A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics
Leon, Sofia
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https://hdl.handle.net/2142/18353
Description
Title
A unified library of nonlinear solution schemes: An excursion into nonlinear computational mechanics
Author(s)
Leon, Sofia
Issue Date
2011-01-14T22:47:14Z
Director of Research (if dissertation) or Advisor (if thesis)
Paulino, Glaucio H.
Department of Study
Civil & Environmental Eng
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(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.
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