Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2012-6pp.695-699

Archive of Issues

Total articles in the database: 12788
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8028
In English (Mech. Solids): 4760

<< Previous article | Volume 47, Issue 6 / 2012 | Next article >>
A.V. Saakyan, "Quadrature Formulas of Maximum Algebraic Accuracy for Cauchy Type Integrals with Complex Exponents of the Jacobi Weight Function," Mech. Solids. 47 (6), 695-699 (2012)
Year 2012 Volume 47 Number 6 Pages 695-699
DOI 10.3103/S002565441206012X
Title Quadrature Formulas of Maximum Algebraic Accuracy for Cauchy Type Integrals with Complex Exponents of the Jacobi Weight Function
Author(s) A.V. Saakyan (Institute of Mechanics, National Academy of Sciences of Republic of Armenia, Marshal Baghramian ave., 24B, Erevan, 375019 Republic of Armenia, avsah@mechins.sci.am)
Abstract The present paper presents a Gauss type quadrature formula for a Cauchy type integral whose density is the product of a Hölder function by the weight function (1−x)α(1+x)β (Reα,Reβ>−1) of orthogonal Jacobi polynomials. It is shown that at the roots of the function of the second kind corresponding to the Jacobi polynomial Pn(α,β)(x), the quadrature formula with n nodes gives the exact value of a Cauchy type integral for an arbitrary polynomial of order k≤2n. This formula was tested when solving several contact and mixed problems of the theory of elasticity.
Keywords singular integral, Jacobi polynomial, quadrature formula, theory of elasticity, crack, inclusion
References
1.  A. V. Saakyan, "Numerical Method for Solving Singular Integral Equations of the Second Kind with a Complex Coefficient," Dokl. NAN RA 97 (4), 32-36 (1997).
2.  N. Kh. Arutyunyan, "Contact Problem for a Half-Plane with Elastic Reinforcement," Prikl. Mat. Mekh. 32 (4), 632-646 (1968) [J. Appl. Math. Mech. (Engl. Transl.) 32 (4), 652-665 (1968)].
3.  H. Bateman and A. Erdélyi, Higher Transcendental Functions. Vol.  2: Bessel Functions, Functions of Parabolic Cylinder, Orthogonal Polynomials (McGraw-Hill, 1953; Nauka, Moscow, 1974).
4.  V. I. Krylov, Approximate Computations of Integrals (Nauka, Moscow, 1967) [in Russian].
5.  A. A. Korneichuk, "Quadrature Formulas for Singular Integrals," in Numerical Methods for Solving Differential and Integral Equations and Quadrature Formulas (Nauka, Moscow, 1964), pp. 64-74.
6.  A. V. Saakyan, "The Method of Discrete Singularities for Solutions of Singular Integral and Integro-Differential Equations," Proc. A. Razmadze Math. Inst., Georgia 156, 101-111 (2011).
7.  A. V. Andreev, "Direct Numerical Method for Solving Singular Integral Equations of the First Kind with Generalized Kernels," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 126-146 (2005) [Mech. Solids (Engl. Transl.) 40 (1), 104-119 (2005)].
8.  V. N. Akopyan and A. V. Saakyan, "Numerical Analysis of Mixed Problem for Compound Plane with a Thin Rigid Inclusion by the Method of Discrete Singlarities," in Problems of Optimal Control, Stability, and Strength of Mechanical Systems (Izdat. ErGU, Erevan, 1997).
9.  A. V. Saakyan and L. L. Dashtoyan, "On One Problem for Compound Plane with Crack and Inclusion with Existence of Temperature Field," in Proc. 5th Intern. Cong. on Thermal Stresses and Related Topics. Blacksburg, VA, 2003, pp. TM-4-1-1-TM-4-1-4.
10.  V. N. Akopyan and A. V. Saakyan, "On One Mixed Problem for an Elastic Wedge Weakened by a Crack," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 66-78 (1999) [Mech. Solids (Engl. Transl.)].
11.  V. N. Akopyan and A. V. Saakyan, "The Stress State of a Homogeneous Elastic Plane with a Star-Shaped Crack under Mixed Boundary Conditions on the Crack Faces," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 106-113 (1999) [Mech. Solids (Engl. Transl.)].
Received 18 July 2012
Link to Fulltext
<< Previous article | Volume 47, Issue 6 / 2012 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100