In this work, a finite element formulation and associated computer program is developed for the transient large deformation analysis of laminated composite plate/shell structures. In order to satisfy the plate/shell surface traction boundary conditions and to have accurate stress description while maintaining the low cost of the analysis, a newly assumed displacement field theory is formulated by adding higher-order terms to the transverse displacement component of the first-order shear deformation theory. The laminated shell theory is formulated using the Updated Lagrangian description of a general continuum-based theory with assumptions on thickness deformation. The transverse deflection is approximated through the thickness by a quartic polynomial of the thickness coordinate. As a result both the plate/shell surface tractions (including nonzero tangential tractions and nonzero normal pressure) and the interlaminar shear stress continuity conditions at interfaces are satisfied simultaneously. Furthermore, the rotational degree of freedoms become layer dependent quantities and the laminate possesses a transverse deformation capability (i.e. the normal strain is no longer zero). Analytical integration through the thickness direction is performed for both the linear analysis and the nonlinear analysis. Resultants of the stress integrations are expressed in terms of the laminate stacking sequence. Consequently, the laminate characteristics in the normal direction can be evaluated precisely and the cost of the overall analysis is reduced. The standard Newmark method and the modified Newton Raphson method are used for the solution of the nonlinear dynamic equilibrium equations. Finally, a variety of numerical examples are presented to demonstrate the validity and efficiency of the finite element program developed herein. / Ph. D.

Time dependent deformations in concrete, both creep and shrinkage, play a critical role in prestressed concrete structures, such as bridge girders, nuclear containment vessels, etc. These strains result in lossess, through release of prestress, and thereby influence the safety of these structures. The present study comprises of an experimental and analytical program to assess the levels of creep and shrinkage in normal and heavy density concrete. The experimental program includes tests on creep using standard cylinder specimen, while shrinkage studies have been conducted using prism specimen, both under controlled environmental conditions. The experimental results suggest that creep and shrinkage strains are higher in heavy density concrete than in normal concrete. This may be attributed to the relatively smaller pore structure of heavy density concrete, that results in larger availability of free water and a relatively slower hydration process in comparison to normal concrete. While there is some scatter in the results, creep strains decrease with age of loading and both creep and shrinkage strains are smaller when the relative humidity is higher. Statistical model reported in the literature for normal concrete is able to predict the test results for both normal and heavy density concrete quite well. Long term predictions of creep and shrinkage using this model, accounting for uncertainties, is also projected and shown to predict some long term measured results not used in the model calibration. The long term predictions are sensitive to the initial data used in model calibration.

The first part of this dissertation is an introduction describing a brief historical background of carbon nanotubes (CNTs) and their pseudo 1D structure responsible for many exotic electronic properties. The second part describes our experimental setup. The third part is about the growing of Multi-Walled Carbon Nanotubes (MWCNTs) by the chemical vapor deposition (CVD) method. Then the fourth part demonstrates a simple but reliable method to make firm contact junctions between MWCNTs and metals such as tungsten (W). The novel point of our method consists, after making a mechanical preliminary contact at a selected MWCNT, in applying a series of voltage pulses across the contact. Thin oxide layers that may form between the MWCNT and the W wire, are removed in steps by the resistive heating and electron impact during the application of each voltage pulse. Furthermore, this simple process of contact welding in steps does not bring about any permanent change in the electronic transport properties of the MWCNTs. The fifth part discusses our bending experiments. We apply a uniform and continuous bending to a selected MWCNT at room and liquid nitrogen temperatures to study the strain effect on the electrical transport in the MWCNT. There are a few published experimental works related to the bending deformation; however, this is the first study of electronic transport properties in continuous bending and releasing deformations. We observed a saturation behavior with the MWCNT and also found the bending deformation causing an anomalous change in the saturation behavior. In the sixth part we depict some interesting phenomena due to the stretching deformation of MWCNT, where we were able to propose a simple model for electron localization induced by the deformation. The last part deals with the formation of the "X-junction" between two MWCNTs. A strong X-junction can be formed simply by means of the e-beam inside the Scanning Electron Microscope (SEM). The X-junctions may form the basic elements of nano-electronic circuits such as various metal-insulator junctions, quantum dots, and similar devices. / text

No description available.

Thesis: Sc. D., Massachusetts Institute of Technology, Department of Civil Engineering, 1977 / Vita. / Sc. D. / Sc. D. Massachusetts Institute of Technology, Department of Civil Engineering

Integrable systems arise in nonlinear processes and, both in their classical and quantum version, have many applications in various fields of mathematics and physics, which makes them a very active research area. In this thesis, the problem of integrability of multidimensional equations, especially in three dimensions (3D), is explored. We investigate systems of differential, differential-difference and discrete equations, which are studied via a novel approach that was developed over the last few years. This approach, is essentially a perturbation technique based on the so called method of dispersive deformations of hydrodynamic reductions . This method is used to classify a variety of differential equations, including soliton equations and scalar higher-order quasilinear PDEs. As part of this research, the method is extended to differential-difference equations and consequently to purely discrete equations. The passage to discrete equations is important, since, in the case of multidimensional systems, there exist very few integrability criteria. Complete lists of various classes of integrable equations in three dimensions are provided, as well as partial results related to the theory of dispersive shock waves. A new definition of integrability, based on hydrodynamic reductions, is used throughout, which is a natural analogue of the generalized hodograph transform in higher dimensions. The definition is also justified by the fact that Lax pairs the most well-known integrability criteria are given for all classification results obtained.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

