SVIBOR - Papers quoted in CC - project code: 2-11-449
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Papers quoted in Current Contents on project 2-11-449
Quoted papers: 3
Other papers: 3
Total: 6
Title: The Finite Element Formulation of a Finite Rotation Solid
Element
- Authors:
- KOŽAR, IVICA (146206)
- Ibrahimbegović, Adnan
Journal: Finite Elements in Analysis and Design
ISSN: 0168-874X
Volume: 20
Year: 1995
Pages: from 101 to 126
Language: engleski
Summary: The paper describes the development of an 8 node solid
finite element capable of undergoing both large displacements and large
rotations. The constitutive law chosen is for an elastic material. The
element is developed imploying consistent linearisation.The incompatible
modes are employed to produce a 'locking' free performance. The operator
split method is employed in solving equilibrium equations which resulted in
the minimal secondary storage requirements. The rotation vector is chosen
as a parameterization of large rotations and, as a consequence, the
stiffness matrix obtained by the consistent linearization is a symmetric
one. Also, the rotation vector is expressed in a unique
way so that it can be additively composed and the update procedure is the
simplest one possible. In order to improve behavior of the element for very
large rotations, we have somewhat modified the total Lagrangian formulation
to allow for incremental rotations to appear. The correctness of the
procedure is proved with a set of numerical examples.
Keywords: nonlinear analysis, finite rotations, solid finite elements
Title: Computational Aspects of Vector-like Parameterization of
Three-dimensional Finite Rotations
- Authors:
- Ibrahimbegović, Adnan
- KOŽAR, IVICA (146206)
Journal: International Juornal for Numerical Methods in Engineering
ISSN: 0029-5981
Volume: 38
Year: 1995
Pages: from 1 to 15
Language: engleski
Summary: Analysis of slender structures undergoing finite rotations
is encountered in a number of engineering fields. Finite three-dimensional
rotations are, in general, represented by an orthogonal tensor. It has been
established that for a unique global representation of finite rotations one
needs a minimum of five parameters.
Subsequently, a number of authors have explored the applications
of the quaternion method in the analyses of finite rotations
of rods, plates and shells, making it thus a currently dominant procedure.
In contrast with those works, in this work we explore computational issues
of finite rotation representation with three parameters only.
The central role is played by the unique representation
of the orthogonal matrix by the 'rotation vector', expressed through the
well-known Rodrigues formula.
The main results can be summarized as follows:
As the main difference from the quaternion method, the finite
element implementation of the rotation vector parameterization does not
require any secondary storage manipulation and update of the rotation
parameters is simply additive.
As the final note we have addressed the issues of the
consistent linearization procedure leading to the quadratic rate of
convergence.
The model problem chosen to illustrate here presented considerations is the
three-dimensional beam theory of Reissner Š1981Ć. Explicit forms of the
residual and the tangent stiffness matrix for Reissner's beam are given.
However, the same considerations would apply to the finite rotations of
shells with drilling rotations.
Keywords: finite rotations, nonlinear 3-D analysis, quaternions, rotation vector, consistent linearization
Title: Nonlinear Wilson's Brick Element for Finite Elastic
Deformation of Three-dimensional Solids
- Authors:
- Ibrahimbegović, Adnan
- KOŽAR, IVICA (146206)
Journal: Communications in Numerical Methods in Engineering
Number: 8
ISSN: 0748-8025
Volume: 11
Year: 1995
Pages: from 655 to 664
Language: engleski
Summary: Geometrically nonlinear version of the well known 8-node
Wilson's brick element is presented. The element is based on a sound
variational formulation and the modified method of incompatible modes,
which are shown to render quite a satisfying, locking-free performance in
some challeging large displacement problems.
Keywords: Wilson's brick element, finite rotations, variational formulation, incompatible modes
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