• Vadim A. Krysko
  • Jan AwrejcewiczEmail author
  • Maxim V. Zhigalov
  • Valeriy F. Kirichenko
  • Anton V. Krysko
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 42)


The achievements of today’s material culture are obviously quantified by the results of scientific investigation in the fields of mathematical modeling of numerous evolutionary changes and in particular in the design of inhomogeneous mechanical structures.


  1. 1.
    Vorovich, I. I. (1999). Nonlinear theory of shallow shells. New York: Springer.zbMATHGoogle Scholar
  2. 2.
    Vekua, I. N. (1982). Some general methods of constructing various variants of the shell theory. Moscow: Nauka (in Russian).Google Scholar
  3. 3.
    Ciarlet, P. G., & Rabier, P. (1980). Les Equations de von Kármán. Berlin: Springer.zbMATHGoogle Scholar
  4. 4.
    Berdichevsky, V. L. (2009). Variational principles of continuum mechanics. Berlin: Springer.zbMATHGoogle Scholar
  5. 5.
    Grigolyuk, E. I., & Kogan, F. A. (1972). State-of-the art of the theory of multilayer shells. International Journal of Applied Mechanics, 8(6), 583–595.Google Scholar
  6. 6.
    Piskunov, V. G., Verijenko, V. E., & Prysyazhnyuk, V. K. (1987). Calculation of inhomogeneous shallow shells and plates by the finite element method. Kiev: Vyscha Shkola (in Russian).Google Scholar
  7. 7.
    Ambartsumayan, S. A. (1970). Theory of anisotropic plates. strength, stability, and vibrations. Stamford: Technomic Publication.Google Scholar
  8. 8.
    Ambartsumyan, S. A. (1974). General theory of anisotropic shells. Moscow: Nauka (in Russian).Google Scholar
  9. 9.
    Andreev, A. N., & Nemirovsky, Y. V. (1977). The theory of elastic laminated anisotropic shells. Mechanics of Solids, 5, 87–96.Google Scholar
  10. 10.
    Gribanov, V. F., Krokhin, I. A., Panichkin, N. G., Sannikov, M. V., & Fomichev, Yu. I. (1990). Strength, stability and oscillations of thermal stress shell structures. Moscow: Mashinostroenie (in Russian).Google Scholar
  11. 11.
    Grigolyuk, E. I., & Kulikov, G. M. (1988). Multilayer reinforced shells: calculation of pneumatic tyres. Moscow: Mashinostroenie (in Russian).Google Scholar
  12. 12.
    Grigolyuk, E. I., & Chulkov, P. P. (1973). Stability and vibration of three-layer shells. Moscow: Mashinostroyeniye.Google Scholar
  13. 13.
    Khoma, I. Y. (1987). Generalized theory of anisotropic shells. Kiev: Naukova Dumka (in Russian).Google Scholar
  14. 14.
    Paimushin, V. N. (1987). Generalized Reissner variational principle in nonlinear mechanics of three-dimensional composite solids, with applications to the theory of multilayer shells. Mechanics of Solids, 2, 171–180 (in Russian).Google Scholar
  15. 15.
    Pikul, V. V. (2009). Mechanics of shells. Vladivostok: Dal’nauka (in Russian).Google Scholar
  16. 16.
    Rasskazov, A. O., Sokolov, I. I., & Shul’ga, N. A. (1986). Theory and calculation of layered orthotropic plates and shells. Kiev: Vishcha Shkola (in Russian).Google Scholar
  17. 17.
    Gawinecki, J. (1981). On the first boundary initial value problem for thermal stresses equation of generalized thermomechanics. Bulletin of Polish Academy of Sciences, 29(7–8), 405–411.MathSciNetzbMATHGoogle Scholar
  18. 18.
    Gawinecki, J. A. (1983). Existence uniqueness and regularity of the first boundary - initial value problem for thermal stress equation of classical and generalized the thermomechanics. Journal of Technical Physics, 34(4), 467–479.MathSciNetzbMATHGoogle Scholar
  19. 19.
