Imperfection Insensitive Thin Shells

The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century.

This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells.

Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression with superior mass efficiency.

An efficient computational method for the buckling analysis of corrugated and stiffened cylindrical shells subject to axial compression has been developed in this thesis. This method modifies the traditional Bloch wave method based on the stiffness matrix method of rotationally periodic structures. A highly efficient algorithm has been developed to implement the modified Bloch wave method. This method is applied in buckling analyses of a series of corrugated composite cylindrical shells and a large-scale orthogonally stiffened aluminum cylindrical shell. Numerical examples show that the modified Bloch wave method can achieve very high accuracy and require much less computational time than linear and nonlinear analyses of detailed full finite element models.

This thesis presents parametric studies on a series of externally pressurized pseudo-spherical shells, i.e., polyhedral shells, including icosahedron, geodesic shells, and triambic icosahedra. Several optimization methods have been developed to further improve the performance of pseudo-spherical shells under external pressure. It has been shown that the buckling pressures of the shell designs obtained from the optimizations are much higher than the spherical shells and not sensitive to imperfections.

Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Energy inequalities and error estimates for axisymmetric torsion of thin elastic shells of revolution

The problem motivating this investigation is that of pure axisymmetric torsion of an elastic shell of revolution. The analysis is carried out within the framework of the three-dimensional linear theory of elastic equilibrium for homogeneous, isotropic solids. The objective is the rigorous estimation of errors involved in the use of approximations based on thin shell theory.

The underlying boundary value problem is one of Neumann type for a second order elliptic operator. A systematic procedure for constructing pointwise estimates for the solution and its first derivatives is given for a general class of second-order elliptic boundary-value problems which includes the torsion problem as a special case.

The method used here rests on the construction of “energy inequalities” and on the subsequent deduction of pointwise estimates from the energy inequalities. This method removes certain drawbacks characteristic of pointwise estimates derived in some investigations of related areas.

Special interest is directed towards thin shells of constant thickness. The method enables us to estimate the error involved in a stress analysis in which the exact solution is replaced by an approximate one, and thus provides us with a means of assessing the quality of approximate solutions for axisymmetric torsion of thin shells.

Finally, the results of the present study are applied to the stress analysis of a circular cylindrical shell, and the quality of stress estimates derived here and those from a previous related publication are discussed.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.

Some problems in nonlinear elasticity

Two separate problems are discussed: axisymmetric equilibrium configurations of a circular membrane under pressure and subject to thrust along its edge, and the buckling of a circular cylindrical shell.

An ordinary differential equation governing the circular membrane is imbedded in a family of n-dimensional nonlinear equations. Phase plane methods are used to examine the number of solutions corresponding to a parameter which generalizes the thrust, as well as other parameters determining the shape of the nonlinearity and the undeformed shape of the membrane. It is found that in any number of dimensions there exists a value of the generalized thrust for which a countable infinity of solutions exist if some of the remaining parameters are made sufficiently large. Criteria describing the number of solutions in other cases are also given.

Donnell-type equations are used to model a circular cylindrical shell. The static problem of bifurcation of buckled modes from Poisson expansion is analyzed using an iteration scheme and pertubation methods. Analysis shows that although buckling loads are usually simple eigenvalues, they may have arbitrarily large but finite multiplicity when the ratio of the shell's length and circumference is rational. A numerical study of the critical buckling load for simple eigenvalues indicates that the number of waves along the axis of the deformed shell is roughly proportional to the length of the shell, suggesting the possibility of a "characteristic length." Further numerical work indicates that initial post-buckling curves are typically steep, although the load may increase or decrease. It is shown that either a sheet of solutions or two distinct branches bifurcate from a double eigenvalue. Furthermore, a shell may be subject to a uniform torque, even though one is not prescribed at the ends of the shell, through the interaction of two modes with the same number of circumferential waves. Finally, multiple time scale techniques are used to study the dynamic buckling of a rectangular plate as well as a circular cylindrical shell; transition to a new steady state amplitude determined by the nonlinearity is shown. The importance of damping in determining equilibrium configurations independent of initial conditions is illustrated.

Bifurcation theory of nonlinear boundary value problems

The theory of bifurcation of solutions to two-point boundary value problems is developed for a system of nonlinear first order ordinary differential equations in which the bifurcation parameter is allowed to appear nonlinearly. An iteration method is used to establish necessary and sufficient conditions for bifurcation and to construct a unique bifurcated branch in a neighborhood of a bifurcation point which is a simple eigenvalue of the linearized problem. The problem of bifurcation at a degenerate eigenvalue of the linearized problem is reduced to that of solving a system of algebraic equations. Cases with no bifurcation and with multiple bifurcation at a degenerate eigenvalue are considered.

