Microstructure design of magneto-dielectric materials via topology optimization
El-Kahlout, Yasser (2009) Microstructure design of magneto-dielectric materials via topology optimization. [Thesis]
Official URL: http://192.168.1.20/record=b1301370 (Table of Contents)
Engineered materials, such as new composites, electromagnetic bandgap and periodic structures have attracted considerable interest in recent years due to their remarkable and unique electromagnetic behavior. As a result, an extensive literature on the theory and application of artificially modified materials exists. Examples include photonic crystals (regular, degenerate or magnetic) illustrating that extraordinary gain and high transmittance can be achieved at specific frequencies. Of importance is that recent investigations of material loading demonstrate that substantial improvements in antenna performance (smaller size, larger bandwidth, higher gain etc.) can be attained by loading bulk materials such as ferrites or by simply grading the material subject to specific design objectives. Multi-tone ceramic materials have also been used for miniaturization and pliable polymers offer new possibilities in three dimensional antenna design and multilayer printed structures, including 3D electronics. However, as the variety of examples in the literature shows, the perfect combination of materials is unique and extremely difficult to determine without optimization. In addition, existing artificial dielectrics are mostly based on intuitive studies, i.e. a formal design framework to predict the exact spatial combination of dielectrics, magnetics and conductors does not exist. In the first part of this thesis, an inverse design framework integrating FE based analysis tool (COMSOL MULTIPHYSICS-PDE Coefficient Module) with an optimization technique (MATLAB-Genetic Algorithm and Direct Search toolbox) suitable for designing the microstructure of artificial magneto-dielectrics from isotropic material phases is proposed. Homogenizing Maxwell's Equations (MEQ) in order to estimate the effective material parameters of the desired composite made of periodic microstructures is the initial task of the framework. The FE analysis tool is used to evaluate intermediate fields at the "micro-scale" level of a unit cell that is integrated with the homogenized MEQ's in order to estimate the "macro-scale" effective constitutive parameters of the overall bulk periodic structure. Simulation of the periodic structure is an extremely challenging task due to the mesh at micro-level (inclusions much smaller than the periodic cell dimension) that spans over the entire bulk structure turning the computational problem into a very intensive one. Therefore, the proposed framework based on the solution of homogenized MEQ's via the micro-macro approach, allows topology design capabilities of microstructures with desired properties. The goal is to achieve predefined material constitutive parameters via artificial electromagnetic substrates. Physical material bounds on the attainable properties are studied to avoid infeasible effective parameter requirements via available multi-constituents. The proposed framework is applied on examples such as microstructure layers of non-reciprocal magnetic photonic crystals. Results show that the homogenization technique along with topology optimization is able to design non-intuitive material compositions with desired electromagnetic properties. In the second part of the thesis, approximation techniques to speed-up large scale topology optimization studies of devices with complex frequency responses are investigated. Miniaturization of microstrip antennas via topology optimization of both the conductor and material substrate via multi-tone ceramic shades is a typical example treated here. Long computational times required for both the electromagnetic analysis over a frequency range and the need for a heuristic based optimization tool to locate the global minima for complex devices present themselves as two important bottlenecks for practical design studies. In this thesis, two new techniques for speeding up the optimization process by reducing the number of frequency calls needed to accurately predict a multi-resonance type response of a candidate design are proposed. The proposed techniques employ adaptive sampling methods along with novel rational function interpolations. The first technique relies on a heuristic based rational interpolation using Bayes' theory and rational functions. Second, a rational function interpolation employing a new adaptive path based on Stoer-Bulirsch algorithm is used. Both techniques prove to efficiently predict resonances and significantly reduce the computational time by at least three folds.
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