify several conclusions that apply to validation. These conclusions provide perspective on the limitations of the described framework. Although the framework is not a complete solution to the validation problem, it serves as is a conceptual roadmap to understanding and solving the problem. As such, this work raises many fundamental questions about validation and represents a starting point for future investigation.