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On the development of the method of integro-differential equations in the theory of plates and shells

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References

  1. A. A. Berezovskii, “Integro-differential equations of statics of shallow shells,” Vestnik Kievsk. gos. un-ta, vol. 2, no. 1, 1958.

  2. A. A. Berezovskii, “Integro-differential equations of the theory of shallow shells,” Ukr. matem. zhurnal, vol. 12, no. 2, 1960.

  3. A. A. Berezovskii, “Nonlinear integral equations of shallow shells of revolution,” Inzhenernofizicheskii zhurnal, no. 5, 1961.

  4. A. A. Berezovskii, “On the problem of large deflections of shallow shells,” DAN URSR, no. 6, 1961.

  5. A. A. Berezovskii, “Nonlinear integral equations of the theory of shallow thin shells,” Theory of Plates and Shells. Proceedings of the Second All-Union Conference (L'vov, 1961) [in Russian], AN UkrSSR, Kiev, 1962.

    Google Scholar 

  6. A. A. Berezovskii, “Nonlinear integral and integro-differential equations of shallow shells and their applications,” Theory of Shells and Plates. Proceedings of the Fourth All-Union Conference on the Theory of Shells and Plates (Erevan, 1962) [in Russian], Izd-vo AN ArmSSR, 1964.

  7. A. A. Berezovskii and V. S. Dovgopol, “The approximate solution of the integral equations of a shallow spherical shell,” Scientific Year-Book of Kiev State University [in Russian], 1957.

  8. A. A. Berezovskii and A. F. Shestopal, “Integro-differential equations of local stability of shallow shells,” Ukr. matem. zhurnal, vol. 11, no. 4, 1959.

  9. N. A. Birger, Certain Mathematical Methods of Solving Engineering Problems [in Russian] Oborongiz, Moscow, 1956.

    Google Scholar 

  10. N. A. Birger, Circular Plates and Shells of Revolution [in Russian], Oborongiz, Moscow, 1961.

    Google Scholar 

  11. D. V. Vainberg, V. O. Zaruts'kii, and B. Z. Itenberg, “The stress state of cylindrical shells reinforced by ribs,” Prikladnaya mekhanika, vol. 6, no. 4, 1960.

  12. D. V. Vainberg and O. L. Sinyavskii, “Use of the method of potentials in analyzing deformations of a cylindrical shell,” DAN URSR, no. 7, 1960.

  13. D. V. Vainberg and A. L. Sinyavskii, Calculation of Shells [in Russian], Gosstroiizdat UkrSSR, Kiev, 1961.

    Google Scholar 

  14. S. P. Gavelya and A. M. Kuzemko, “On elastic equilibrium of a rigidly clamped shallow shell of constant curvature and arbitrary outline,” Proceedings of the Conference on Theory of Plates and Shells (1960) [in Russian], Kazan, 1961.

  15. G. A. Izdebskaya and N. A. Kil'chevskii, “On the effectiveness of finite difference methods of solving problems of plate and shell kinetics, and methods worked out for use on integro-differential equations,” Prikladnaya mekhanika, vol. 10, no. 1, 1964.

  16. G. A. Izdebskaya and N. A. Kil'chevskii, “On the analogy between the collocation method and the optimal choice of the collocation points for intergro-differential equations of equilibrium of the theory of plates”, DAN URSR, no. 4, 1964.

  17. G. E. Kazantseva, On Vibrations of Thin Circular Plates [in Russian], Candidate's dissertation, Kiev Polytechnic Institute, 1956.

  18. G. E. Kazantseva, “On vibrations of circular plates of variable thickness”, Prikladnaya mekhanika, vol. 4, no. 2, 1958.

  19. G. E. Kazantseva, “Forced vibrations of a circular plate with a hole”, Izv. Kievsk. politekhn. in-ta, vol. 31, 1961.

  20. N. A. Kil'chevskii, “Certain methods of integrating equations of equilibrium of elastic shells”, Prikl. matem. i mekh., vol. 4, no. 2, 1940.

  21. N. A. Kil'chevskii, “The basic equations of the theory of shells and certain methods of their integration,” Zb. prats In-tu matematiki AN URSR, no. 6, 1940.

  22. N. A. Kil'chevskii, “An approximate method of determining displacements in cylindrical shells”, Zb. prats In-tu matematiki AN URSR, no. 8, 1946.

  23. N. A. Kil'chevskii, “Investigation of certain problems of the theory of elasticity”, Izv. Kievsk. Politekhn. in-ta, vol. 15, 1955.