    Kowalski, T., & Piskarek, A. (1975). Existenz der Losung einer Anfangsrandwertaufgabe in der linearen Termoelastizitatstheorie. ZAMM, 9, 337–351.Google Scholar
  20. 20.
    Kupradze, V. D., & Burchuladze, T. V. (1969). Boundary value problems of thermoelasticity. Differential Equations, 5(1), 3–43.MathSciNetGoogle Scholar
  21. 21.
    Ladyzhenskaya, O. A. (1969). The mathematical theory of viscous incompressible flow. New York: Gordon and Breach.zbMATHGoogle Scholar
  22. 22.
    Ladyzhenskaya, O. A. (1973). The boundary value problems of mathematical physics. Berlin: Springer.Google Scholar
  23. 23.
    Lions, J.-L. (1969). Some problems of solving non-linear boundary value problems. Paris: Dunod-Gauthier-Villars.Google Scholar
  24. 24.
    Mikhaylovskaya, I. B., & Novik, O. B. (1980). The Cauchy problem in the class of growing functions for nonhyperbolic system of evolutionary equations which are not parabolic. Sib. Mat. Well, 21(4), 228–229 (in Russian).Google Scholar
  25. 25.
    Nowacki, W. (1975). Dynamic problems of thermoelasticity. Berlin: Springer.zbMATHGoogle Scholar
  26. 26.
    Temam, E. (1995). Navier–Stokes equations and nonlinear functional analysis. CMBS-NSF, regional conference series in applied mathematics. Paris, France.Google Scholar
  27. 27.
    Wilke, V. G. (1979). On the existence and uniqueness of solutions of some classes of dynamic problems of the nonlinear theory of elasticity. Journal of Applied Mathematics and Mechanics, 43(1), 124–132.MathSciNetGoogle Scholar
  28. 28.
    Morozov, N. F. (1967). Nonlinear vibrations of thin plates taking into account the inertia of rotation. Lectures of Academy of Sciences of USSR, 176(3), 522–525 (in Russian).Google Scholar
  29. 29.
    Morozov, N. F. (1978). Selected two-dimensional problems of theory of elasticity. Leningrad: LGU (in Russian).Google Scholar
  30. 30.
    Karchevskii, M. M. (1995). On the solvability of geometrically nonlinear problems of the theory of thin shells. News of Universities. Mathematics, 6(397), 30–36 (in Russian).Google Scholar
  31. 31.
    Timergaliev, S. N. (1996). Proof of solvability of a boundary problem of nonlinear theory of shallow shells. News of Universities. Mathematics, 9(412), 60–70 (in Russian).Google Scholar
  32. 32.
    Sedenko, V. I. (1991). Uniqueness of a generalized solution of the initial-boundary value problem of nonlinear theory of oscillations of shallow shells. Proceedings Academy of Sciences of USSR, 316(6), 1319–1322 (in Russian).Google Scholar
  33. 33.
    Sedenko, V. I. (1993). Classical solvability of initial-boundary value problems of the nonlinear theory of oscillations of shallow shells. Proceedings Academy of Sciences of USSR, 331(3), 283–285.Google Scholar
  34. 34.
    Sedenko, V. I. (1995). The existence in whole by time solutions of classical initial-boundary value problem for the equations of Marghera–Vlasov nonlinear theory of oscillations of shallow shells. Proceedings Academy of Sciences of USSR, 340(6), 745–747.MathSciNetGoogle Scholar
  35. 35.
    Vorovich, I. I. (1957). On some direct methods in the non-linear theory of vibrations of curved shells. Izv. Akad. Nauk SSSR. Ser. Mat., 21, 747–784 (in Russian).Google Scholar
  36. 36.
    Vorovich, I. I., & Morozov, N. F. (1998). On the correctness of the problem of static nonlinear theory of elastic shallow shells. Applied Mathematics and Mechanics, 68(4), 678–682 (in Russian).Google Scholar
  37. 37.
    Lebedev, L. P., Vorovich, I. I., & Cloud, M. J. (2013). Functional analysis in mechanics. New York: Springer.Google Scholar
  38. 38.
