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
Relations
Items
| Thumbnail | Title | Date Uploaded | Visibility | Actions |
|---|---|---|---|---|
|
|
PDF of thesis T15539 | 2021-07-02 | Public | Download |