Niu, Z., Ge, D., Cheng, C. et al. (2 more authors) (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 h 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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Keywords: | Stress singularity orders, Ordinary differential equations (ODEs), The interpolating matrix method, V-notch, Bonded dissimilar materials, Orthotropic material |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Civil Engineering (Leeds) |
Depositing User: | Ms Caroline Wilson |
Date Deposited: | 18 Nov 2008 09:27 |
Last Modified: | 24 Oct 2016 16:06 |
Published Version: | http://dx.doi.org/10.1016/j.apm.2008.03.007 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.apm.2008.03.007 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:4916 |