The iteration method employed is shown to generate approximate solutions which contain those obtained by formal perturbation theory. Thus the formal perturbation solutions are rigorously justified. A theory of continuation of a solution branch out of the neighborhood of its bifurcation point is presented. Several generalizations and extensions of the theory to other types of problems, such as systems of partial differential equations, are described.

The theory is applied to the problem of the axisymmetric buckling of thin spherical shells. Results are obtained which confirm recent numerical computations.

A biochemical and structural characterization of Drosophila neuroglian

A number of cell-cell interactions in the nervous system are mediated by immunoglobulin gene superfamily members. For example, neuroglian, a homophilic neural cell adhesion molecule in Drosophila, has an extracellular portion comprising six C- 2 type immunoglobulin-like domains followed by five fibronectin type III (FnIII) repeats. Neuroglian shares this domain organization and significant sequence identity with Ll, a murine neural adhesion molecule that could be a functional homologue. Here I report the crystal structure of a proteolytic fragment containing the first two FnIII repeats of neuroglian (NgFn 1,2) at 2.0Å. The interpretation of photomicrographs of rotary shadowed Ng, the entire extracellular portion of neuroglian, and NgFnl-5, the five neuroglian Fn III domains, is also discussed.

The structure of NgFn 1,2 consists of two roughly cylindrical β-barrel structural motifs arranged in a head-to-tail fashion with the domains meeting at an angle of ~120, as defined by the cylinder axes. The folding topology of each domain is identical to that previously observed for single FnIII domains from tenascin and fibronectin. The domains of NgFn1,2 are related by an approximate two fold screw axis that is nearly parallel to the longest dimension of the fragment. Assuming this relative orientation is a general property of tandem FnIII repeats, the multiple tandem FnIII domains in neuroglian and other proteins are modeled as thin straight rods with two domain zig-zag repeats. When combined with the dimensions of pairs of tandem immunoglobulin-like domains from CD4 and CD2, this model suggests that neuroglian is a long narrow molecule (20 - 30 Å in diameter) that extends up to 370Å from the cell surface.

In photomicrographs, rotary shadowed Ng and NgFn1-5 appear to be highly flexible rod-like molecules. NgFn 1-5 is observed to bend in at least two positions and has a mean total length consistent with models generated from the NgFn1,2 structure. Ng molecules have up to four bends and a mean total length of 392 Å, consistent with a head-to-tail packing of neuroglian's C2-type domains.

Three-dimensional models of mantle convection : influence of phase transitions and temperature-dependent viscosity

Two of the most important questions in mantle dynamics are investigated in three separate studies: the influence of phase transitions (studies 1 and 2), and the influence of temperature-dependent viscosity (study 3).

(1) Numerical modeling of mantle convection in a three-dimensional spherical shell incorporating the two major mantle phase transitions reveals an inherently three-dimensional flow pattern characterized by accumulation of cold downwellings above the 670 km discontinuity, and cylindrical 'avalanches' of upper mantle material into the lower mantle. The exothermic phase transition at 400 km depth reduces the degree of layering. A region of strongly-depressed temperature occurs at the base of the mantle. The temperature field is strongly modulated by this partial layering, both locally and in globally-averaged diagnostics. Flow penetration is strongly wavelength-dependent, with easy penetration at long wavelengths but strong inhibition at short wavelengths. The amplitude of the geoid is not significantly affected.

(2) Using a simple criterion for the deflection of an upwelling or downwelling by an endothermic phase transition, the scaling of the critical phase buoyancy parameter with the important lengthscales is obtained. The derived trends match those observed in numerical simulations, i.e., deflection is enhanced by (a) shorter wavelengths, (b) narrower up/downwellings (c) internal heating and (d) narrower phase loops.

(3) A systematic investigation into the effects of temperature-dependent viscosity on mantle convection has been performed in three-dimensional Cartesian geometry, with a factor of 1000-2500 viscosity variation, and Rayleigh numbers of 10^5-10^7. Enormous differences in model behavior are found, depending on the details of rheology, heating mode, compressibility and boundary conditions. Stress-free boundaries, compressibility, and temperature-dependent viscosity all favor long-wavelength flows, even in internally heated cases. However, small cells are obtained with some parameter combinations. Downwelling plumes and upwelling sheets are possible when viscosity is dependent solely on temperature. Viscous dissipation becomes important with temperature-dependent viscosity.

