The introduction of composition gradients into the already hierarchical structure of martensitic steel leads to difficulties in modeling that arise from events occurring in the material at different length scales. In this thesis we isolate the features that are important to describing the mechanical properties of martensite and constitutively couple them through their respective length scales. The idea of a representative volume element is rigorously explored in which the microstructure is represented through a Masing model as well as more advanced structures akin to a nanocomposite. As such, we are able to keep track of microscopic yielding and internal stress evolution at the smallest scales (nanoscale through microscale). With the use of representative volume elements, we are able to track events at the largest scale as well by freely being able to change scale. As such, macroscopic phenomenon such as: thermal fields, composition fields, macroscopic loads, and the associated macroscopic phase distributions and stress distributions are evaluated. We conclude by demonstrating the power of this modelling technique in the design and optimization of compositionally graded steel structures via virtual prototyping. / Dissertation / Doctor of Philosophy (PhD)

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth and Planetary Science, 1982. / Microfiche copy available in Archives and Science / Bibliography: leaves 31-32. / by Jeremy Robert Henderson. / M.S.

The material presented in this thesis uses concepts of the finite element and doublet panel methods to develop a structural-aerodynamic coupled mathematical model for the analysis of a morphing wing tip composed of smart materials. Much research is currently being performed within many facets of engineering on the use of smart or intelligent materials. Examples of the beneficial characteristics of smart materials might include altering a structure's mechanical properties, controlling its dynamic response(s) and sensing flaws that might progressively become detrimental to the structure. This thesis describes a bio-inspired adaptive structure that will be used in morphing an aircraft's wing tip. The actuation system is derived from individual flexible matrix composite tube actuators embedded in a matrix medium that when pressurized, radical structural shape change is possible. A driving force behind this research, as with any morphing wing related studies, is to expand the limitations of an aircraft's mission, usually constrained by the wing design. Rather than deploying current methods of achieving certain flight characteristics, changing the shape of a wing greatly increases the flight envelope. This thesis gives some insight as to the structural capability and limitations using current numerical methods to model a morphing wing in a flow. / Master of Science

The crystal structures of zircon, scheelite, and monazite are very closely related. All three have chains of alternating polyhedra and planes of closest packed or pseudo-closest packed cations. Using these similarities the unit cells of these structures can be placed in analogous orientations. This in turn leads to a better understanding of the geometrical aspects of the reconstructive phase transformations that occur among the structure types as functions of temperature and pressure. In essence the phase transformations require the cation planes of one structure to the cation planes of another. Phase transformations also occur via compositional pathways. Crystal structure parameters were modeled for compounds with the zircon, scheelite and monazite structure types using multiple regression techniques. Data consisted of structure refinements of 26 zircon-, 13 scheelite-, and 13 monazite-type compounds. These compounds include but are not limited to the lanthanide vanadates and phosphates, the alkali earth molybdates and tungstates, and KTcO₄. The structural parameters studied included bond lengths, bond angles, polyhedral volumes, unit cell edge lengths, tetrahedral quadratic elongations and atomic coordinates of individual atoms; they were modeled as a function of the Shannon radii of the cations and the product of the M and T cation charges. Correlation coefficients for these regressions exceeded 0.9 for nearly all parameters studied except for the y coordinate of M, the z coordinate of O1, and T-O1-M2 angle of the monazite compounds. / Master of Science

In recent years it has been shown that the folding pattern of an RNA molecule plays an important role in its function, likened to a lock and key system. γ-structures are a subset of RNA pseudoknot structures filtered by topological genus that lend themselves nicely to combinatorial analysis. Namely, the coefficients of their generating function can be approximated for large n. This paper is an investigation into the length-spectrum of the longest block in random γ-structures. We prove that the expected length of the longest block is on the order n - O(n^1/2). We further compare these results with a similar analysis of the length-spectrum of rainbows in RNA secondary structures, found in Li and Reidys (2018). It turns out that the expected length of the longest block for γ-structures is on the order the same as the expected length of rainbows in secondary structures. / Master of Science / Ribonucleic acid (RNA), similar in composition to well-known DNA, plays a myriad of roles within the cell. The major distinction between DNA and RNA is the nature of the nucleotide pairings. RNA is single stranded, to mean that its nucleotides are paired with one another (as opposed to a unique complementary strand). Consequently, RNA exhibits a knotted 3D structure. These diverse structures (folding patterns) have been shown to play important roles in RNA function, likened to a lock and key system. Given the cost of gathering data on folding patterns, little is known about exactly how structure and function are related. The work presented centers around building the mathematical framework of RNA structures in an effort to guide technology and further scientific discovery. We provide insight into the prevalence of certain important folding patterns.

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