Browsing by Subject "elasticity"
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Item An Efficient Nonlinear Structural Dynamics Solver for Use in Computational Aeroelastic Analysis(2011-08-08) Freno, Brian AndrewAerospace structures with large aspect ratio, such as airplane wings, rotorcraft blades, wind turbine blades, and jet engine fan and compressor blades, are particularly susceptible to aeroelastic phenomena. Finite element analysis provides an effective and generalized method to model these structures; however, it is computationally expensive. Fortunately, these structures have a length appreciably larger than the largest cross-sectional diameter. This characteristic is exploitable as these potential aeroelastically unstable structures can be modeled as cantilevered beams, drastically reducing computational time. In this thesis, the nonlinear equations of motion are derived for an inextensional, non-uniform cantilevered beam with a straight elastic axis. Along the elastic axis, the cross-sectional center of mass can be o set in both dimensions, and the principal bending and centroidal axes can each be rotated uniquely. The Galerkin method is used, permitting arbitrary and abrupt variations along the length that require no knowledge of the spatial derivatives of the beam properties. Additionally, these equations consistently retain all third-order nonlinearities that account for flexural-flexural-torsional coupling and extend the validity of the equations for large deformations. Furthermore, linearly independent shape functions are substituted into these equations, providing an efficient method to determine the natural frequencies and mode shapes of the beam and to solve for time-varying deformation. This method is validated using finite element analysis and is extended to swept wings. The importance of retaining cubic terms, in addition to quadratic terms, for nonlinear analysis is demonstrated for several examples. Ultimately, these equations are coupled with a fluid dynamics solver to provide a structurally efficient aeroelastic program.Item Constitutive modeling for biodegradable polymers for application in endovascular stents(Texas A&M University, 2008-10-10) da Silva Soares, Joao FilipePercutaneous transluminal balloon angioplasty followed by drug-eluting stent implantation has been of great benefit in coronary applications, whereas in peripheral applications, success rates remain low. Analysis of healing patterns in successful deployments shows that six months after implantation the artery has reorganized itself to accommodate the increase in caliber and there is no purpose for the stent to remain, potentially provoking inflammation and foreign body reaction. Thus, a fully biodegradable polymeric stent that fulfills the mission and steps away is of great benefit. Biodegradable polymers have a widespread usage in the biomedical field, such as sutures, scaffolds and implants. Degradation refers to bond scission process that breaks polymeric chains down to oligomers and monomers. Extensive degradation leads to erosion, which is the process of mass loss from the polymer bulk. The prevailing mechanism of biodegradation of aliphatic polyesters (the main class of biodegradable polymers used in biomedical applications) is random scission by passive hydrolysis and results in molecular weight reduction and softening. In order to understand the applicability and efficacy of biodegradable polymers, a two pronged approach involving experiments and theory is necessary. A constitutive model involving degradation and its impact on mechanical properties was developed through an extension of a material which response depends on the history of the motion and on a scalar parameter reflecting the local extent of degradation and depreciates the mechanical properties. A rate equation describing the chain scission process confers characteristics of stress relaxation, creep and hysteresis to the material, arising due to the entropy-producing nature of degradation and markedly different from their viscoelastic counterparts. Several initial and boundary value problems such as inflation and extension of cylinders were solved and the impacts of the constitutive model analyzed. In vitro degradation of poly(L-lactic acid) fibers under tensile load was performed and degradation and reduction in mechanical properties was dependent on the mechanical environment. Mechanical testing of degraded fibers allowed the proper choice of constitutive model and its evolution. Analysis of real stent geometries was made possible with the constitutive model integration into finite element setting and stent deformation patterns in response to pressurization changed dramatically as degradation proceeded.Item Effect of Boundary Conditions on Performance of Poroelastographic Imaging Techniques in Non Homogenous Poroelastic Media(2012-02-14) Chaudhry, AnujIn the study of the mechanical behavior of biological tissues, many complex tissues are often modeled as poroelastic systems due to their high fluid content and mobility. Fluid content and fluid transport mechanisms in tissues are known to be highly correlated with several pathologies. Thus, imaging techniques capable of providing accurate information about these mechanisms can potentially be of great diagnostic value. Ultrasound elastography is an imaging modality that is currently used as a complement to sonographic methods to detect a variety of tissue pathologies. Poroelastography is a new elastographic technique that has been recently proposed to image the mechanical behavior of tissues that can be modeled as poroelastic media. The few poroelastographic studies retrievable focus primarily on homogeneous poroelastic media. In this study, a statistical analysis of the performance of poroelastographic techniques in a non-homogeneous poroelastic simulation model under different loading conditions was carried out. The two loading conditions simulated were stress relaxation (application of constant strain) and creep compression (application of constant stress), both of which have been commonly used in the field of poroelastography. Simulations were performed using a FE poroelastic simulation software combined with ultrasound simulation software techniques and poroelastography processing algorithms developed in our laboratory. The non-homogeneous poroelastic medium was modeled as a cube (background) containing a cylindrical inclusion (target). Different permeability, Young?s modulus and Poisson?s ratio contrasts between the underlying matrix of the background and the target were considered. Both stress relaxation and creep compression loading conditions were simulated. The performance of poroelastography techniques was quantified in terms of accuracy, elastographic contrast?to?noise ratio and contrast transfer efficiency. The results of this study show that, in general, image quality of both axial strain and effective Poisson?s ratio poroelastograms is a complex function of time, which depends on the contrast between the poroelastic material properties of the background and the poroelastic material properties of the target and the boundary conditions. The results of this study could have important implications in defining the clinical range of applications of poroelastographic techniques and in the methodologies currently deployed.Item Fundamental Properties and Processes of Energetic Materials(2012-10-19) Ojeda Mota, Oscar UlisesEnergetic materials comprise a set of systems of tremendous technological importance. Besides helping shape landscapes to establish communications, they have been used to reach fuel reservoirs, deploy safety bags and prevent heart strokes. Understanding its behavior can help in attaining strategic and tactical superiority, and importantly, preserve lives of people who handle these materials. The large discrepancy in length and time scales at which characteristic processes of energetic materials are of relevance pose a major challenge for current simulation techniques. We present a systematic study of crystalline energetic materials of different sensitivity and analyze their properties at different theoretical levels. Equilibrium structures, vibrational frequencies, conformational rearrangement and mechanical properties can be calculated within the density functional theory and molecular dynamics at finite temperatures. We have found marked differences in the calculated properties in systems with ranging sensitivities. Reactions at elevated temperatures have been studied using ab initio molecular dynamics method for crystals of nitroethane. Furthermore, while presenting the state of the art of energetic materials modeling, the limitations of each methodology are also discussed. Prospective systems and an elasticity driven approach that can be applied to other type of materials is also presented.