The sensitivity of mantle flow and structure to these various complexities illustrates the importance of performing mantle convection calculations with rheological and thermodynamic properties matching as closely as possible those of the Earth.

Structure of the earth's core and lowermost mantle from seismic PKP waves

This thesis addresses the fine structure, both radial and lateral, of compressional wave velocity and attenuation of the Earth's core and the lowermost mantle using waveforms, differential travel times and amplitudes of PKP waves, which penetrate the Earth's core.

The structure near the inner core boundary (ICB) is studied by analyzing waveforms of a regional sample. The waveform modeling approach is demonstrated to be an effective tool for constrainning the ICB structure. The best model features a sharp velocity jump of 0.78km/s at the ICB and a low velocity gradient at the lowermost outer core (indicating possible inhomogeneity) and high attenuation at the top of the inner core.

A spherically symmetric P-wave model of the core, is proposed from PKP differential times, waveforms and amplitudes. The ICB remains sharp with a velocity jump of 0. 78km/ s. A very low velocity gradient at the base of the fluid core is demonstrated to be a robust feature, indicating inhomogeneity is practically inevitable. The model also indicates that the attenuation in the inner core decreases with depth. The velocity at D" is smaller than PREM.

The inner core is confirmed to be very anisotropic, possessing a cylindrical symmetry around the Earth spin axis with the N-S direction 3% faster than the E-W direction. All of the N-S rays through the inner core were found to be faster than the E-W rays by 1.5 to 3.5s. Exhaustive data selection and efforts in insolating contributions from the region above ensure that this is an inner core feature.

The anisotropy at the very top of the inner core is found to be distinctly different from the deeper part. The top 60km of the inner core is not anisotropic. From 60km to 150km, there appears to be a transition from isotropy to anisotropy.

PKP differential travel times are used to study the P velocity structure in D". Systematic regional variations of up to 2s in AB-DF times were observed, attributed primarily to heterogeneities in the lower 500km of the mantle. However, direct comparisons with tomographic models are not successful.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

Metasomatism and magmatic assimilation at a gabbro-limestone contact, Christmas Mountains, Big Bend region, Texas

A composite stock of alkaline gabbro and syenite is intrusive into limestone of the Del Carmen, Sue Peake and Santa Elena Formations at the northwest end of the Christmas Mountains. There is abundant evidence of solution of wallrock by magma but nowhere are gabbro and limestone in direct contact. The sequence of lithologies developed across the intrusive contact and across xenoliths is gabbro, pyroxenite, calc-silicate skarn, marble. Pyroxenite is made up of euhedral crystals of titanaugite and sphene in a leucocratic matrix of nepheline, Wollastonite and alkali feldspar. The uneven modal distribution of phases in pyroxenite and the occurrence' of nepheline syenite dikes, intrusive into pyroxenite and skarn, suggest that pyroxenite represents an accumulation of clinopyroxene "cemented" together by late-solidifying residual magma of nepheline syenite composition. Assimilation of limestone by gabbroic magma involves reactions between calcite and magma and/or crystals in equilibrium with magma and crystallization of phases in which the magma is saturated, to supply energy for the solution reaction. Gabbroic magma was saturated with plagioclase and clinopyroxene at the time of emplacement. The textural and mineralogic features of pyroxenite can be produced by the reaction 2( 1-X) CALCITE + AN_XAB_l-X = (1-X) NEPHELINE+ 2(1-X) WOLLASTONITE+ X ANORTHITE+ 2(1-X) CO₂. Plagioclase in pyroxenite has corroded margins and is rimmed by nepheline, suggestive of resorption by magma. Anorthite and wollastonite enter solid solution in titanaugite. For each mole of calcite dissolved, approximately one mole of clinopyroxene was crystallized. Thus the amount of limestone that may be assimilated is limited by the concentration of potential clinopyroxene in the magma. Wollastonite appears as a phase when magma has been depleted in iron and magnesium by crystallization of titanaugite. The predominance of mafic and ultramafic compositions among contaminated rocks and their restriction to a narrow zone along the intrusive contact provides little evidence for the generation of a significant volume of desilicated magma as a result of limestone assimilation.

