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CivilComp Proceedings
ISSN 17593433 CCP: 81
PROCEEDINGS OF THE TENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping
Paper 96
Geometric and Material Nonlinear Analyses of Elastically Restrained Arches Y.L. Pi, M.A. Bradford, F. TinLoi and R.I. Gilbert
School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia Y.L. Pi, M.A. Bradford, F. TinLoi, R.I. Gilbert, "Geometric and Material Nonlinear Analyses of Elastically Restrained Arches", in B.H.V. Topping, (Editor), "Proceedings of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 96, 2005. doi:10.4203/ccp.81.96
Keywords: arches, elastic restraints, elastoplastic, finite element, geometric, material, nonlinearity.
Summary
This paper presents a new curvedbeam element for the inplane geometric and material nonlinear large deformation analysis of elastically restrained arches (Figure 96.1).
When the lateral and torsional deformations of an arch are fully restrained, the arch may buckle in an inplane bifurcational mode or snapthrough mode
under inplane loading. After buckling, deformations of the arch increase rapidly and become very large. Hence, in order to predict postbuckling behaviour
correctly, the effects of large deformations have to be considered [1]. However, in the conventional formulations of curvedbeam elements,
the nonlinear strains under inplane loading consist of nonlinear membrane strains and linear bending strains. The higherorder bending strain
components produced by the higherorder curvature terms do not appear to have been considered. In addition to the higherorder curvature components due to bending,
the axial deformations may affect the deformed curvatures and yield additional higherorder curvature terms. This appears to be ignored
in the conventional formulations of curvedbeam elements. Because of this, some significant terms in strains due to large deformations may be lost and the large postbuckling
deformations cannot be predicted correctly. It is wellknown that when an arch is subjected to inplane loading, the axial compression is
the major primary action in the arch. In order to produce the axial compression, the supports of arches are usually fixed or pinended.
However, in practice, arches may be supported by elastic foundations or by other structural members which provide elastic types of restraint to the arches.
The elastically restrained actions of the other elements of the structure on an arch can be replaced by equivalent springs and the arch can
be considered to be restrained by the elastic springs. In many cases, by knowing the structural configuration connecting to the arch,
the stiffness of the corresponding elastic springs (or spring constant) can be accurately estimated. The elastic restraints participate
in the structural behaviour of the arch and may influence significantly the structural behaviour of the arch.
These elastic restraints may be continuous or discrete. The curvedbeam element, therefore, should consider the effects of these elastic restraints.
In addition to elastic buckling and postbuckling, steel, concrete or concretefilled tubular section arches may buckle elastoplastically
in many cases. Hence, the nonlinearity of the material needs to be included in the curvedbeam element as well.
A curvedbeam element is developed in this paper based on an accurate rotation matrix that satisfies the orthogonality and unimodular conditions. Therefore, the higher order terms of the deformed curvatures in strains and the effects of the axial deformations on the deformed curvatures are retained and thus the large deformations can be predicted accurately by the element. At the same time, the membrane locking problem that occurs in a number of curvedbeam elements is naturally avoided because the same order interpolation polynomials can be used for both radial and axial deformations. In addition, the curved beam element includes the effects of the elastic restraints on the structural behaviour of arches. Furthermore, material nonlinearity in the elastic and elastoplastic ranges are considered in the curvedbeam element as well. Comparisons of results of the finite element model with the analytical closed form solutions [2] for buckling and postbuckling of elastically restrained arches, and with the test results [3] demonstrate that the curved beam element provides a good prediction accuracy for nonlinear analysis. References
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