Enriched isogeometric analysis of elliptic boundary value problems in domains with cracks and/or corners

SUMMARYThe mapping method was introduced in Jeong et al. (2013) for highly accurate isogeometric analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned with constructions of novel geometrical mappings by which push‐forwards of B‐splines from the...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in engineering 2014-01, Vol.97 (3), p.149-180
Main Authors: Oh, Hae-Soo, Kim, Hyunju, Jeong, Jae Woo
Format: Article
Language:English
Subjects:
B-spline
Boundary value problems
control points
Corners
corners and cracks
Cracks
Design engineering
elasticity
enriched IGA
Enrichment
isogeometric analysis
knot vectors
Mapping
mapping technique
Mathematical analysis
Mathematical models
NURBS
partition of unity IGA
Singularities
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:SUMMARYThe mapping method was introduced in Jeong et al. (2013) for highly accurate isogeometric analysis (IGA) of elliptic boundary value problems containing singularities. The mapping method is concerned with constructions of novel geometrical mappings by which push‐forwards of B‐splines from the parameter space into the physical space generate singular functions that resemble the singularities. In other words, the pullback of the singularity into the parameter space by the novel geometrical mapping (a non‐uniform rational basis spline (NURBS) surface mapping) becomes highly smooth. One of the merits of IGA is that it uses NURBS functions employed in designs for the finite element analysis. However, push‐forwards of rational NURBS may not be able to generate singular functions. Moreover, the mapping method is effective for neither the k‐refinement nor the h‐refinement. In this paper, highly accurate stress analysis of elastic domains with cracks and ∕ or corners are achieved by enriched IGA, in which push‐forwards of NURBS via the design mapping are combined with push‐forwards of B‐splines via the novel geometrical mapping (the mapping technique). In a similar spirit of X‐FEM (or GFEM), we propose three enrichment approaches: enriched IGA for corners, enriched IGA for cracks, and partition of unity IGA for cracks. Copyright © 2013 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4580