Within 60 m of the intrusive contact with the gabbro, nodular chert in the Santa Elena Limestone reacted with the enveloping marble to form spherical nodules of high-temperature calc-silicate minerals. The phases wollastonite, rankinite, spurrite, tilleyite and calcite, form a series of sharply-bounded, concentric monomineralic and two-phase shells which record a step-wise decrease in silica content from the core of a nodule to its rim. Mineral zones in the nodules vary 'with distance from the gabbro as follows:

0-5 m CALCITE + SPURRITE + RANKINITE + WOLLASTONITE
5-16 m CALCITE + TILLEYITE ± SPURRITE + RANKINITE + WOLLASTONITE
16-31 m CALCITE + TILLEYITE + WOLLASTONITE
31-60 m CALCITE + WOLLASTONITE
60-plus CALCITE + QUARTZ

The mineral of a one-phase zone is compatible with the phases bounding it on either side but these phases are incompatible in the same volume of P-T-X_CO2.

Growth of a monomineralio zone is initiated by reaction between minerals of adjacent one-phase zones which become unstable with rising temperature to form a thin layer of a new single phase that separates the reactants and is compatible with both of them. Because the mineral of the new zone is in equilibrium with the phases at both of its contacts, gradients in the chemical potentials of the exchangeable components are established across it. Although zone boundaries mark discontinuities in the gradients of bulk composition, two-phase equilibria at the contacts demonstrate that the chemical potentials are continuous. Hence, Ca, Si and CO₂ were redistributed in the growing nodule by diffusion. A monomineralic zone grows at the expense of an adjacent zone by reaction between diffusing components and the mineral of the adjacent zone. Equilibria between two phases at zone boundaries buffers the chemical potentials of the diffusing species. Thus, within a monomineralic zone, the chemical potentials of the diffusing components are controlled external to the local assemblage by the two-phase equilibria at the zone boundaries.

Mineralogically zoned calc-silicate skarn occurs as a narrow band that separates pyroxenite and marble along the intrusive contact and forms a rim on marble xenoliths in gabbro. Skarn consists of melilite or idocrase pseudomorphs of melili te, one or two . stoichiometric calcsilicate phases and accessory Ti-Zr garnet, perovskite and magnetite. The sequence of mineral zones from pyroxenite to marble, defined by a characteristic calc-silicate, is wollastonite, rankinite, spurrite, calcite. Mineral assemblages of adjacent skarn zones are compatible and the set of zones in a skarn band defines a facies type, indicating that the different mineral assemblages represent different bulk compositions recrystallized under identical conditions. The number of phases in each zone is less than the number that might be expected to result from metamorphism of a general bulk composition under conditions of equilibrium, trivariant in P, T and u_CO2. The "special" bulk composition of each zone is controlled by reaction between phases of the zones bounding it on either side. The continuity of the gradients of composition of melilite and garnet solid solutions across the skarn is consistent with the local equilibrium hypothesis and verifies that diffusion was the mechanism of mass transport. The formula proportions of Ti and Zr in garnet from skarn vary antithetically with that of Si Which systematically decreases from pyroxenite to marble. The chemical potential of Si in each skarn zone was controlled by the coexisting stoichiometric calc-silicate phases in the assemblage. Thus the formula proportion of Si in garnet is a direct measure of the chemical potential of Si from point to point in skarn. Reaction between gabbroic magma saturated with plagioclase and clinopyroxene produced nepheline pyroxenite and melilite-wollastonite skarn. The calcsilicate zones result from reaction between calcite and wollastonite to form spurrite and rankinite.

Self-assembly of brush polymers

The unique structure and properties of brush polymers have led to increased interest in them within the scientific community. This thesis describes studies on the self-assembly of these brush polymers.

Chapter 2 describes a study on the rapid self-assembly of brush block copolymers into nanostructures with photonic bandgaps spanning the entire visible spectrum, from ultraviolet to near infrared. Linear relationships are observed between the peak wavelengths of reflection and polymer molecular weights. This work enables "bottom-up" fabrication of photonic crystals with application-tailored bandgaps, through synthetic control of the polymer molecular weight and the method of self-assembly.

Chapter 3 details the analysis of the self-assembly of symmetrical brush block copolymers in bulk and thin films. Highly ordered lamellae with domain spacing ranging from 20 to 240 nm are obtained by varying molecular weight of the backbone. The relationship between degree of polymerization and the domain spacing is reported, and evidence is provided for how rapidly the brush block copolymers self-assemble and achieve thermodynamic equilibrium.

Chapter 4 describes investigations into where morphology transitions take place as the volume fraction of each block is varied in asymmetrical brush block copolymers. Imaging techniques are used to observe a transition from lamellar to a cylindrical morphology as the volume fraction of one of the blocks exceeds 70%. It is also shown that the asymmetric brush block copolymers can be kinetically trapped into undulating lamellar structures by drop casting the samples.

