http://orbilu.uni.lu/handle/10993/12159
The isogeometric analysis (IGA) based on finite element methods was proposed by [2].
The idea of IGA is to use the same shape functions to describe the known CAD geometry and
the unknown eld variables. However, CAD systems typically only provide the boundary of
the domain [1] and do not provide any description of its interior. Hence, in its original form,
as proposed in [2], IGA still requires an additional parametrization of the domain’s interior,
which has been the subject of much e ort since the rst inception of the method.
To resolve this issue, the isogeometric collocation BEM was developed and exercised in
elastostatics by Simpson et al [3] to perform stress analysis directly from CAD and without
any meshing [4]. Implementation aspects of the method were provided in [5] and the method
was extended to three-dimensional stress analysis of complex structures in [6].
In this work, we advance the concept we proposed in [3] to predict the fatigue life of
engineering structures using a simple Paris law. In conventional fatigue simulations as performed
industrially [7] using the nite element based methods, the key di culty is the accurate
computation of the crack driving force, namely the stress intensity factors (SIFs). The
second di culty is that the domain mesh used for stress analysis and hence for the detection
of “sensitive” regions in the component, where initial aws are introduced, is typically
at least one order of magnitude too coarse to provide quality SIFs. The third di culty lies
in the geometrical complexity of the domain which, if the predicted fatigue life is deemed
inadequate must be redesigned. For each new design, and for each crack conguration, a new
mesh typically needs to be generated, not only to conform to the new chosen geometry, but
also to properly resolve stresses in the vicinity of the crack tip. Even when enriched nite
element methods are used, some level of remeshing is required [7].
Collocation BEM is an strong contender to attack fracture mechanics problems, because
it requires only boundary discretization, simplies the insertion of new crack segments during
growth and o ers superior accuracy for the computation of the SIFs for the same number
of degrees of freedom compared to other methods. Since BEM requires only boundary discretization,
it is also an ideal partner for IGA. We show that isogeometric dual BEM with or
without partition of unity enrichment is a robust and accurate method to deal with for fracture
simulations and that such simulations require no meshing nor remeshing in the conventional
sense.
References
[1] L. Piegl, W. Tiller, The NURBS book, Springer, 1995.
[2] T J R Hughes, J A Cottrell, and Y Bazilevs, Isogeometric analysis: CAD, nite elements,
NURBS, exact geometry and mesh renement. Comp. Meth. in App. Mech. and
Engng., Vol. 194(39-41), 4135-4195, 2005.
[3] R. N. Simpson, S. P. A. Bordas, J. Trevelyan and T. Rabczuk, A two-dimensional isogeometric
boundary element method for elastostatic analysis. Comp. Meth. in App. Mech.
and Engng., Vol. 209-212(0), 87-100, 2012. http://orbilu.uni.lu/handle/10993/13849
[4] H. Lian, R. N. Simpson and S. P. A. Bordas, Stress analysis without meshing:
Isogeometric boundary-element method. Proceedings of the Institution of Civil
Engineers: Engineering and Computational Mechanics, Vol. 166(2), 88-99, 2013.
http://orbilu.uni.lu/handle/10993/10039
[5] R. N. Simpson, S. P. A. Bordas, H. Lian and J. Travelyan, An isogeometric boundary
element method for elastostatic analysis: 2D implementation aspects. Computers &
Structures, Vol. 118, 2-12, 2013. http://orbilu.uni.lu/handle/10993/12157
[6] M. A. Scott, R. N. Simpson, J. A. Evans, S. Lipton, S. P. A. Bordas, T. J. R. Hughes and
T.W. Sederberg, Isogeometric boundary element analysis using unstructured T-splines.
Comp. Meth. in App. Mech. and Engng., Vol. 254(0), 197-221, 2013.
http://orbilu.uni.lu/handle/10993/11850
[7] S. P. A. Bordas and B. Moran, Enriched nite elements and level sets for damage tolerance
assessment of complex structures. Engineering Fracture Mechanics, Vol. 73(9), 1176-
1201, 2006. http://orbilu.uni.lu/handle/10993/14470
Other references
http://orbilu.uni.lu/handle/10993/12159
http://orbilu.uni.lu/handle/10993/14135
http://orbilu.uni.lu/handle/10993/13847
http://orbilu.uni.lu/handle/10993/12157
http://orbilu.uni.lu/handle/10993/12157
http://orbilu.uni.lu/handle/10993/11850
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