Browsing by Subject "Finite Elements"
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Item A Multiscale Framework for the Characterization of Damage in Textile Composites Under Thermomechanical Loads(2013-11-08) McLendon, Wesley RThis work examines composite failure at multiple scales. The ?rst scale that is examined is the ?ber-matrix scale, where ?bers and matrix are discretely modeled. A model is developed at this scale which includes randomness in the ?ber positions. This randomness is found to signi?cantly in?uence the stress ?eld and resulting failure that occurs under thermo mechanical loads as compared to ?ber-matrix microstructures with regular arrays of ?bers. The ?ber-matrix model is utilized to characterize variability and temperature dependence of the composite strength arising from microstructural randomness and the presence of thermally induced stresses. The second scale that is examined is that of a textile unit cell. Failure initiation behavior is examined for a variety of thermo mechanical loadings at this scale, and it is found that failure tends to initiate in a limited number of ways for a wide variety of loadings. A new progressive failure model is then examined for the textile unit cell. This model utilizes cohesive interface elements in the tows, neat matrix pockets, and tow and matrix interfaces to account for crack opening in the textile, as well as a continuum damage model to account for di?use damage in the tows. Variability and temperature dependence of the transverse tow strength is introduced by specifying varying cohesive strengths in the intra-tow cohesive zones using a Weibull distribution characterized using the random ?ber-matrix model. Progressive failure analyses are then performed for the textile unit cell under a variety of thermomechanical loads, and the resulting behaviors are compared to identify characteristic modes of damage development and their e?ect on the textile response. A continuum damage model for the textile material, which can be applied to engineering structures, is developed based on the characteristic damage modes observed in the textile unit cell analyses. This model tracks the evolution of each characteristic mode of damage based on the structural-scale stress and predicts the degradation in the textile response as a result of this damage. The ability of this model to predict the textile?s response under various damage-inducing loads is then compared to the response obtained from textile unit cell progressive failure analysis, and both models are found to be in good agreement for most loadings.Item Approximation Techniques for Incompressible Flows with Heterogeneous Properties(2011-10-21) Salgado Gonzalez, Abner JonatanWe study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous medium, where the permeability of the medium depends on the pressure. The second is the ow of a viscous incompressible fluid with variable density. The heterogeneity is the permeability and the density, respectively. For the first problem, we propose a finite element discretization and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence is exponential, we propose a splitting scheme which involves solving only two linear systems. For the second problem, we introduce a fractional time-stepping scheme which, as opposed to other existing techniques, requires only the solution of a Poisson equation for the determination of the pressure. This simpli cation greatly reduces the computational cost. We prove the stability of first and second order schemes, and provide error estimates for first order schemes. For all the introduced discretization schemes we present numerical experiments, which illustrate their performance on model problems, as well as on realistic ones.Item B-spline finite elements for plane elasticity problems(Texas A&M University, 2007-04-25) Aggarwal, BhavyaThe finite element method since its development in the 1950??????s has been used extensively in solving complex problems involving partial differential equations. The conventional finite element methods use piecewise Lagrange interpolation functions for approximating displacements. The aim of this research is to explore finite element analysis using B-spline interpolation. B-splines are piecewise defined polynomial curves which provide higher continuity of derivatives than piecewise Lagrange interpolation functions. This work focuses on the implementation and comparison of the B-spline finite elements in contrast with the conventional finite elements. This thesis observes that the use of B-spline interpolation functions can reduce the computational cost significantly. It is an efficient technique and can be conveniently implemented into the existing finite element programs.