Browsing by Subject "numerical analysis"
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Item Anisotropic Characterization and Performance Prediction of Chemically and Hydraulically Bounded Pavement Foundations(2010-10-12) Salehi Ashtiani, RezaThe aggregate base layer is a vital part of the flexible pavement system. Unlike rigid pavements, the base layer provides a substantial contribution to the load bearing capacity in flexible pavements, and this contribution is complex: stress dependent, moisture dependent, particle size dependent, and is anisotropic in nature. Furthermore, the response of the aggregate layer in the pavement structure is defined not only by resilient properties of the base layer but also by permanent deformation properties of the aggregate layer. Before the benefits of revolutionary changes in the typical pavement structures, such as deep unbound aggregate base (UAB) layers under thin hot mix asphalt surfaces and inverted pavement systems can be justified, an accurate assessment of the UAB is required. Several researchers identified that in order to properly assess the contribution of the UAB in the pavement structure, it is necessary to consider not only the vertical modulus but also the horizontal modulus as this substantially impacts the distribution of stresses within the pavement structure. Anisotropy, which is defined as the directional dependency of the material properties in unbound granular bases, is inherent even before the aggregate layer is subjected to traffic loads due to random arrangement of particles upon compaction. Distribution of particle contacts is dominated by the geometry of the aggregates as well as the compaction effort at the time of construction. Critical pavement responses and therefore performance of flexible pavements are significantly influenced by the level of anisotropy of aggregate layers. There are several ways to characterize the level of anisotropy in unbound aggregate systems. Previous research at Texas A&M University suggests functions of fitting parameters in material models (kvalues) as characterizers of the level of anisotropy. In the realm of geotechnical engineering, the ratio of the horizontal modulus to vertical modulus is commonly referred to as the level of anisotropy. When the vertical and horizontal moduli are equal, the system is isotropic, but when they differ, the system is anisotropic. This research showed that the level of anisotropy can vary considerably depending on aggregate mix properties such as gradation, saturation level, and the geometry of the aggregate particles. Cross anisotropic material properties for several unbound and stabilized aggregate systems were determined. A comprehensive aggregate database was developed to identify the contribution level of aggregate features to the directional dependency of material properties. Finally a new mechanistic performance protocol based on plasticity theory was developed to ensure the stability of the pavement foundations under traffic loads.Item Approximation of linear partial differential equations on spheres(Texas A&M University, 2004-09-30) Le Gia, Quoc ThongThe theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both the finite element method and the collocation method are discussed. In the heat equation, only the collocation method is considered. Error estimates in the supremum norms and the Sobolev norms are obtained when certain regularity conditions are imposed on the spherical basis functions.Item Modeling of Shape Memory Alloys Considering Rate-independent and Rate-dependent Irrecoverable Strains(2011-02-22) Hartl, Darren J.This dissertation addresses new developments in the constitutive modeling and structural analysis pertaining to rate-independent and rate-dependent irrecoverable inelasticity in Shape Memory Alloys (SMAs). A new model for fully recoverable SMA response is derived that accounts for material behaviors not previously addressed. Rate-independent and rate-dependent irrecoverable deformations (plasticity and viscoplasticity) are then considered. The three phenomenological models are based on continuum thermodynamics where the free energy potentials, evolution equations, and hardening functions are properly chosen. The simultaneous transformation-plastic model considers rate-independent irrecoverable strain generation and uses isotropic and kinematic plastic hardening to capture the interactions between irrecoverable plastic strain and recoverable transformation strain. The combination of theory and implementation is unique in its ability to capture the simultaneous evolution of recoverable transformation strains and irrecoverable plastic strains. The simultaneous transformation-viscoplastic model considers rate-dependent irrecoverable strain generation where the theoretical framework is modfii ed such that the evolution of the viscoplastic strain components are given explicitly. The numerical integration of the constitutive equations is formulated such that objectivity is maintained for SMA structures undergoing moderate strains and large displacements. Experimentally validated analysis results are provided for the fully recoverable model, the simultaneous transformation-plastic yield model, and the transformation-viscoplastic creep model.