BEM analysis for curved cracks. (1st June 2021)

• Record Type: Journal Article
• Authors: Wen, P.H.; Tang, Y.D.; Sladek, J.; Sladek, V.
• Is Part Of: Engineering analysis with boundary elements. Volume 127(2021)
• Page Start: 91
• Page End: 101
• Publication Date: 2021-06-01
• Subjects: Direct/indirect boundary element methods -- Fracture mechanics -- Boundary integral equation -- Displacement discontinuity method -- Reissner's plate theory -- Stress intensity factors; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.03.014
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The boundary integral equations (BIE) and displacement discontinuity methods (DDM) are formulated for solution of smooth curved crack problems within 2D elasticity and Reissner's plate bending theory. The equivalence between the direct boundary element method and the indirect boundary element method is shown here. The Chebyshev polynomials of the second kind are employed to solve the integral equations numerically. This enables determination of the stress intensity factors at the crack tips directly5 by the coefficients of Chebyshev polynomials. In the DDM, the coefficients of stress influence for the constant displacement discontinuity element are derived in closed form for the Reissner's plate bending problem. The degree of convergence of BIE is demonstrated with increasing numbers of the collocation points. Comparison is made with the analytical solutions from the stress intensity factor handbook for an embedded circular crack in a flat plate under tensile force. High accuracy of the presented numerical solutions makes possible to use them as benchmarks to evaluate the degree of accuracy for any numerical algorithms.