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Original Articles

Weakly singular, singular and hypersingular integrals in 3‐D elasticity and fracture mechanics

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Pages 763-775 | Received 20 Apr 1999, Accepted 20 Aug 1999, Published online: 03 Mar 2011

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Mingxu Yi & Jun Huang. (2015) CAS wavelet method for solving the fractional integro-differential equation with a weakly singular kernel. International Journal of Computer Mathematics 92:8, pages 1715-1728.
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Weishan Zheng & Yanping Chen. (2022) Numerical approach for weakly singular equation with nonlinear delay. Bulletin of the Malaysian Mathematical Sciences Society 45:6, pages 2821-2842.
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Hong Du, Zhong Chen & Tiejun Yang. (2020) A stable least residue method in reproducing kernel space for solving a nonlinear fractional integro-differential equation with a weakly singular kernel. Applied Numerical Mathematics 157, pages 210-222.
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Elham Keshavarz & Yadollah Ordokhani. (2019) A fast numerical algorithm based on the Taylor wavelets for solving the fractional integro‐differential equations with weakly singular kernels. Mathematical Methods in the Applied Sciences 42:13, pages 4427-4443.
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Jafar Biazar & Khadijeh Sadri. (2019) Solution of weakly singular fractional integro-differential equations by using a new operational approach. Journal of Computational and Applied Mathematics 352, pages 453-477.
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Somayeh NEMATİ. (2018) An Efficient Operational Matrix Method for Solving a Class of Two-Dimensional Singular Volterra Integral Equations. Journal of Mathematical Sciences and Modelling 1:3, pages 192-201.
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Zhong Chen, Longbin Wu & Yingzhen Lin. (2018) Exact solution of a class of fractional integro‐differential equations with the weakly singular kernel based on a new fractional reproducing kernel space. Mathematical Methods in the Applied Sciences 41:10, pages 3841-3855.
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S. Nemati & P.M. Lima. (2018) Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions. Applied Mathematics and Computation 327, pages 79-92.
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P. Mokhtary. (2017) Numerical analysis of an operational Jacobi Tau method for fractional weakly singular integro-differential equations. Applied Numerical Mathematics 121, pages 52-67.
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S. Nemati, S. Sedaghat & I. Mohammadi. (2016) A fast numerical algorithm based on the second kind Chebyshev polynomials for fractional integro-differential equations with weakly singular kernels. Journal of Computational and Applied Mathematics 308, pages 231-242.
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P. K. Sahu & S. Saha Ray. (2016) Sinc-Galerkin Technique for the Numerical Solution of Fractional Volterra–Fredholm Integro-Differential Equations with Weakly Singular Kernels. International Journal of Nonlinear Sciences and Numerical Simulation 17:6, pages 315-323.
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Yanxin Wang & Li Zhu. (2016) SCW method for solving the fractional integro-differential equations with a weakly singular kernel. Applied Mathematics and Computation 275, pages 72-80.
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V. V. Zozulya. (2015) Regularization of divergent integrals: A comparison of the classical and generalized-functions approaches. Advances in Computational Mathematics 41:4, pages 727-780.
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V. V. Zozulya. (2013) RETRACTED ARTICLE: Regularization of Divergent Integrals: An Approach Using Generalized Functions. Advances in Computational Mathematics 41:4, pages 953-953.
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Chaolang Hu, Xiaoming He & Tao Lü. (2015) Euler-Maclaurin expansions and approximations of hypersingular integrals. Discrete and Continuous Dynamical Systems - Series B 20:5, pages 1355-1375.
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V.V. Zozulya. (2014) An Approach Based on Generalized Functions to Regularize Divergent Integrals. Engineering Analysis with Boundary Elements 40, pages 162-180.
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Zhong Chen & Xue Cheng. (2014) An efficient algorithm for solving Fredholm integro-differential equations with weakly singular kernels. Journal of Computational and Applied Mathematics 257, pages 57-64.
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V. V. Zozulya. (2011) Divergent Integrals in Elastostatics: General Considerations. ISRN Applied Mathematics 2011, pages 1-25.
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V.V. Zozulya. (2010) Regularization of hypersingular integrals in 3-D fracture mechanics: Triangular BE, and piecewise-constant and piecewise-linear approximations. Engineering Analysis with Boundary Elements 34:2, pages 105-113.
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Oleksandr V. Menshykov & Igor A. Guz. (2008) Elastodynamic Problem for Two Penny-Shaped Cracks: The Effect of Cracks’ Closure. International Journal of Fracture 153:1, pages 69-76.
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O. V. Menshykov & I. A. Guz. (2007) Effect of contact interaction of the crack faces for a crack under harmonic loading. International Applied Mechanics 43:7, pages 809-815.
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V. V. Zozulya. (2007) Contact problem for a plane crack under a normally incident antiplane shear wave. International Applied Mechanics 43:5, pages 586-590.
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Oleksandr Menshykov & I.A. Guz. (2006) Effect of Contact Interaction on the Stress Intensity Factors for a Crack under Harmonic Loading. Applied Mechanics and Materials 5-6, pages 173-180.
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Oleksandr Menshykov & Igor Guz. (2006) Contact Interaction of Crack Faces under Oblique Incidence of a Harmonic Wave. International Journal of Fracture 139:1, pages 145-152.
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A.N. Guz, O.V. Menshykov & V.V. Zozulya. (2003) Surface contact of elliptical crack under normally incident tension–compression wave. Theoretical and Applied Fracture Mechanics 40:3, pages 285-291.
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A. N. Guz & V. V. Zozulya. (2001) Fracture Dynamics with Allowance for Crack Edge Contact Interaction. International Journal of Nonlinear Sciences and Numerical Simulation 2:3.
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V.V. Zozulya & P.I. Gonzalez-Chi. (2000) Dynamic fracture mechanics with contact interaction at the crack edges. Engineering Analysis with Boundary Elements 24:9, pages 643-659.
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