The purpose of the research was to develop a quantitative method which could be used to obtain a clearer understanding of the time-dependent fluid filteration and load-deformation behavior of soft, porous, fluid filled materials (e.g. biological tissues, soil). The focus of the study was on the development of a finite strain theory for multiphasic media and associated computer models capable of predicting the mechanical stresses and the fluid transport processes in porous structures (e.g. across the large blood vessels walls). The finite element (FE) formulation of the nonlinear governing equations of motion was the method of solution for a poroelastic (PE) media. This theory and the FE formulations included the anisotropic, nonlinear material; geometric nonlinearity; compressibility and incompressibility conditions; static and dynamic analysis; and the effect of chemical potential difference across the boundaries (known as swelling effect in biological tissues). The theory takes into account the presence and motion of free water within the biological tissue as the structure undergoes finite straining. Since it is well known that biological tissues are capable of undergoing large deformations, the linear theories are unsatisfactory in describing the mechanical response of these tissues. However, some linear analyses are done in this work to help understand the more involved nonlinear behavior. The PE view allows a quantitative prediction of the mechanical response and specifically the pore pressure fluid flow which may be related to the transport of the macromolecules and other solutes in the biological tissues. A special mechanical analysis was performed on a representative arterial walls in order to investigate the effects of nonlinearity on the fluid flow across the walls. Based on a finite strain poroelastic theory developed in this work; axisymmetric, plane strain FE models were developed to study the quasi-static behavior of large arteries. The accuracy of the FE models was verified by comparison with analytical solutions wherever is possible. These numerical models were used to evaluate variables and parameters, that are difficult or may be impossible to measure experimentally. For instance, pore pressure distribution within the tissue, relative fluid flow; deformation of the wall; and stress distribution across the wall were obtained using the poroelastic FE models. The effect of hypertension on the mechanical response of the arterial wall was studied using the nonlinear finite element models. This study demonstrated that the finite element models are powerful tools for the study of the mechanics of complicated structures such as biological tissue. It is also shown that the nonlinear multiphasic theory, developed in this thesis, is valid for describing the mechanical response of biological tissue structures under mechanical loadings.

This study presents an approach based on the floating frame of reference method to model complex three-dimensional bodies in a multibody system. Unlike most of the formulations based on the floating frame of reference method, which assume small or moderate deformations, the present formulation allows large elastic deformations within each frame by using the co-rotational form of the updated Lagrangian description of motion. The implicit integration scheme is based on the Generalized-alpha method, and kinematic joints are invoked in the formulation through the coordinate partitioning method. The resulting numerical scheme permits the usage of relatively large time steps even though the flexible bodies may experience large elastic deformations. A triangular element, based on the first order shear deformable theory, has been developed specifically for folded plate and shell structures. The plate element does not suffer from either shear or aspect-ratio locking under transverse and membrane bending, respectively. A stiffened plate element has been developed that combines a shear deformable plate with a Timoshenko beam. A solid element, that utilized the isoparametric formulation along with incompatible modes, and one-dimensional elements are also included in the element library. The tools developed in the present work are then utilized for detailed rotorcraft applications. As opposed to the conventional approach of using beam elements to represent the rotor blade, the current approach focuses on detailed modeling of the blade using plate and solid elements. A quasi-steady model based on lifting line theory is utilized to compute the aerodynamic loads on the rotor blade in order to demonstrate the capabilities of the proposed tool to model rotorcraft aeroelasticity.

In this thesis we present the deformation theory of Lie groupoid morphisms, Lie subgroupoids and symplectic groupoids. The corresponding deformation complexes governing such deformations are defined and used to investigate a Moser argument in each of these contexts. We also apply this theory to the case of Lie group morphisms and Lie subgroups, obtaining rigidity results of these structures. Moreover, in the case of symplectic groupoids, we define a map between the differentiable and deformation cohomology of the underlying groupoid, which is regarded as the global counterpart of a map $i$ defined by Crainic and Moerdijk (2004) which relates the (Poisson) cohomology of the Poisson structure on the base $M$ of the groupoid to the deformation cohomology of the Lie algebroid $T^{*}M$ associated to it. / Nesta tese apresentamos a teoria de deformação de morfismos de grupoides de Lie, subgrupoides de Lie e grupoides simpléticos, definimos os correspondentes complexos de deformação que controlam as deformações destas estruturas, e usamos estes complexos para desenvolver o argumento de Moser em cada um destes contextos. Também aplicamos esta teoria ao caso de morfismos de grupos de Lie e subgrupos de Lie obtendo resultados de rigidez de tais estruturas. Ademais, no caso de grupoides simpléticos, definimos uma função entre a cohomologia diferenciável e a cohomologia de deformação do grupoide, que é interpretada como o análogo global da aplicação $i$ definida por Crainic e Moerdijk (2004) que relaciona a cohomologia de Poisson da estrutura de Poisson induzida na base $M$ do grupoide com a cohomologia de deformação do algebroide de Lie $T^{*}M$ associado à estrutura de Poisson.