Niu, Z., Ge, D., Cheng, C., Ye, J. and Recho, N. (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
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.
|Keywords:||Stress singularity orders, Ordinary differential equations (ODEs), The interpolating matrix method, V-notch, Bonded dissimilar materials, Orthotropic material|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Civil Engineering (Leeds)|
|Depositing User:||Ms Caroline Wilson|
|Date Deposited:||18 Nov 2008 09:27|
|Last Modified:||17 Sep 2016 12:50|