Thesis

Patterns in an elastic bar

Creator
Rights statement
Awarding institution
  • University of Strathclyde
Date of award
  • 2020
Thesis identifier
  • T15539
Person Identifier (Local)
  • 201684026
Qualification Level
Qualification Name
Department, School or Faculty
Abstract
  • We consider Yip's formulation of the Ericksen model for an elastic bar on an elastic foundation [63] which leads to the Euler-Lagrange equation for the functional ε(u) = ∫ between 0 and 1 (γu²xx +W(ux) + ɑu²)dx, where x is an element of the set (0, 1). with double Dirichlet boundary conditions. Here the potential W(p) = ((|p| - 1)²), is not differentiable at p = 0.;We define and prove existence and uniqueness of periodic solutions with any number n ≥ 0 of internal zeroes for all ɑ, γ > 0 and discuss the existence of non-periodic solutions.;The Euler-Lagrange equation contains conditions that make it diffcult to track, and then dropping one of them we obtain a weak formulation for this reduced problem,which we then prove it has a unique solution. Next, we use a combination of two numerical methods, namely the Finite Elements Method (FEM) to approximate the model and the Derivative Free Optimization (DFO) to find the location of the jump.
Advisor / supervisor
  • Grinfeld, Michael (Mathematician)
  • Barrenechea, Gabriel
Resource Type
DOI
Date Created
  • 2020
Former identifier
  • 9912881692602996

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