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Carbon nanotubes (CNTs) are tubular structure of a layer or layers of carbon atoms. CNTs serve as a prototypical nanomaterial holding great promises for various basic and applied research applications in the fields of electrical, thermal, and structural materials owing to their superlative mechanical, thermal, electrical, optical, and chemical properties. Since the discovery of CNTs by Iijima in 1991, numerous researches have been conducted to quantify and understand the atomic origin of their high strength, exceptional thermal conductivity, and unique electrical properties. CNTs are also widely used as nanofillers in composite materials to enhance their mechanical properties such as fracture toughness and to serve as sensing agents. There is thus an imperative need to deeply understand the physical properties of CNTs and their responses to various models of deformations such as stretching, bending, twisting, and combinations thereof. In this thesis, we apply all-atom molecular dynamics simulations to study in detail the behavior of several single-walled, armchair CNTs under stretching and bending deformations, realized by imposing appropriate boundary conditions on the CNTs. The simulation results reveal unique scaling properties of the stretching and bending stiffness with respect to the CNT radius and length, which indicate that a single-walled CNT is best modeled as a thin cylindrical shell with a cross-sectional radius equal to the CNT radius and a constant wall thickness much smaller than the CNT radius. By studying the thermal fluctuations of carbon atoms on the CNT wall, the wall thickness is determined to be about 0.45~AA~for all the single-walled CNTs studied in this thesis and correspondingly, Young's modulus is estimated to be about 8.78 TPa for these CNTs. / Master of Science / Carbon atoms are magic building blocks of our world and the basis of life on the earth, and likely in the universe too. They can also form amazing materials with dimensionalities ranging from 0 to 3. For example, carbon atoms can form soccer-ball like spherical structures called fullerenes, with 0 dimensionality. They can also form 1-dimensional tubular structures with only one wall (i.e., one layer of carbon atoms) or multiple walls, called carbon nanotubes (CNTs) that have diameters typically in the nanometer range and lengths as long as 0.5 meter. Carbon atoms also form graphene sheets, which can be regarded as 2-dimensional structures, and 3-dimensional materials including graphite and diamond. In this work, we model CNTs using the molecular dynamics simulation method, where the motion of each atom is resolved and controlled if needed. Specifically, we study CNTs under stretching by fixing one end while pulling the other end in the axial direction, or bending by pulling the middle of a CNT along the radial direction in its cross-section while fixing its two ends. By fitting the simulation results to the continuum mechanics models, we show that a CNT is best described as a thin cylindrical shell with a radius equal to the CNT radius and a wall thickness much smaller than the radius. At the end, the wall thickness of all the CNTs studied here is determined to be about $0.45times 10^{-10}$ meter and their Young's modulus is estimated to be about $8.78times 10^{12}$ Pa, confirming that CNTs are one of the strongest and stiffest materials.

The National Highway Traffic Safety Administration (NHTSA) reported that in 2008 there were a total of 37,261 automotive related fatalities, 26,689 of which were vehicle occupants. It has been reported that in automotive collisions chest injuries rank second only to head injuries in overall number of fatalities and serious injuries. In frontal collisions, chest injuries constitute 37.6% of all AIS 3+ injuries, 46.3% of all AIS 4+ injuries, and 43.3% of all AIS 5+ injuries. In side impact collisions, it has been reported that thoracic injuries are the most common type of serious injury (AIS≥3) to vehicle occupants in both near side and far side crashes which do not involve a rollover. In addition, rib fractures are the most frequent type of thoracic injury observed in both frontal and side impact automotive collisions. Anthropomorphic test devices (ATDs), i.e. crash test dummies, and finite element models (FEMs) have proved to be integral tools in the assessment and mitigation of thoracic injury risk. However, the validation of both of these tools is contingent on the availability of relevant biomechanical data. In order to develop and validate FEMs and ATDs with improved thoracic injury risk assessment capabilities, it is necessary to generate biomechanical data currently not presented in the literature. Therefore, the purpose of this dissertation is to present novel material, structural, and global thoracic skeletal response data as well as quantify thoracic injury timing in both frontal belt loading and side impact tests using cadaveric specimens. / Ph. D.

