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Evaluation of the stress singularities of plane V-notches in bonded dissimilar materials

Research output: Contribution to journalJournal article

Published

  • Zhongrong Niu
  • Dali Ge
  • Changheng Cheng
  • Jianqiao Ye
  • Naman Recho
Journal publication date03/2009
JournalApplied Mathematical Modelling
Journal number3
Volume33
Number of pages17
Pages1776-1792
Original languageEnglish

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.