(to be submitted for journal publication)
Glaucio 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 / PUC-Rio de Janeiro, Rua Marques de Sao Vicente 225, 22453-900,
Rio de Janeiro, R.J., Brazil
E. N. Lages,
Department of Structural Engineering, UFAL Federal University of Alagoas,
57055, Maceio, AL, Brazil
Abstract
By means of a unified framework for solving nonlinear finite element equations, the
various solution algorithms (e.g. Newton-Raphson, arc-length, work control, etc.) can
share a common interface, just differing on their constraint equation, which is typical of
each particular algorithm. In this approach, the solution process is reformulated in
N+1 dimensional space, which includes N displacements and one load-type parameter as the
basic unknowns. This paper shows how to render the orthogonal residual procedure
(ORP) in the unified scheme described above. Theoretical and implementation issues
are discussed in detail. A concise (and complete) algorithm, together with its
computational implementation, is provided. An important feature of the algorithm is
that is allows easy addition of new problems, which can be defined by the user. To
validate the approach proposed herein, problems involving geometrical and material
nonlinearities are solved using the revisited ORP (i.e. within the unified scheme), and it
is verified that the results obtained with previous versions of the ORP are recovered.
Whenever appropriate, the results are also compared with those obtained by other
solution schemes or with those available in the technical literature.
Key words: Non-linear finite elements; orthogonal residual procedure; incremental-iterative methods; non-linear equations; path-following techniques
Representative Results:
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3D Truss example |