An innovative implementation of the skin concept for the reduction of the radiated sound power from a vibrating structure is proposed. The skin has a periodic structure and continuously covers a vibrating beam. Thus, this skin decouples the vibrating structure from the acoustic field by modifying the wavenumber spectrum of the radiating surface. First, structural acoustics and periodic structure theories are reviewed in order to predict how bending waves propagate along a periodic beam and how this beam radiates sound. These theories are then extended to the case of multi-layered structures in order to understand the behavior of a beam loaded with a periodic skin. In order to design the beam and skin structural periods, two different methods are used: Galois sequences and an optimization process using a real-valued genetic algorithm. Simulations are run for the case of periodic beams and beams coupled with periodic smart skins in both finite and infinite configurations. Results show that periodic beam can radiate less sound than equivalent uniform structures. Results also show the potential of periodic skin for application to the structural radiation problem for frequencies higher than approximately 100Hz with an approximately 10dB of radiated sound power attenuation. / Master of Science

This investigation is concerned with the flexural response of linear viscoelastic plates of constant thickness. Fundamental equations for both quasi-static and dynamic response of such plates are developed and solved for important cases of each. The term quasi-static ls used to indicate that Inertia forces due to deformation are neglected. These are included, of course, in the dynamic analysis. Solutions of the quasi-static equation are compared with experimental results obtained by measuring the deflection of a test plate made of Plexiglas. The basic viscoelastic stress-strain relations used in the derivation of the fundamental plate equations are taken in the form of a differential time operator equation. Use of this equation leads to results that are In a convenient form for reduction to a particular material such as a Kelvin or a Maxwell plate. Using a generalized virtual work principle based upon irreversible thermodynamic considerations the fundamental plate equation, including shear effects, ls established. The procedure involved ls that of determining a stationary value of a certain operational invariant by means of the calculus of variations. A simplified form of this equation, omitting the shear effects, is deduced and solutions for various load conditions obtained. An extended version of this simplified form which includes inertia effects due to deformation is developed by the principle of correspondence. This is used to study free vibrations of rectangular viscoelastic plates simply supported on all edges. Solutions of the simplified form of the fundamental equation for the case of so-called proportional loading, I.e. when the load function is the product of a space function multiplied by a time function, are given in terms of the equivalent elastic solution multiplied by a function of time. For more general types of loading the deflection and the load are expanded Into suitable infinite series and these series representations are inserted directly into the previously mentioned variational expression of the generalized virtual work principle. This leads to a set of ordinary differential situations in time the unknowns of which are the coefficients of the deflection expansion. These equations, as were the similar ones arising in the case of proportional loading, are solved by the Laplace transform method of the operational calculus. As an example of such a general loading the case of a moving line load on a rectangular plate is worked out. As a means of establishing a correlation between the deflection predicted by the analytical solution and actual deflections of Inelastic plates a set of static load tests were carried out on a square plate made or Plexiglas. The results are plotted and a comparison of the theoretical and experimental values given. The problem of determining the dynamic response of viscoelastic plates is treated using the method given above for solving the case of general loading for the quasi-static deflection. Under the assumption of incompressibility of the plate material explicit solutions in terms of the physical parameters involved are presented and discussed. For compressible plate materials methods are developed to give approximate solutions the accuracy of which depends on the degree of approximation used in determining the roots of certain cubics appearing in the transformed form of the governing dynamics equation. Conditions for the dynamic solutions to be oscillatory are indicated. / Ph. D.

