Summary
The problem of the evaluation of the stiffness matrix for finite elements enriched by discontinuous/non-linear functions is investigated. If the introduction of discontinuities inside the elements through enrichment functions is nowadays well established by local partition of unity techniques, the evaluation of the element stiffness requires splitting the element into quadrature subcells where appropriate quadrature rules apply. To overcome this problem a technique is suggested, called polynomial mapping, based on replacing the enrichment function with polynomials having the same integral of the original function. These polynomials are function of the position of the discontinuity and are defined on the entire element domain, therefore avoiding the generation of quadrature subcells. The technique is applied to discontinuities in the displacement and strain and is introduced for regularized jumps in the displacement. An integration error analysis is shown in the latter case.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Melenk J M, Babuska I (1996) Comp Meth Appl Mech Engng 39:289–314.
Belytschko T, Black T (1999) Int J Numer Meth Engng 45:601–620.
Belytschko T, Moës N, Usui S, Parimi C (2001) Int J Numer Meth Engng 50:993–1013.
Sukumar N, Chopp D L, Moës N, Belytschko T (2001) Comp Meth Appl Mech Engng 90:6183–6200.
Chessa J, Smolinski P, Belytschko T (2002) Int J Numer Meth Engng 53:1957– 1977.
Moës N, Gravouil A, Belytschko T (2002) Int J Numer Meth Engng 53:2549– 2568.
Sukumar N, Moës N, Moran B, Belytschko T (2000) Int J Numer Meth Engng 48:1549–1570.
Ventura G (2006) Int J Numer Meth Engng 66:761–795.
Patzák B, Jirásek M (2003) Engrg Fracture Mech 70:957–977.
Areias P M A, Belytschko T (2006) Int J Numer Meth Engng 66:878–910.
Stazi F, Budyn E, Chessa J, Belytschko T (2003) Comput Mech 31:38–48.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer
About this paper
Cite this paper
Ventura, G. (2007). Single Domain Quadrature Techniques for Discontinuous and Non-Linear Enrichments in Local Partion of Unity FEM. In: Combescure, A., De Borst, R., Belytschko, T. (eds) IUTAM Symposium on Discretization Methods for Evolving Discontinuities. IUTAM Bookseries, vol 5. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6530-9_20
Download citation
DOI: https://doi.org/10.1007/978-1-4020-6530-9_20
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-6529-3
Online ISBN: 978-1-4020-6530-9
eBook Packages: EngineeringEngineering (R0)