Niu, Zhongrong and Ge, Dali and Cheng, Changheng and Ye, Jianqiao and Recho, Naman (2009) *Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials.* Applied Mathematical Modelling, 33 (3). pp. 1776-1792. ISSN 0307-904X

## Abstract

According to the linear theory of elasticity, there exists a combination of different orders of stress singularity at a V-notch tip of bonded dissimilar materials. The singularity reflects a strong stress concentration near the sharp V-notches. In this paper, a new way is proposed in order to determine the orders of singularity for two-dimensional V-notch problems. Firstly, on the basis of an asymptotic stress field in terms of radial coordinates at the V-notch tip, the governing equations of the elastic theory are transformed into an eigenvalue problem of ordinary differential equations (ODEs) with respect to the circumferential coordinate 0 around the notch tip. Then the interpolating matrix method established by the first author is further developed to solve the general eigenvalue problem. Hence, the singularity orders of the V-notch problem are determined through solving the corresponding ODEs by means of the interpolating matrix method. Meanwhile, the associated eigenvectors of the displacement and stress fields near the V-notches are also obtained. These functions are essential in calculating the amplitude of the stress field described as generalized stress intensity factors of the V-notches. The present method is also available to deal with the plane V-notch problems in bonded orthotropic multi-material. Finally, numerical examples are presented to illustrate the accuracy and the effectiveness of the method.

Item Type: | Article |
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Journal or Publication Title: | Applied Mathematical Modelling |

Subjects: | T Technology > TA Engineering (General). Civil engineering (General) |

Departments: | Faculty of Science and Technology > Engineering |

ID Code: | 54224 |

Deposited By: | ep_importer_pure |

Deposited On: | 21 May 2012 09:07 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 14 Jan 2016 01:14 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/54224 |

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