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Extended isogeometric analysis for simulation of stationary and propagating cracks

Extended isogeometric analysis for simulation of stationary and propagating cracks A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B‐splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two‐dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two‐dimensional static and quasi‐static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed‐mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

Extended isogeometric analysis for simulation of stationary and propagating cracks

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References (32)

Publisher
Wiley
Copyright
Copyright © 2012 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
DOI
10.1002/nme.3277
Publisher site
See Article on Publisher Site

Abstract

A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B‐splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two‐dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two‐dimensional static and quasi‐static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed‐mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Jan 2, 2012

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