Patterns in an elastic bar

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.

Name dc:type.qualificationname

phd

Level dc:type.qualificationlevel

doctoral-pg

Grantor dc:publisher.institution

University of Strathclyde

Year dc:date.issued

2020

Author dc:creator

• Alruwaili, Abdulmohsen

Advisors dc:contributor.advisor

• Grinfeld, Michael (Mathematician)
• Barrenechea, Gabriel

DOI

10.48730/g1ma-hz45

Identifier

T15539

Author Identifier

201684026

OAI identifier oai:identifier

oai:strathclyde:jh343s35t