Chapter 5 explores the capability of macromolecules to interdigitate into densely grafted molecular brush copolymers using stereocomplex formation as a driving force. The stereocomplex formation between complementary linear polymers and brush copolymers is demonstrated, while the stereocomplex formation between complementary brush copolymers is shown to be restricted.

High-strain composites and dual-matrix composite structures

Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.

The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.

A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.

High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.

A multi-scale approach to shaping carbon nanotube structures for hollow microneedles

The concept of a carbon nanotube microneedle array is explored in this thesis from multiple perspectives including microneedle fabrication, physical aspects of transdermal delivery, and in vivo transdermal drug delivery experiments. Starting with standard techniques in carbon nanotube (CNT) fabrication, including catalyst patterning and chemical vapor deposition, vertically-aligned carbon nanotubes are utilized as a scaffold to define the shape of the hollow microneedle. Passive, scalable techniques based on capillary action and unique photolithographic methods are utilized to produce a CNT-polymer composite microneedle. Specific examples of CNT-polyimide and CNT-epoxy microneedles are investigated. Further analysis of the transport properties of polymer resins reveals general requirements for applying arbitrary polymers to the fabrication process.

The bottom-up fabrication approach embodied by vertically-aligned carbon nanotubes allows for more direct construction of complex high-aspect ratio features than standard top-down fabrication approaches, making microneedles an ideal application for CNTs. However, current vertically-aligned CNT fabrication techniques only allow for the production of extruded geometries with a constant cross-sectional area, such as cylinders. To rectify this limitation, isotropic oxygen etching is introduced as a novel fabrication technique to create true 3D CNT geometry. Oxygen etching is utilized to create a conical geometry from a cylindrical CNT structure as well as create complex shape transformations in other CNT geometries.

CNT-polymer composite microneedles are anchored onto a common polymer base less than 50 µm thick, which allows for the microneedles to be incorporated into multiple drug delivery platforms, including modified hypodermic syringes and silicone skin patches. Cylindrical microneedles are fabricated with 100 µm outer diameter and height of 200-250 µm with a central cavity, or lumen, diameter of 30 µm to facilitate liquid drug flow. In vitro delivery experiments in swine skin demonstrate the ability of the microneedles to successfully penetrate the skin and deliver aqueous solutions.

An in vivo study was performed to assess the ability of the CNT-polymer microneedles to deliver drugs transdermally. CNT-polymer microneedles are attached to a hand actuated silicone skin patch that holds a liquid reservoir of drugs. Fentanyl, a potent analgesic, was administered to New Zealand White Rabbits through 3 routes of delivery: topical patch, CNT-polymer microneedles, and subcutaneous hypodermic injection. Results demonstrate that the CNT-polymer microneedles have a similar onset of action as the topical patch. CNT-polymer microneedles were also vetted as a painless delivery approach compared to hypodermic injection. Comparative analysis with contemporary microneedle designs demonstrates that the delivery achieved through CNT-polymer microneedles is akin to current hollow microneedle architectures. The inherent advantage of applying a bottom-up fabrication approach alongside similar delivery performance to contemporary microneedle designs demonstrates that the CNT-polymer composite microneedle is a viable architecture in the emerging field of painless transdermal delivery.

Radiation from a short electric dipole antenna in a hot uniaxial plasma

The effects of electron temperature on the radiation fields and the resistance of a short dipole antenna embedded in a uniaxial plasma have been studied. It is found that for ω < ω_p the antenna excites two waves, a slow wave and a fast wave. These waves propagate only within a cone whose axis is parallel to the biasing magnetostatic field B_o and whose semicone angle is slightly less than sin ^(-1) (ω/ω_p). In the case of ω > ω_p the antenna excites two separate modes of radiation. One of the modes is the electromagnetic mode, while the other mode is of hot plasma origin. A characteristic interference structure is noted in the angular distribution of the field. The far fields are evaluated by asymptotic methods, while the near fields are calculated numerically. The effects of antenna length ℓ, electron thermal speed, collisional and Landau damping on the near field patterns have been studied.

The input and the radiation resistances are calculated and are shown to remain finite for nonzero electron thermal velocities. The effect of Landau damping and the antenna length on the input and radiation resistances has been considered.

The radiation condition for solving Maxwell's equations is discussed and the phase and group velocities for propagation given. It is found that for ω < ω_p in the radial direction (cylindrical coordinates) the power flow is in the opposite direction to that of the phase propagation. For ω > ω_p the hot plasma mode has similar characteristics.