Analysis of Functionally Graded Material Object Representation Methods

Solid Freeform Fabrication (SFF) processes have demonstrated the ability to produce parts with locally controlled composition. To exploit this potential, methods to represent and exchange parts with varying local composition need to be proposed and evaluated. In modeling such parts efficiently, any such method should provide a concise and accurate description of all of the relevant information about the part with minimal cost in terms of storage. To address these issues, several approaches to modeling Functionally Graded Material (FGM) objects are evaluated based on their memory requirements. Through this research, an information pathway for processing FGM objects based on image processing is proposed. This pathway establishes a clear separation between design of FGM objects, their processing, and their fabrication. Similar to how an image is represented by a continuous vector valued function of the intensity of the primary colors over a two-dimensional space, an FGM object is represented by a vector valued function spanning a Material Space, defined over the threedimensional Build Space. Therefore, the Model Space for FGM objects consists of a Build Space and a Material Space. The task of modeling and designing an FGM object, therefore, is simply to accurately represent the function m(x) where x ∈ Build Space. Data structures for representing FGM objects are then described and analyzed, including a voxelbased structure, finite element method, and the extension of the Radial-Edge and Cell-Tuple-Graph data structures with FGMDomains in order to represent spatially varying properties. All of the methods are capable of defining the function m(x) but each does so in a different way. Along with introducing each data structure, the storage cost for each is derived in terms of the number of instances of each of its fundamental classes required to represent an object. In order to determine the optimal data structure to model FGM objects, the storage cost associated with each data structure for representing several hypothetical models is calculated. Although these models are simple in nature, their curved geometries and regions of both piece-wise constant and non-linearly graded compositions reflect the features expected to be found in real applications. In each case, the generalized cellular methods are found to be optimal, accurately representing the intended design. Thesis Supervisor: Nicholas M. Patrikalakis, Ph.D. Title: Kawasaki Professor of Engineering Thesis Supervisor: Emanuel M. Sachs, Ph.D. Title: Professor of Mechanical Engineering