Title page for ETD etd-0408104-111231

Document Type thesis

Author Name Kohengadol, Roni A

Email Address mrroni2000 at yahoo.com

URN etd-0408104-111231

Title Nonlinear Solvers For Plasticity Problems

Degree MS

Department Mathematical Sciences

Advisors
Marcus Sarkis, Advisor

Keywords
elastoviscoplasticity

Date of Presentation/Defense 2004-04-29

Availability unrestricted

Abstract
The partial differential equation governing the problem of elastoplasticity is linear in the
elastic region and nonlinear in the plastic region. In the elastic region, we encounter the
problem of elasticity which is governed by the Navier Lame equations. We present a solution to the above problem through numerical schemes such as the finite element method.

In the plastic region, we encounter a nonlinear partial differential equation. This PDE is hard to solve numerically and therefore we rewrite our PDE with a penalty parameter. It is known that when the penalty parameter associated to the above PDE is zero we achieve an exact solution to the problem. This is hard to achieve from a numerical point of view however.

We will see that when we linearize the partial differential equation with Newton's method, the method fails to converge when the penalty parameter is small. In this thesis, the failure of Newton's method is explained and a new method to solve the problem is proposed. The path
following method will help us improve Newton's method by a better choice of the initial guess.

We obtain the convergence of this method for the penalty parameter as close to zero as we want and thereby we obtain an exact solution to our original PDE.

Plots with results are presented.

Files
main.pdf

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Document Type	thesis
Author Name	Kohengadol, Roni A
Email Address	mrroni2000 at yahoo.com
URN	etd-0408104-111231
Title	Nonlinear Solvers For Plasticity Problems
Degree	MS
Department	Mathematical Sciences
Advisors	Marcus Sarkis, Advisor
Keywords	elastoviscoplasticity
Date of Presentation/Defense	2004-04-29
Availability	unrestricted
Abstract The partial differential equation governing the problem of elastoplasticity is linear in the elastic region and nonlinear in the plastic region. In the elastic region, we encounter the problem of elasticity which is governed by the Navier Lame equations. We present a solution to the above problem through numerical schemes such as the finite element method. In the plastic region, we encounter a nonlinear partial differential equation. This PDE is hard to solve numerically and therefore we rewrite our PDE with a penalty parameter. It is known that when the penalty parameter associated to the above PDE is zero we achieve an exact solution to the problem. This is hard to achieve from a numerical point of view however. We will see that when we linearize the partial differential equation with Newton's method, the method fails to converge when the penalty parameter is small. In this thesis, the failure of Newton's method is explained and a new method to solve the problem is proposed. The path following method will help us improve Newton's method by a better choice of the initial guess. We obtain the convergence of this method for the penalty parameter as close to zero as we want and thereby we obtain an exact solution to our original PDE. Plots with results are presented.
Files	main.pdf