• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• Journal of the Korean Mathmatical Society
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• v.4 no.1
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• pp.1-4
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• 1967

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.279-296
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• 2008

This paper presents an exact integration for the hypersingular boundary integral equation of two-dimensional elastostatics. The boundary is discretized by straight segments and the physical variables are approximated by discontinuous quadratic elements. The integral for the hypersingular boundary integral equation analysis is given in a closed form. It is proven that using the exact integration for discontinuous boundary element, the singular integral in the Cauchy Principal Value and the hypersingular integral in the Hadamard Finite Part can be obtained straightforward without special treatment. Two numerical examples are implemented to verify the correctness of the derived exact integration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.8
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• pp.2524-2539
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• 1996

A design process and an axisymmetric boundary integral equation method for precise structural analysis of the aircraft gas turbine rotor disk were developed. This axisymmetric boundary integral equation method for stress and steady-state thermal analysis was improved in solution accuracy by appling an implicit technique for Cauchy principal value evaluation, a subelement technique for weak singular integral evaluation and a double exponentical integral technoque for internal point solution near boundary surfaces. Stresses, temperatures, low cycle fatigue lifes and critical speeds for the turbine rotor disk of the thrust 1421 N class turbojet engine were analysed in a pratical calculation model problem.