Higher order tip enrichment of eXtended Finite Element Method in thermoelasticity |
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Authors: | Arash Zamani Robert Gracie M Reza Eslami |
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Affiliation: | (1) Division of Civil Engineering, School of Engineering, Cardiff University, Cardiff, CF24 0YF, UK |
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Abstract: | An eXtended Finite Element Method (XFEM) is presented that can accurately predict the stress intensity factors (SIFs) for
thermoelastic cracks. The method uses higher order terms of the thermoelastic asymptotic crack tip fields to enrich the approximation
space of the temperature and displacement fields in the vicinity of crack tips—away from the crack tip the step function is
used. It is shown that improved accuracy is obtained by using the higher order crack tip enrichments and that the benefit
of including such terms is greater for thermoelastic problems than for either purely elastic or steady state heat transfer
problems. The computation of SIFs directly from the XFEM degrees of freedom and using the interaction integral is studied.
Directly computed SIFs are shown to be significantly less accurate than those computed using the interaction integral. Furthermore,
the numerical examples suggest that the directly computed SIFs do not converge to the exact SIFs values, but converge roughly to values near the exact result. Numerical simulations of straight
cracks show that with the higher order enrichment scheme, the energy norm converges monotonically with increasing number of
asymptotic enrichment terms and with decreasing element size. For curved crack there is no further increase in accuracy when
more than four asymptotic enrichment terms are used and the numerical simulations indicate that the SIFs obtained directly
from the XFEM degrees of freedom are inaccurate, while those obtained using the interaction integral remain accurate for small
integration domains. It is recommended in general that at least four higher order terms of the asymptotic solution be used
to enrich the temperature and displacement fields near the crack tips and that the J- or interaction integral should always be used to compute the SIFs. |
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