Semi-analytical approach for torsion problems of a circular bar containing multiple holes and/or cracks. (1st October 2019)

• Record Type: Journal Article
• Authors: Lee, Ying-Te; Chen, Jeng-Tzong; Kuo, Shyh-Rong
• Is Part Of: Engineering fracture mechanics. Volume 219(2019)
• Publication Date: 2019-10-01
• Subjects: Torsional rigidity -- Stress intensity factor -- Degenerate kernel -- Warping function -- Crack; Fracture mechanics -- Periodicals; Rupture, Mécanique de la -- Périodiques; Fracture mechanics; Periodicals; 620.112605
• DOI: 10.1016/j.engfracmech.2019.106547
• Languages: English
• ISSNs: 0013-7944

Abstract

Highlights: This approach does not face the calculation of the principal value. Don't separate the solved problem containing the cracks into several subdomains. Make the length of semi-major axis close to semi-minor one to simulate circular bar. Make the length of semi-minor axis close to zero to simulate line crack. Abstract: A semi-analytical approach of the null-field integral equation in conjunction containing the degenerate kernels is used to deal with the torsion problems of a circular bar with circular or elliptic holes and/or line cracks. In order to fully capture the elliptic geometry, the use of the addition theorem in terms of the elliptic coordinates plays an important role to expand the fundamental solution into the degenerate form. The boundary densities are expressed by using the eigenfunction expansion for the elliptic boundary. It is worthy of noting that the model of elliptic hole in companion with the limiting process of approaching the length of the semi-minor axis to zero is adopted to simulate the line crack. Besides, we also make the length of the semi-major axis close to the length of the semi-minor axis to approximate the circular boundary. By collocating the observation point exactly on the real boundary and matching the boundary conditions, a linear algebraic system is easily constructed to determine the unknown eigenfucntion coefficients. This approach can be seen as a semi-analytical manner since error purely attributes to the truncation of eigenfunction expansions and the convergence rate of exponential order is better than the linear order of the conventional boundary element method. Finally, several numerical examples of a circular bar with circular or elliptic holes and/or line cracks are employed to show the validity of the proposed approach. Not only the torsional rigidity but also the stress intensity factors are calculated to compare with the available results in the literature.