A review of some integral equations for solving the Saint-Venant torsion problem
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OpenAlex topics: Electromagnetic Scattering and Analysis · Electromagnetic Simulation and Numerical Methods · Experimental and Theoretical Physics Studies
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References (47)
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1. Aleksidze, M. A., On Approximate Solutions of a Certain Mixed Boundary Value Problem in the Theory of Harmonic Functions,Differential Equations 2 (1966) 515?518. (Differentsial'nye Uravneniya 2 (1966) 988?994).
2. Bhargava, R. D. and Saxena, R. S., Integral Equation Method of solving Two-dimensional Laplace Equation-I,Indian Jour. Pure Appl. Math. 1 (1970) 552?564.
3. Bhargava, R. D. and Saxena, R. S., Integral Equation Method of solving Two-dimensional Laplace Equation-II,Indian Journ. Pure Appl. Math. 2 (1971) 246?256.
4. Christiansen, S., On Kupradze's Functional Equations for Plane Harmonic Problem, pp. 205?243 in: R. P. Gilbert and R. Weinacht (eds.),Function Theoretic Methods in Differential Equations, Research Notes in Mathematics, No. 8, Pitman Publishing, London, September 1976.
5. Christiansen, S., Integral Equations without a Unique Solution can be made Useful for Solving some Plane Harmonic Problems,Jour. Inst. Math. Appl. 16 (1975) 143?159.10.1093/imamat/16.2.143 ↗
6. Christiansen, S., In preparation 1977.10.1016/0014-5793(77)80942-3 ↗
7. Courant, R. and Hilbert, D.,Methods of Mathematical Physics, Vol. II (Partial Differential Equations, R. Courant), Interscience Publishers, New York, 1962.
8. Filonenko-Borodich, M.,Theory of Elasticity, Dover Publications, New York, 1965.
9. Harrington, R. F., Pontoppidan, K., Abrahamsen, P., and Albertsen, N. C., Computation of Laplacian Potentials by an Equivalent-Source Method,Proc. Instn. Elect. Engrs. 116 (1969) 1715?1720.10.1049/piee.1969.0311 ↗
10. Hayes, J. and Kellner, R., The Eigenvalue Problem for A Pair of Coupled Integral Equations Arising in the Numerical Solution of Laplace's Equation,SIAM Jour. Appl. Math. 22 (1972) 503?513.10.1137/0122044 ↗
11. Hille, E.,Analytic Function Theory, Vol. II, Ginn and Company, Boston, 1962.
12. Hönl, H., Maue, A. W., and Westpfahl, K., Theorie der Beugung, pp. 218?573 in: S. Flügge (ed.),Handbuch der Physik, Band XXV/1, Kristalloptik, Beugung, Springer-Verlag, Berlin, 1961.
13. Hsiao, G. and MacCamy, R. C., Solution of Boundary Value Problems by Integral Equations of the First Kind,SIAM Review 15 (1973) 687?705.10.1137/1015093 ↗
14. Jaswon, M. A. and Ponter, A. R., An integral equation solution of the torsion problem,Proc. Roy. Soc. London, Ser, A 273 (1963) 237?246.10.1098/rspa.1963.0085 ↗
15. Kandler, P., Numerische Behandlung des SAINT-VENANTschen Torsionsproblems bei beliebigen Querschnittsbereichen mit Hilfe von Integralgleichungen,Monatsber. Deutschen Akad. Wiss. Berlin 9 (1967) 637?649.
16. Kanwal, R. P.,Linear Integral Equations, Theory and Technique, Academic Press, New York, 1971.
17. Kermanidis, Th., Ein Beitrag zur Torsion prismatischer Stäbe,Zeit. Angew. Math. Mech. 54 (1974) T87-T88.10.1002/zamm.19740541235 ↗
18. Kermanidis, Th., Kupradze's functional equation for the torsion problem of prismatic bars-Part 1, Computer methods in applied mechanics and engineering 7 (1976a) 39?46.10.1016/0045-7825(76)90004-9 ↗
19. Kermanidis, Th., Kupradze's functional equation for the torsion problem of prismatic bars-Part 2, Computer methods in applied mechanics and engineering 7 (1976b) 249?259.10.1016/0045-7825(76)90016-5 ↗
20. Kupradze, V. D.,Dynamical Problems in Elasticity (in Progress in Solid Mechanics, III; eds. J. N. Sneddon and R. Hill), North-Holland, Amsterdam, 1963.
21. Kupradze, V. D.,Potential Methods in the Theory of Elasticity, Israel Program for Scientific Translations, Jerusalem, 1965. (Metody potentsiala v teorii uprugosti, Gosudarstvennoe Izdatel'stvo Fiziko-Matematicheskoi Literatury, Moskva 1963).