An analytical investigation was performed to study the effect of applied bending loads on laminated composite tubes. Elasticity-based linear models were developed using finite element software to predict stresses within the individual plies of the tubes. The tubes under investigation were graphite/epoxy laminated composites with a stacking sequence of [0/-45/+45/90/90/+45/ -45/0] X 2 (Sixteen plies per tube). End pieces of isotropic titanium were integrally constructed with bonded interface joints. The material properties of the cylinder plies were orthotropic in the fiber direction. The analytical models were developed to simulate two concentric laminated composite cylinders with a gap of 0.158 in between them. In the first part of the analysis, the gap was left void to simulate a completely debonded condition between the cylinders and material that is sandwiched between them. The second part of the analysis incorporated isotropic tungsten material filling the gap along two-thirds of the length of the cylinders in a perfectly bonded condition. The final part of the analysiS included a local model incorporating a bond joint at the titanium/composite interface. Under applied bending loads, the analytical models predicted the highest stresses would occur in the 90° (axial) plies, the lowest stresses would occur in the 0° (hoop) plies, and median stresses would occur in the ±45° plies. The stresses in the cylinders when in a debonded condition were much higher than when the cylinders were perfectly bonded to the tungsten filler material. Stress concentrations occurred at the titanium/composite interfaces as well as at the tungsten/honeycomb interface. In the current investigation, the orthotropic plies showed no danger of failing under the applied bending load. The local model produced similar results as in the two global analyses. However, high shear stresses were apparent along the bond line. / Master of Science

A new method for stress-rupture experiments in bending has been developed and used to characterize unidirectional polymer matrix composites. The method. which makes use of very simple fixtures, led to coherent results. These results have been modeled using the large deflection of buckled bars theory (elastica) and it is possible to predict with good accuracy the strain at each point of the specimen if the end-to-end distance is known. The failure process has been experimentally characterized. The formation and propagation of microbuckles leads to a compressive failure. Based on the elastica and the classical lamination theory, a model for the distribution of the Young's modulus along the length of the specimen has been established. Three different micromechanical models have been applied to analyze the time-to-failure versus strain behavior at two temperatures - one below and one above the glass transition. The first micromechanical model considers the nucleation of the microbuckles as the main cause of failure. In addition, the stiffness and stress distributions at any time before failure are calculated based upon the rotation of the fibers in the damaged region. The second and last models, respectively based upon a Paris Law and energy considerations relate the time-to-failure to the propagation of the main microbuckle. For this last model, a good correlation between experimental and theoretical data has been obtained. Finally the influence of the temperature on these models has been studied. / Master of Science

Thin structures exist as one dimensional slender objects (hairs, tendrils, telephone cords, etc.) and two dimensional thin sheets (tree leaves, Mobius bands, eggshells, etc.). Geometric and material nonlinearities can conspire together to create complex phenomena in thin structures. This dissertation studies snap-through, multi-stability, and localization in thin rods and sheets through a combination of experiments and numerics. The first work experimentally explores the multi-stability and bifurcations of buckled elastic strips subject to clamping and lateral end translations, and compares these results with numerical continuation of a perfectly anisotropic Kirchhoff rod model. It is shown that this naive Kirchhoff rod model works surprisingly well as an organizing framework for thin bands with various widths. Thin sheets prefer to bend rather than to stretch because of the high cost of stretching energy. Knowing the bending response of thin sheets can aid in simulating deformations such as creasing. The second work introduces an exact pure bending linkage mechanism for potential use in a bend tester that measures the moment-curvature relationship of soft sheets and filaments. Mechanical rotary pleating is a bending-deformation-dominant process that deforms nonwoven materials into zigzag filter structures. The third work studies what combinations of processing and material parameters lead to successful rotary pleating. The rotary pleating process is formulated as a multi-point variable-arc-length boundary value problem for an inextensible rod, with a moment-curvature constitutive law, such as might be measured by a bend tester, as input. Through parametric studies, this work generates pleatability surfaces that may help avoid pleating failure in the real pleating process. Creased thin sheets are generally bistable. The final work of this dissertation studies bistability of creased thin disks under the removal of singularities. A hole is cut in the disk and, through numerical continuation of an inextensible strip model, this work studies how the crease stiffness, crease angle, and hole geometry affect the bistability. / Doctor of Philosophy / Thin structures are those that have at least one dimension smaller than the other dimensions, such as hairs, telephone cords, and tree leaves, to name just a few. They can generate rich mechanical behaviors (e.g., snapping, crumpling) and complex shapes. A simple example is to rotate the two ends of a thin strip that has been deformed into an arch. Snapping will happen at a certain rotation angle. The first work studies snapping behaviors of thin bands subject to rotations and displacements at the two ends. This work employs a mechanical model based on force and moment balance on a spatial curve to solve the shapes of thin strips and capture the rich snapping behaviors. It is much harder to stretch a thin sheet than to bend it, which can be easily seen by deforming a piece of paper. The physics behind this is that stretching requires more energy than bending in thin objects. Knowing the bending response of thin sheets can aid in simulating deformations of thin structures. The second work introduces a new pure bending mechanism that can subject a sheet to pure bending and measure its bending response through a moment-curvature relationship. Thin sheets find broad applications in engineering. Mechanical pleating is a long-standing technique that deforms thin sheets into zigzag filter structures, but the mechanics behind it is unclear. The third work studies a rotary pleating process and aims to answer a basic question: What combinations of processing and material parameters lead to successful pleating? This work employs a one-dimensional model of an inextensible rod, with a moment-curvature constitutive law as input. The moment-curvature relationship of pleating materials can be measured by the pure bending mechanism developed in the second work. Thin sheets with prescribed crease patterns can create complicated and targeted shapes, such as origami (paper folding) and kirigami (paper cutting). A simple creased thin sheet is bistable: A stable configuration can be obtained by inverting the crease, which leads to a conical vertex/singularity. The fourth work of this dissertation finds that the bistability of creased thin sheets will be destroyed if a large hole is made around the vertex. This work studies the loss of bistability of creases under removal of singularities by quantifying how the hole size, hole geometry, and other factors such as the crease angle and crease stiffness affect the bistability.