  24. N. A. Kil'chevskii, “The theorem of reciprocity of work and the construction of the tensor of Green in the theory of small elastic-plastic deformations”, Prikl. matem. i mekh., vol. 21, no. 5, 1957.

  25. N. A. Kil'chevskii, “The integro-differential and integral equations of equilibrium of thin elastic shells”, Prikl. matem. i mekh., vol. 23, no. 1, 1959.

  26. N. A. Kil'chevskii, “The functional equations of equilibrium of thin elastic shells”, Izv. Kievsk. politekhn. in-ta, vol. 31, 1961.

  27. N. A. Kil'chevskii, Fundamentals of Analytical Mechanics of Shells [in Russian], AN UkrSSR, Kiev, 1963.

    Google Scholar 

  28. N. A. Kil'chevskii, “The theorem of reciprocity of work in the nonlinear theory of elasticity”, DAN URSR, no. 10, 1963.

  29. N. A. Kil'chevskii, “Integro-differential and integral equations of statics and dynamics of thin elastic shells”, Theory of Shells and Plates. Proceedings of the Fourth All-Union Conference on Theory of Shells and Plates (Erevan, 1962) [in Russian], AN ArmSSR, 1964.

  30. N. A. Kil'chevskii, G. O. Kil'chinskaya, and N. I. Remizova, “Analytical theory of shells”, Prikladnaya mekhanika, vol. 9, no. 1, 1963.

  31. N. A. Kil'chevskii and A. Kh. Konstantinov, “Forced vibrations of a thick conic panel in a nonclassical formulation”, DAN AN URSR, no. 2, 1964.

  32. N. A. Kil'chevskii, A. Kh. Konstantinov, and N. I. Remizova, “Solution of dynamic boundary value problems of the theory of shells, arising from the integro-differential equations of motion, Proceedings of the Second All-Union Conference on Theoretical and Applied Mechanics [in Russian], Nauka, Moscow, 1966.

    Google Scholar 

  33. N. A. Kil'chevskii and N. I. Remizova, “Integro-differential equations of equilibrium of shells with focussing kernels”, Theory of Shells and Plates. Proceedings of the Fourth All-Union Conference on Theory of Shells and Plates (Erevan, 1962) [in Russian], AN ArmSSR, 1964.

  34. N. A. Kil'chevskii and G. I. Tkachuk, “On certain properties of integral equations set up on the basis of the theorem of reciprocity of work”, Prikladnaya mekhanika, vol. 5, no. 2, 1956.

  35. V. G. Klyuchnikova, “Theoretical and experimental investigation of flexural vibrations of thick plates in a nonclassical formulation”, Prikladnaya mekhanika [Soviet Applied Mechanics], vol. 2, no. 9, 1966.

  36. V. G. Klyuchnikova, “A correction of the approximate solution of the problem concerned with natural vibrations of a plate in a nonclassical formulation”, Prikladnaya mekhanika [Soviet Applied Mechanics], vol. 2, no. 12, 1966.

  37. A. Kh. Konstantinov, “An approximate construction of the tensor of Green for a thick conic panel”, Prikladnaya mekhanika, vol. 1, no. 9, 1965.

  38. A. A. Nazarov and A. A. Berezovskii, “Integro-differential equations of statics of shallow shells”, Scientific Year-Book of Kiev State University [in Russian], 1957.

  39. A. A. Nazarov and A. F. Shestopal, “The stability of a shallow shell of double curvature with a given rectangular plan view”, Scientific Year-Book of Kiev State University [in Ukrainian], 1957.

  40. E. I. Obolashvili, “On a boundary value problem of the momentless theory of an ellipsoidal shell”, Soobshch. AN GruzSSR, vol. 22, no. 4, 1959.

  41. L. G. Odnoral, “Free vibrations of plates of nonlinearly elastic material”, Prikladnaya mekhanika [Soviet Applied Mechanics], vol. 2, no. 5, 1966.

  42. L. G. Odnoral, “Determination of displacements in nonlinearly elastic plates and shells”, DAN URSR, no. 8, 1966.

  43. N. I. Remizova, “Determination of elastic displacements in cylindrical shells by the method of integral equations”, DAN URSR, no. 3, 1958.

  44. N. I. Remizova, “Calculation of cylindrical shells for strength by the method of integral equations”, Prikladnaya mekhanika, vol. 4, no. 3, 1958.

  45. N. I. Remizova, Integral Equations of Equilibrium of Thin Elastic Cylindrical Shells [in Russian], Candidate's dissertation, Kiev Polytechnic Institute, 1958.

  46. N. I. Remizova, “Integral equations of equilibrium of thin elastic shells”, Prikl. matem. i mekh., vol. 23, no. 3, 1959.

