SFF-Oriented Modeling and Process Planning of Functionally Graded Materials Using a Novel Equal Distance Offset Approach

This paper deals with the modeling and process planning of solid freeform fabrication (SFF) of 3D functionally graded materials (FGMs). A novel approach of representation and process planning of FGMs, termed as equal distance offset (EDO), is developed. In EDO, a neutral arbitrary 3D CAD model is adaptively sliced into a series of 2D layers. Within each layer, 2D material gradients are designed and represented via dividing the 2D shape into several sub-regions enclosed by iso-composition contours. If needed, the material composition gradient within each of sub-regions can be further determined by applying the equal distance offset algorithm to each sub-region. Using this approach, an arbitrary-shaped 3D FGM object with linear or non-linear composition gradients can be represented and fabricated via suitable SFF machines.Mechanical Engineerin

Knowledge composition methodology for effective analysis problem formulation in simulation-based design

In simulation-based design, a key challenge is to formulate and solve analysis problems efficiently to evaluate a large variety of design alternatives. The solution of analysis problems has benefited from advancements in commercial off-the-shelf math solvers and computational capabilities. However, the formulation of analysis problems is often a costly and laborious process. Traditional simulation templates used for representing analysis problems are typically brittle with respect to variations in artifact topology and the idealization decisions taken by analysts. These templates often require manual updates and "re-wiring" of the analysis knowledge embodied in them. This makes the use of traditional simulation templates ineffective for multi-disciplinary design and optimization problems. Based on these issues, this dissertation defines a special class of problems known as variable topology multi-body (VTMB) problems that characterizes the types of variations seen in design-analysis interoperability. This research thus primarily answers the following question: How can we improve the effectiveness of the analysis problem formulation process for VTMB problems? The knowledge composition methodology (KCM) presented in this dissertation answers this question by addressing the following research gaps: (1) the lack of formalization of the knowledge used by analysts in formulating simulation templates, and (2) the inability to leverage this knowledge to define model composition methods for formulating simulation templates. KCM overcomes these gaps by providing: (1) formal representation of analysis knowledge as modular, reusable, analyst-intelligible building blocks, (2) graph transformation-based methods to automatically compose simulation templates from these building blocks based on analyst idealization decisions, and (3) meta-models for representing advanced simulation templates VTMB design models, analysis models, and the idealization relationships between them. Applications of the KCM to thermo-mechanical analysis of multi-stratum printed wiring boards and multi-component chip packages demonstrate its effectiveness handling VTMB and idealization variations with significantly enhanced formulation efficiency (from several hours in existing methods to few minutes). In addition to enhancing the effectiveness of analysis problem formulation, KCM is envisioned to provide a foundational approach to model formulation for generalized variable topology problems.Ph.D.Committee Co-Chair: Dr. Christiaan J. J. Paredis; Committee Co-Chair: Dr. Russell S. Peak; Committee Member: Dr. Charles Eastman; Committee Member: Dr. David McDowell; Committee Member: Dr. David Rosen; Committee Member: Dr. Steven J. Fenve

A uniform definition of stochastic process calculi

We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s; α;P). The first andthe second components are the source state, s, and the label, α, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s0. For example, in the case of stochastic process algebras the value of the continuation function on s0 represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s0 from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the coexistence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics

Unstructured spline spaces for isogeometric analysis based on spline manifolds

Based on spline manifolds we introduce and study a mathematical framework for analysis-suitable unstructured B-spline spaces. In this setting the parameter domain has a manifold structure, which allows for the definition of function spaces that have a tensor-product structure locally, but not globally. This includes configurations such as B-splines over multi-patch domains with extraordinary points, analysis-suitable unstructured T-splines, or more general constructions. Within this framework, we generalize the concept of dual-compatible B-splines, which was originally developed for structured T-splines. This allows us to prove the key properties that are needed for isogeometric analysis, such as linear independence and optimal approximation properties for $h$-refined meshes

Stratifying multiparameter persistent homology

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter family of spaces obtained from the data. In applications data often depend on several parameters, and in this case one is interested in studying the persistent homology of a multiparameter family of spaces associated to the data. While the theory of persistent homology for one-parameter families is well-understood, the situation for multiparameter families is more delicate. Following Carlsson and Zomorodian we recast the problem in the setting of multigraded algebra, and we propose multigraded Hilbert series, multigraded associated primes and local cohomology as invariants for studying multiparameter persistent homology. Multigraded associated primes provide a stratification of the region where a multigraded module does not vanish, while multigraded Hilbert series and local cohomology give a measure of the size of components of the module supported on different strata. These invariants generalize in a suitable sense the invariant for the one-parameter case.Comment: Minor improvements throughout. In particular: we extended the introduction, added Table 1, which gives a dictionary between terms used in PH and commutative algebra; we streamlined Section 3; we added Proposition 4.49 about the information captured by the cp-rank; we moved the code from the appendix to github. Final version, to appear in SIAG