Abstract
This study is dedicated to modeling cracks in plane problems by applying the recent technique analysis-suitable T-splines in the extended isogeometric analysis. A new local refinement algorithm is integrated for increasing the solution accuracy and reducing the excessive propagation of control points. However the singular fields near a crack tip are reproduced by the crack tip enrichment functions, and the Heaviside function is used to represent crack discontinuity. The results accuracy is tested by evaluation the mixed mode stress intensity factors which are computed by means of the interaction integral approach (M -integral). The obtained results are compared with the analytical methods.DOI: http://dx.doi.org/10.5755/j01.mech.23.1.13475
Highlights
The brutal fracture problem has a great importance in some industrial fields, such as in aeronautics, aerospace and nuclear
Several researches in various fields have been investigated by this method, including: structural dynamics [7], composite materials [8], fluid– structure interaction [9], electromagnetic problems [10], contact problems [11], turbulent flow [12], aero-dynamics [13] and thermomechanical problems [14]
There are many computer aided design (CAD) basis functions can be used in isogeometric analysis, the most widely used of them are Non Uniform Rational B-splines (NURBS) due to their properties like continuity, smoothness, variation diminishing, convex hull and possibility of using Knot insertion and degree elevation refinements
Summary
The brutal fracture problem has a great importance in some industrial fields, such as in aeronautics, aerospace and nuclear. In fracture mechanics problems, Benson et al [15] and De Luycker et al [16] have proposed extended isogeometric analysis (XIGA) for modelling cracks In this method the general principle of the XFEM is used into IGA by including the asymptotic and signed distance enrichment functions. There are many CAD basis functions can be used in isogeometric analysis, the most widely used of them are Non Uniform Rational B-splines (NURBS) due to their properties like continuity, smoothness, variation diminishing, convex hull and possibility of using Knot insertion and degree elevation refinements They have the ability to describe exactly all conic sections but they are not well for all complex geometries, even for multiple patches NURBS generate a complicated mesh of control points and this leads to produce superfluous control points. The asymptotic functions are used to model the crack tip, and the M-integral is used to evaluate the stress intensity factors
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