Rotary draw bending, which has very good flexibility and easy tooling, is one of the most preferred bending types for tubular profiles. Cross-section distortion and the spring-back phenomena are commonly faced problems in bending processes. Spring-back is the inevitable problem that is to be solved by manufacturer, generally by overbending. For hollow tubes cross-section distortion is another difficulty since using hollow tubes results in higher strain rates and distortions. During the process the thickness of the hollow tube at the inner surface, which is contacting with the die, increases and the thickness of the tube at the outer surface decreases. Wrinkling is another important defect that occurs at the inner surface of the tube in large diameter thin walled tube bendings. This research compares the experimental results with the finite element analysis of the rotary draw bending process. The aim is to obtain bending characteristics of the two material types, SS304 and St37 and so, to reduce the number of the bending in manufacturing. The main parameters in rotary draw bending process are the bending angle, bend radius, material properties and the geometry of the tube that is to be bent. In this study, to deal with the process, two different materials, three different bending angles and three different tube geometries are used in experiments as well as in finite element analysis. In finite element analysis explicit method is used. It is seen that the experimental results are in good agreement with the numerical results.

The study presents the results of an experimental and analytical investigation aimed at examining the lateral stability of rectangular reinforced concrete slender beams. In the experimental part of the investigation, a total of eleven reinforced concrete beams having a depth to width ratio between 10.20 and 12.45 and a length to width ratio between 96 and 156 were tested. Beam thickness, depth and unbraced length were 1.5 to 3.0 in., 18 to 44 in., and 12 to 39.75 ft, respectively. Each beam was subjected to a single concentrated load applied at midspan by means of a gravity load simulator that allowed the load to always remain vertical when the section displaces out of plane. The loading mechanism minimized the lateral translational and rotational restraints at the load application point to simulate the nature of gravity load. Each beam was simply-supported in and out of plane at the ends. The supports allowed warping deformations, yet prevented twisting rotations at the beam ends. In the analytical part of the study, a formula was developed for determining the critical loads of lateral torsional buckling of rectangular reinforced concrete beams free from initial geometric imperfections. The influences of shrinkage cracking and inelastic stress-strain properties of concrete and the contribution of longitudinal reinforcement to the lateral stability are accounted for in the critical load formula. The experiments showed that the limit load of a concrete beam with initial geometric imperfections can be significantly lower than the critical load corresponding to its geometrically perfect configuration. Accordingly, a second formula was developed for the estimation of limit loads of reinforced concrete beams with initial lateral imperfections, by introducing the destabilizing effect of sweep to the critical load formula. The experimental results were compared to the proposed analytical solution and to various lateral torsional buckling solutions in the literature. The formulation proposed in the present study was found to agree well with the experimental results. The incorporation of the geometric and material nonlinearities into the formula makes the proposed solution superior to the previous lateral torsional buckling solutions for rectangular reinforced concrete beams.