S. Omid R. Biabanaki's blog
https://imechanica.org/blog/4359
enA Problem in Nature Of XFEM Approximation
https://imechanica.org/node/6640
<div class="field field-name-taxonomy-vocabulary-6 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/76">research</a></div></div></div><div class="field field-name-taxonomy-vocabulary-8 field-type-taxonomy-term-reference field-label-hidden"><div class="field-items"><div class="field-item even"><a href="/taxonomy/term/418">xfem</a></div><div class="field-item odd"><a href="/taxonomy/term/419">gfem</a></div><div class="field-item even"><a href="/taxonomy/term/4307">approximation</a></div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>There is a basic problem in NATURE of approximation of discontinuity in element using XFEM.I tried to illustrate that below:<br />
for example, If you consider an element with strong discontinuity( like fracture or contact) which usually we use heaviside function as enrichment function. we expect two parts of element deform independently because of nature of problem.</p>
<p>In equation for approximation of this element we have two main parts. First is 'regular' or 'standard' part which uses the standard shape functions of element and Second is the enriched part.</p>
<p>In the 'regular' part we use standard shape functions which are continuous over the interface. it means because of 'regular' part in approximation, displacements of nodes which are on two different sides of enriched element are dependent, and it is a paradox the nature of problem.</p>
<p>for example if we enrich a 4-noded quadratic element using heaviside enrichment function with an interface cross the middle, by investigating the stiffness matrix (assume nodes 1 and 3 are at two different sides of interface) components (1,5),(1,6),(2,5),(2,6) are NOT zero( which is because of regural part in our approximation) which <br />
means there is an internal bonding between two parts of element in two sides of interface.
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How can we omit this internal bonding?
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</div></div></div>Sun, 16 Aug 2009 17:54:24 +0000S. Omid R. Biabanaki6640 at https://imechanica.orghttps://imechanica.org/node/6640#commentshttps://imechanica.org/crss/node/6640