22. Kupradze, V. D., On the approximate solution of problems in mathematical physics,Russian Math. Surveys 22, 2 (1967) 58?108. (Uspehi Mat. Nauk 22, 2 (1967) 59?107).10.1070/RM1967v022n02ABEH001210 ↗
23. Kupradze, V. D., Über numerische Verfahren der Potential- und der Elastizitätstheorie,Zeit. Angew. Math. Mech. 49 (1969) 1?9.10.1002/zamm.19690490102 ↗
24. Kupradze, V. D. and Aleksidze, M. A., The Method of Functional Equations for the Approximate Solution of Certain Boundary Value Problems,U.S.S.R. Computational Math. and Math. Physics 4, 4 (1964) 82?126. (Z. Vy?isl. Mat. i Mat. Fiz. 4 (1964) 683?715).10.1016/0041-5553(64)90006-0 ↗
25. Kupradze, V. D., Gegelia, T. G., Baselejsvili, M. O., and Burculadze, T. V.,Trechmernye Zadaci Matematiceskoj Teorii Uprugosti, Izdatel'stvo Tbilisskogo Universiteta, Tbilisi, 1968.
26. Lawrentjew, M. A. and Schabat, B. W.,Methoden der komplexen Funktionen-theorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1967.
27. Lo, C. C. and Niedenfuhr, F. W., Singular Integral Equation Solution for Torsion, Proc. Amer. Soc. Civil Eng.,Jour. Engng. Mech. Div. 96 EM 4 (1970) 535?542.10.1061/JMCEA3.0001265 ↗
28. Maue, A.-W., Zur Formulierung eines allgemeinen Beugungsproblems durch eine Integralgleichung,Zeit. Physik 126 (1949) 601?618.10.1007/BF01328780 ↗
29. Mendelson, A., Boundary-integral methods in elasticity and plasticity, NASA TN D-7418 (1973), 37 pp.
30. Mikhlin, S. G.,Integral Equations and their applications, 2nd rev. ed., Pergamon Press, Oxford, 1964.
31. Muschelischwili, N. I.,Singuläre Integralgleichungen, Akademie-Verlag, Berlin, 1965.
32. Muskhelishvili, N. I.,Some Basic Problems of the Mathematical Theory of Elasticity, 2nd English ed., P. Noordhoff, Groningen, 1963.
33. Osgood, W. F.,Lehrbuch der Funktionentheorie, erster Bd., zweite Aufl., B. G. Teubner, Leipzig, 1912.
34. Polozhiy, G. N.,Equations of Mathematical Physics, Hayden Book Company, New York, 1967.
35. Pólya, G. and Szegö, G. Über den transfiniten Durchmesser (Kapazitätskonstante) von ebenen und räumlichen Punktmengen,Jour. Reine Angew. Math. 165 (1931) 4?49.
36. Pólya, G. and Szegö, G.,Isoperimetric Inequalities in Mathematical Physics, Princeton University Press, Princeton, 1951.10.1515/9781400882663 ↗
37. Ponter, A. R. S., On plastic torsion,International Journal of Mechanical Sciences 8 (1966a) 227?235.10.1016/0020-7403(66)90038-5 ↗
38. Ponter, A. R. S., An Integral Equation Solution of the Inhomogeneous Torsion Problem.SIAM Jour. Appl. Math. 14 (1966b) 819?830.10.1137/0114069 ↗
39. Rieder, G., Iterationsverfahren und Operatorgleichungen in der Elastizitätstheorie,Abh. Braunschweig. Wiss. Gesellsch. 14, zweiter Halbband (1962) 109?343.
40. Rieder, G., Eine Variante zur Integralgleichung von Windisch für das Torsionsproblem,Zeit. Angew. Math. Mech. 49 (1969) 351?358.10.1002/zamm.19690490605 ↗
41. Rizzo, F. J., An integral equation approach to boundary value problems of classical elastostatics,Quart. Appl. Math., 25 (1967) 83?95.10.1090/qam/99907 ↗
42. Sokolnikoff, I. S.,Mathematical Theory of Elasticity, 2nd ed., McGraw-Hill, New York, 1956.
43. Timoshenko, S. and Goodier, J. N.,Theory of Elasticity, 2nd ed., McGraw-Hill, New York, 1951.
44. Vekua, I. N.,New Methods for Solving Elliptic Equations, North-Holland, Amsterdam, 1967.
45. Windisch, E., Eine neue allgemeine Methode zur Lösung des Torsions problems,Wiss. Zeit. Techn. Univ. Dresden 15 (1966) 685?688.
46. Windisch, E., Eine numerische Methode zur Lösung des Torsionsproblems, I,Acta Mechanica 4 (1967) 191?199.10.1007/BF01263430 ↗
47. Windisch, E., Eine numerische Methode zur Lösung des Torsionsproblems, II,Acta Mechanica 10 (1970) 181?191.10.1007/BF01175879 ↗