(to be submitted for journal publication)
G.H. Paulino,
Department of Civil and Environmental Engineering, University of Illinois
at Urbana-Champaign, Newmark Laboratory, 205 North Mathews Avenue, IL 61801,
U.S.A.
I.F. M. Menezes,
TeCGraf (Computer Graphics Technology Group), PUC-Rio, Rio de Janeiro, RJ,
22453-900, Brazil
E.N. Lages,
Department of Structural Engineering, Universidade Federal de Alagoas (UFAL),
Maceio, AL, 57072-970, Brazil
Abstract
Load, displacement, generalized displacement, arc-length, energy, and orthogonal
residual solution schemes are cast onto 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. Here, the governing equations
together with the constaint equation for each solution scheme are combined into a single
matrix equation, which characterizes the unified approach. It is shown that this
theoretical model leads naturally to an effective object-oriented implementation. In
this way, the details of the actual solution strategy can be made transparent for the user
of nonlinear solution algorithms. Essentially, this approach provides a multiple
choice solution, which can be explored in incremental-iterative solutions of the
finite element method. Numerical examples are presented and solved using the various
nonlinear solution schemes which are available in the present unified approach. The
examples illustrate some of the strengths and weaknesses of the various solution schemes.
Key words: finite element analysis (FEA), object oriented programming (OOP), nonlinear solution schemes, structural mechanics, geometric nonlinearity, physical nonlinearity.
Representative Results:
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Cantilever beam example | |
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Square frame in tension | |
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Square frame in compression |