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New superelements for singular derivative problems of arbitrary order
Author(s) -
Nurse A. D.
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010110)50:1<135::aid-nme25>3.0.co;2-7
Subject(s) - offset (computer science) , singular solution , mathematics , point (geometry) , singular point of a curve , range (aeronautics) , joint (building) , computer science , mathematical analysis , geometry , structural engineering , engineering , programming language , aerospace engineering
The paper describes a new method for development of singular elements through optimal positioning of offset mid‐side nodes using adjacent six‐ and eight‐noded isoparametric elements. By joining the two elements to form a superelement, an attempt to rectify a known problem with existing approaches proves successful. Calculations are made to optimize the mid‐side node positions and the relative size of the two elements for a wide range of singular orders. By way of example, the approach is applied to two different forms of singular stress field in a bimaterial joint in a three‐point‐bend test. Numerical solutions for the singular fields existing at both ends of the material interface compare favourably with those obtained with the more usual refined mesh approach. Copyright © 2001 John Wiley & Sons, Ltd.