    Panteleyev, A. D., & Medvedev, N. G. (1982). On the solvability of linear boundary value problems of the theory of sandwich shells. Mathematical Modeling of Estacionary Processes, 46–51 (in Russian).Google Scholar
  39. 39.
    Grigolyuk, E. I. Vlasov, V. F., & Jurkiewicz, A. A. (1989). Solvability of boundary value problems of the equilibrium state of three-layered shells with a rigid filler that transmits transverse shear. Dokl. Acad. of Sciences of the USSR, 305(4), 817–821 (in Russian).Google Scholar
  40. 40.
    Bert, C. W. (1971). Nonlinear vibration of an arbitrarily laminated anisotropic rectangular plates. In Proc. 3-rd Can. Congr. Appl. Mech (pp. 307–308). Calgary.Google Scholar
  41. 41.
    Bennett, J. A. (1971). Nonlinear vibration of simply supported angle ply laminated plates. AJAA Journal, 9(10), 1997–2003.zbMATHGoogle Scholar
  42. 42.
    Bennett, J. A. (1972). Some approximations in the nonlinear vibrations of unsymmetrically laminated plates. AJAA Journal, 10(9), 1145–1146.Google Scholar
  43. 43.
    Bert, C. W. (1973). Nonlinear vibration of a rectangular plate arbitrarily laminated of anisotropic material. Journal of Applied Mechanics, E40(2), 452–458.Google Scholar
  44. 44.
    Hu, H., & Fu, Y.-M. (2003). Nonlinear dynamic reactions of viscoelastic orthotropic symmetric layered plates. Journal of Hunan University, 30(5), 79–83.Google Scholar
  45. 45.
    Pillai, S. R. R., & Nageswara, R. B. (1993). Reinvestigation of non-linear vibrations of simply supported rectangular cross-ply plates. Journal of Sound and Vibration, 160(1), 1–6.zbMATHGoogle Scholar
  46. 46.
    Sarma, V. S., Venkateshwar, R. A., Pillai, S. R. R., & Nageswara, R. B. (1992). Large amplitude vibrations of laminated hybrid composite plates. Journal of Sound and Vibration, 159(3), 540–545.Google Scholar
  47. 47.
    Shih, Y. S., & Blotter, P. T. (1993). Non-linear vibration analysis of arbitrarily laminated thin rectangular plates on elastic foundations. Journal of Sound and Vibration, 167(3), 433–459.zbMATHGoogle Scholar
  48. 48.
    Sircar, R. (1974). Vibration of rectilinear plates on elastic foundation at large amplitude. Bulletin of Polish Academy of Sciences, 22(4), 293–299.zbMATHGoogle Scholar
  49. 49.
    Yoshiki, O., Yoshihiro, N., & Manabu, S. (1993). Nonlinear vibration of laminated FRP plates. Hokkaido Institute of Technology, 21, 39–46.Google Scholar
  50. 50.
    Wu, C. I., & Vinson, J. P. (1971). Nonlinear oscillations of laminated specially orthotropic plates with clamped and simply supported edges. Journal of the Acoustical Society of America, 49(5), 1561–1567.zbMATHGoogle Scholar
  51. 51.
    Wu, C. I., & Vinson, J. P. (1969). On the nonlinear oscillations of plates composed of composite materials. Journal of Composite Materials, 3, 548–561.Google Scholar
  52. 52.
    Laura, P. A., & Maurizi, M. J. (1972). Comments on Nonlinear oscillations of laminated specially orthotropic plates with clamped and simply supported edges by C. Wu and J. R. Vinson. Journal of the Acoustical Society of America, 52(3), 1053–1059.Google Scholar
  53. 53.
    Bhimaraddi, A. (1992). Nonlinear dynamics of in-plane loaded imperfect rectangular plates. Journal of Applied Mechanics, 59(4), 893–901.zbMATHGoogle Scholar
  54. 54.
    Bhimaraddi, A. (1993). Large amplitude vibrations of imperfect antisymmetric angle-ply laminated plates. Journal of Sound and Vibration, 162(3), 457–470.zbMATHGoogle Scholar
  55. 55.
