Mathematical simulation of singularities for isoparametric elements of arbitrary orders

✍ Scribed by Adnan H. Nayfeh; Elsayed Abdel-Ati M. Nassar

• Publisher: John Wiley and Sons
• Year: 1981
• Tongue: English
• Weight: 259 KB
• Volume: 17
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620170312

✦ Synopsis

Abstract

For the general quadrilateral isoparametric elements with 4(n−1) nodes (i.e. n nodes along each side), it is shown that the inverse square root singularity of the strain field at the crack tip can be obtained by a general but simple rule. This amounts to collapsing the quadrilateral elements into triangular elements around the crack tip and placing the (n−2) mid‐side nodes at locations γ^2^/(n−1)^2^ (γ=1,2,…, n−2) times the length of side emanating from the crack tip. These locations are measured from the crack tip. The known results for n = 3 and n = 4 are thus obtained as special cases.