Faculty Advisor or Committee Member

Robert P. Lipton, Advisor

Faculty Advisor or Committee Member

Konstantin A. Lurie, Committee Member

Faculty Advisor or Committee Member

Bogdan M. Vernescu, Committee Member

Faculty Advisor or Committee Member

Nikos A. Gatsonis, Committee Member

Faculty Advisor or Committee Member

Domokos Vermes, Committee Member

Faculty Advisor or Committee Member

Arthur C. Heinricher, Committee Member

Identifier

etd-0616100-180816

Abstract

"In this work we consider an optimal design problem formulated on a two dimensional domain filled with two isotropic dielectric materials. The objective is to find a design that supports an electric field which is as close as possible to a target field, under a constraint on the amount of the better dielectric. In the case of a zero target field, the practical purpose of this problem is to avoid the so called dielectric breakdown of the material caused due to a relatively large electric field. In general, material layout problems of this type fail to have an optimal configuration of the two materials. Instead one must study the behavior of minimizing sequences of configurations. From a practical perspective, optimal or nearly optimal configurations of the two materials are of special interest since they provide the information needed for the manufacturing of optimal designs. Therefore in this work, we develop theoretical and numerical means to support a tractable method for the numerical computation of minimizing sequences of configurations and illustrate our approach through numerical examples. The same method applies if we were to replace the electric field by electric flux, in our objective functional. Similar optimization design problems can be formulated in the mathematically identical contexts of electrostatics and heat conduction."

Publisher

Worcester Polytechnic Institute

Degree Name

PhD

Department

Mathematical Sciences

Project Type

Dissertation

Date Accepted

2000-06-16

Accessibility

Unrestricted

Subjects

gradient fields, functionally graded materials, laminates, optimal design, Electrostatics, Dielectrics, Mathematical optimization

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