On projection method for numerical solution of hypersingular integral equations of the first kind combined with quadrature methods

Elahi, M. R.; Mahmoudi, Yaghoub; Shamloo, Ali Salimi; Jahangirirad, Mohammad

doi:10.1088/1402-4896/acc493

Cited by 4 publications

(2 citation statements)

References 22 publications

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“…Hyper-singular integral equations (HSIEs) have found extensive application in various physics and engineering fields, notably in tackling crack-related challenges within fracture mechanics [7][8][9][10]. This method stands out due to its numerous advantages over other commonly employed crack analysis techniques.…”

Section: Introductionmentioning

confidence: 99%

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

Mohd Nordin,

Hamzah,

Khashiie

et al. 2023

Math. Model. Comput.

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In this paper, the derivation of hyper-singular integral equations (HSIEs) for thermoelectric bonded materials (TEBM) featuring a crack parallel to interface subject to in-plane shear stress τ∞xy was intensively studied. Generally, stress intensity factors (SIFs) were calculated using HSIEs with the help of modified complex stress variable function (MCSVF), and continuity conditions of the resultant electric force and displacement electric function. The unknown crack opening displacement (COD) function, electric current density, and energy flux load are mapped into the square root singularity function using the curved length coordinate method as the right-hand term. This unknown function is then used to compute the dimensionless SIFs in order to determine the stability behavior of TEBM featuring a crack parallel to interface subject to in-plane shear stress τ∞xy. Numerical results of the dimensionless SIFs at all the crack tips are presented. Our results are totally in good agreement with those of the previous works. It is observed that the dimensionless SIFs at the crack tips depend on the elastic constants ratio, the crack geometries, the electric conductivity, and the thermal expansion coefficients.

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Section: Introductionmentioning

confidence: 99%

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

Mohd Nordin,

Hamzah,

Khashiie

et al. 2023

Math. Model. Comput.

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“…), and the fourth provides a brief assessment of these and other methods, including heuristic methods (genetic algorithm, neural networks, etc.). Other methods for solving integral equations of the first kind are also being developed (see, for example [23,24]). Each method has its own characteristics.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Methods of Inverse Coefficient Problem Solution for One Inhomogeneous Body

Vatulyan,

Uglich,

Dudarev

et al. 2023

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In the present paper, the problems of longitudinal and flexural vibrations of an inhomogeneous rod are considered. The Young’s modulus and density are variable in longitudinal coordinate. Vibrations are caused by a load applied at the right end. The proposed method allows us to consider a wider class of inhomogeneity laws in comparison with other numerical solutions. Sensitivity analysis is carried out. A new inverse problem related to the simultaneous identification of the variation laws of Young’s modulus and density from amplitude–frequency data, which are measured in given frequency ranges, is considered. Its solution is based on an iterative process: at each step, a system of two Fredholm integral equations of the first kind with smooth kernels is solved numerically. The analysis of the kernels is carried out for different frequency values. To find the initial approximation, several approaches are proposed: a genetic algorithm, minimization of the residual functional on a compact set, and additional information about the values of the sought-for functions at the ends of the rod. The Tikhonov regularization and the LSQR method are proposed. Examples of reconstruction of monotonic and non-monotonic functions are presented.

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Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

Strelnikova,

Choudhary,

Degtyariov

et al. 2024

Engineering Analysis with Boundary Elements

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On projection method for numerical solution of hypersingular integral equations of the first kind combined with quadrature methods

Cited by 4 publications

References 22 publications

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

Derivation of hyper-singular integral equations for thermoelectric bonded materials featuring a crack parallel to interface

Efficient Numerical Methods of Inverse Coefficient Problem Solution for One Inhomogeneous Body

Boundary element method for hypersingular integral equations: Implementation and applications in potential theory

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