  47. N. I. Remizova, “Use of integral equations in solving certain problems of the theory of cylindrical shells”, Proceedings of the Conference on Theory of Plates and Shells (1960) [in Russian], Kazan, 1961.

  48. N. I. Remizova, “On the development of the method of integral equations for cylindrical shells”, Izv. Kievsk. politekh. in-ta, vol. 21, 1961.

  49. N. I. Remizova, “On the development of integral equations for the solution of boundary value problems of the theory of shells”, Theory of Plates and Shells. Proceedings of the Second All-Union Confence (L'vov, 1961) [in Russian], AN UkrSSR, Kiev, 1962.

    Google Scholar 

  50. G. I. Tkachuk, “Integro-differential equations of equilibrium of thin elastic shells”, Izv. Kievsk. politekhn. in-ta, vol. 31, 1961.

  51. G. I. Tkachuk, “Integro-differential equations of the problem of equilibrium of shells of revolution of variable thickness”, Prikladnaya mekhanika, vol. 7, no. 3, 1961.

  52. G. I. Tkachuk, “Integro-differential equations of the theory of thin elastic shells of revolution”, Proceedings of the Conference on Theory of Plates and Shells (1960) [in Russian], Kazan, 1961.

  53. E. Trefftz, Mathematical Theory of Elasticity [Russian translation], OTNI Moscow-Leningrad, 1934.

  54. B. N. Fradlin and S. M. Shakhnovskii, “On functional equations of equilibrium of shallow shells”, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, no. 1, 1959.

  55. B. N. Fradlin and S. M. Shaknovskii, “On setting up integro-differential equations of equilibrium of shallow shells”, DAN URSR, no. 4, 1959.

  56. B. N. Fradlin and S. M. Shakhnovskii, “On determining the tensor of Green for the problem of equilibrium of a shallow shell”, Izv. AN SSSR, OTN, Mekhanika i mashinostroenie, no. 6, 1959.

  57. B. N. Fradlin and S. M. Shakhnovskii, “On calculating a shallow shell of double curvature, rectangular in plan view, in the cases of rigid and pinjointed support along its outline”, Izv. vuzov, Stroitel'stvo i arkhitektura, no. 9, 1959.

  58. B. N. Fradlin and S. M. Shakhnovskii, “On calculating a shallow shell that is rectangular in plan view”, DAN URSR, no. 11, 1959.

  59. B. N. Fradlin and S. M. Shakhnovskii, “On setting up the function of Green for the problem of equilibrium of a shallow shell”, Notes on Proceedings of the First All-Union Conference on Mechanics [in Russian], 1960.

  60. B. N. Fradlin and S. M. Shakhnovskii, “Determination of the displacements of a shallow shell subjected to arbitrary loading”, Prikladnaya mekhanika, vol. 6, no. 4, 1960.

  61. B. N. Dradlin and S. M. Shakhnovskii, “Construction of the tensor of Green for the problem of equilibrium of a shallow shell of double curvature”, DAN SSSR, vol. 131, no. 6, 1960.

  62. B. N. Fradlin and S. M. Shakhnovskii, “On vibrations of a shallow shell”, Izv. vuzov, Stroitel'stvo i arkhitektura, no. 1, 1961.

  63. B. N. Fradlin and S. M. Shakhnovskii, “Integral equations of equilibrium of shallow shells, rectangular in plan view”, Izv. Kievsk. Politekhn. in-ta, vol. 31, 1961.

  64. B. N. Fradlin and S. M. Shakhnovskii, “Determination of the tensor of Green for a shallow shell on an elastic foundation”, DAN URSR, no. 1, 1962.

  65. B. N. Fradlin and S. M. Shakhnovskii, “On the equilibrium of a shallow shell”, Prikladnaya mekhanika, vol. 1, no. 5, 1965.

  66. V. N. Shaishmelashvili, “On certain methods of calculating shallow shells”, Trudy In-ta stroitel'nogo dela, AN GruzSSR, vol. 5, 1955.

  67. N. A. Kiltschewskii, “Integro-differential-und Integralgleichungen für das Gleichgewicht dünner elastischer Schalen”, ZAMM, vol. 40, no. 4, 1960.

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  1. Kiev Polytechnic Institute, Kiev, USSR

    B. N. Fradlin & F. A. Tsykunov

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Prikladnaya Mekhanika, Vol. 3, No. 12, pp. 10–15, 1967

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Fradlin, B.N., Tsykunov, F.A. On the development of the method of integro-differential equations in the theory of plates and shells. Soviet Applied Mechanics 3, 8–12 (1967). https://doi.org/10.1007/BF00886224

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