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©2012 Civil-Comp Ltd |
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S.Sh. Ghorashi1,3, N. Valizadeh2 and S. Mohammadi1
1School of Civil Engineering, University of Tehran, Iran
2Department of Civil Engineering, University of Kerman, Iran
3Research Training Group 1462, Bauhaus-Universität Weimar, Germany
Keywords: orthotropic media, crack, extended isogeometric analysis, orthotropic enrichment functions, stress intensity factor, interaction integral.
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In this paper, cracked orthotropic media are analyzed by
applying the novel approach of extended isogeometric analysis (XIGA).
Orthotropic materials such as composites have been increasingly applied
in many engineering applications e.g. aerospace, automobile and marine
structures because of their high strength and stiffness to weight
ratios. Fracture analysis of such media has been the centre of attention
for many researchers in recent decades. As the analytical methods
cannot be simply employed for complex problems which are common in
structural engineering, numerical methods provide better alternatives.
The complexity of engineering problems and the enormous growth in
computer technology has led to the development of several numerical methods.
Among them, the extended finite element method (XFEM) has proved to be
a promising powerful tool in modelling
fracture problems because it enables improved approximations of non-smooth
solutions such as those including jumps and singularities. In this
approach, to crack modelling, the classical finite element approximation
is enriched by a discontinuous function and asymptotic crack-tip displacement
fields using the framework of partition of unity (PU). In the XFEM, the
finite element mesh is not required to conform to the crack boundaries,
and hence a single mesh suffices for modelling the crack stability
and capturing its evolution.
On the other hand, isogeometric analysis (IGA) is a promising computational
scheme that takes advantage of using non-uniform rational B-splines
(NURBS) for both the geometric description and the solution field
approximation to: exactly represent complex geometries; to increase
the order of continuities between elements; to simplify the refinement
process; and to improve solution accuracy. Isogeometric analysis has
been effectively applied to a large variety of problems.
The two powerful approaches of XFEM and IGA have recently been combined
to include the benefits of both [1]. This method
which is also called extended isogeometric analysis (XIGA) has been
successfully applied for simulation of stationary and propagating
cracks in 2D linear-elastic isotropic media.
In this contribution, XIGA is further extended for fracture analysis
of cracked linear-elastic orthotropic materials. For this purpose,
the orthotropic enrichment functions applied in XFEM are adopted.
The Lagrange multiplier method is utilized to impose essential boundary
conditions. The Gauss quadrature rule is applied for integration alongside
the "sub-triangles approach"
and the "almost polar technique"
for split and crack tip elements, respectively [1].
In order to compare the results with those obtained by other semi-analytical
and numerical methods, mixed mode stress intensity factors are calculated
by adopting the interaction integral technique. Finally, several numerical
examples are analysed to demonstrate the accuracy and efficiency of
the proposed approach.
- 1
- S.Sh. Ghorashi, N. Valizadeh, S. Mohammadi, "Extended isogeometric analysis (XIGA) for simulation of stationary and propagating cracks", International Journal for Numerical Methods in Engineering, 89, 1069-1101, 2012. doi:10.1002/nme.3277
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