Particle Simulation for Predicting Effective Properties of Short Fiber Reinforced Composites
We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of the composite material are evaluated. The developed micro-mechanical mathematical modelling of effective moduli is aimed to molding process optimization which results in product quality improvement.
We construct asymptotic solutions to the wave equation with velocity rapidly oscillating a smoothly varying background and with localized initial perturbations. First, using adiabatic approximation in the operator form, we perform homogenization that leads to a linearized Boussinesq-type equation with smooth coefficients and weak “anomalous” dispersion. Then, asymptotic solutions to this and, as a consequence, to the original equations are constructed by means of a modified Maslov canonical operator; for initial perturbations of special form, these solutions are expressed in terms of combinations of products of the Airy functions of a complex argument. On the basis of explicit formulas obtained, we analyze the effect of fast oscillations of the velocity on the solution fronts and solution profiles near the front.
The elastic moduli of a composite material made of high-temperature modified phenolic resins with short carbon fibers are studied. Several analytical formulas used to determine the effective moduli of such composites are compared and experimentally verified.
The system of equations of gravity surface waves is considered in the case where the basin's bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than the characteristic length of the basin bottom's oscillations but can be much less than the characteristic dimensions of the domain where these waves propagate, the adiabatic approximation is used to pass to a reduced homogenized equation of wave equation type or to the linearized Boussinesq equation with dispersion that is “anomalous” in the theory of surface waves (equations of wave equation type with added fourth derivatives).The rapidly varying solutions of the reduced equation can be found (and they were also found in the authors' works) by asymptotic methods, for example, by the WKB method, and in the case of focal points, by the Maslov canonical operator and its generalizations.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.