A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics

A library of nonlinear solution schemes including load, displacement, arc-length, work, generalized displacement, and orthogonal residual control are cast into a unified framework for solving nonlinear finite element systems. Each of these solution schemes differs in the use of a constraint equation for the incremental-iterative procedure. The governing finite element equations and constraint equation for each solution scheme are combined into a single matrix equation, which characterizes the unified approach. This theoretical model leads naturally to an effective object-oriented implementation and potential for integration into a finite element analysis code. Using this framework, the strengths and weaknesses of the various solution schemes are examined through several numerical examples.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Leon, Sofia

Contributors dc:contributor

• Paulino, Glaucio H.

• Nonlinear solution schemes
• nonlinear finite element analysis
• incremental-iterative procedure
• Newton-Raphson method
• displacement control method
• arc-length control method
• work control method
• generalized displacement control method
• orthogonal residual procedure

Statement dc:rights

• Copyright 2010 Sofia E. Leon

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/18353

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/18353