PhD Thesis Defence Presentations - Δήμητρα Λαμπροπούλου
Abstract (Περίληψη)
The mechanics of continuous media, and especially the theory of linear elasticity, constitutes an important part of science and technology. This dissertation deals with the mathematical study of the properties of linear isotropic and anisotropic elasticity with the aim of developing analytical solutions in this field. Starting with isotropic materials, where properties are independent of orientation, linear isotropic elasticity is described by the laws of Hooke and Newton. Then, the theory of anisotropic elasticity is introduced, where the material properties do not remain unchanged under rotational transformations. The construction of mathematical tools for analyzing these two types of elasticity follows, including analytical solutions for Newton's law. The methodology is presented for typical isotropic materials and materials with cubic anisotropy, providing effective mathematical tools for computing more complicated solutions. The methodology is validated by analyzing the degeneration of the results from the anisotropic to the isotropic eigenspace, thus providing a generalized method for the analysis of anisotropic spaces, while it is applied to specific physical problems in linear elasticity.
Speakers Short CV (Σύντομο Βιογραφικό Ομιλητή)
I was born in Athens, Greece, on December 8, 1992. I was admitted the Department of Mathematics at the University of Patras in 2010 and completed my undergraduate studies in 2015, receiving my degree in Applied Mathematics. In 2018, I completed my postgraduate studies in the same Department, obtaining a Master's Degree in the program "Mathematics and Modern Applications", where I successfully attended and passed 8 courses. In 2019, I was selected in the Doctorate program of the Department of Chemical Engineering at the University of Patras, where I am currently pursuing my doctoral studies with a thesis entitled "Mathematical Properties of Linear Elasticity". I attended and successfully passed 3 doctoral courses in the same Department. During my doctoral studies, I provided auxiliary work until 2022 in undergraduate courses such as "Calculus of a Single Variable and Linear Algebra", "Multivariable Calculus and Vector Analysis", and "Partial Differential Equations", as well as I participated in computer laboratories. My research activity mainly focuses on the mathematical modeling of physical problems of mathematical and technological interest with applications in continuous mechanics and especially in linear elasticity.