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Title:A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics
Author(s):Leon, Sofia
Advisor(s):Paulino, Glaucio H.
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Subject(s):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
Abstract: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.
Issue Date:2011-01-14
Rights Information:Copyright 2010 Sofia E. Leon
Date Available in IDEALS:2011-01-14
Date Deposited:December 2

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