    Fu, Y., & Chen, W. (1995). Large amplitude vibration of anti-symmetrically laminated imperfect cylindrical thick shell. Journal of Hunan University, 22(1), 120–128.zbMATHGoogle Scholar
  56. 56.
    Janevski, G. (2005). Two-frequency nonlinear vibrations of antisymmetric laminated angle-ply plate. Facta Univ. Ser. Mech. Autom. Contr. And Rob. Univ. Nis., 4(17), 345–358 (in Russian).Google Scholar
  57. 57.
    Kurpa, L. V., & Timchenko, G. N. (2007). Investigation into nonlinear vibrations of composite plates using the R-function theory. Strength of Materials, 39, 529–538.Google Scholar
  58. 58.
    Singha, M. K., & Rupesh, D. (2007). Nonlinear vibration of symmetrically laminated composite skew plates by finite element method. International Journal of Non-Linear Mechanics, 42(9), 1144–1152.zbMATHGoogle Scholar
  59. 59.
    Xia, Z. Q., & Lukasiewicz, S. (1994). Non-linear free, damped vibrations of sandwich plates. Journal of Sound and Vibration, 175(2), 210–232.zbMATHGoogle Scholar
  60. 60.
    Huang, Z., & Zhu, J. -F. (1998). The forced vibration analysis of symmetrically laminated composite rectangular plates with in-plane shear nonlinearites. In Proceedings of 3rd International Conference on Nonlinear Mechanics, Shanghai, 17–20 August 1998 (pp. 243–247).Google Scholar
  61. 61.
    Tenneti, R., & Chandrashekhara, K. (1994). Large amplitude flexural vibration of laminated plates using a higher order shear deformation theory. Journal of Sound and Vibration, 176(2), 279–285.zbMATHGoogle Scholar
  62. 62.
    Singh, G., Rao, G. V., & Iyengar, N. G. R. (1995). Finite element analysis of the nonlinear vibrations of moderately thick unsymmetrically laminated composite plates. Journal of Sound and Vibration, 181(2), 315–329.zbMATHGoogle Scholar
  63. 63.
    Yamada, G., Kobayashi, Y., & Abe, A. (1996). Multimode response of rectangular laminated plates. Transactions of the Japan Society of Mechanical Engineers C, 62(600), 2976–2982.Google Scholar
  64. 64.
    Shi, Y., Lee, R. Y. Y., & Mei, C. (1997). Finite element method for nonlinear free vibrations of composite plates. AIAA Journal, 35(1), 159–166.zbMATHGoogle Scholar
  65. 65.
    Maruszewski, B., & Rymarz, C. (1997). Coupled fields modelling of materials for modern technologies. Theoretical Mechanics and Applied, 35(4), 901–914.Google Scholar
  66. 66.
    Bakulin, V. N., Obraztsov, I. F., & Potopachin, V. A. (1998). Dynamic problems of the nonlinear theory of multilayered shells. Action of intensive thermal-force loads and concentrated energy fluxes. Moscow: Nauka (in Russian).Google Scholar
  67. 67.
    Duhamel, J. M. C. (1937). Second Memoire Sur Les Phenomens Thermomecanique. J. L’Ecole Polytechn., 15(25), 1–57.Google Scholar
  68. 68.
    Carslaw, H. S., & Jaeger, J. C. (1959). Conduction of heat in solids. Oxford: Oxford Science Publications.zbMATHGoogle Scholar
  69. 69.
    Lykov, A. V. (1967). Theory of thermal conductivity. Moscow: Higher School (in Russian).Google Scholar
  70. 70.
    Kutateladze, S. S. (1963). Fundamentals of heat transfer theory. New York: Academic Press.zbMATHGoogle Scholar
  71. 71.
    Kozdoba, L. A. (1975). Methods for solving nonlinear heat condition problems. Moscow: Nauka (in Russian).Google Scholar
  72. 72.
    Muskhelishvili, N. I. (1977). Some basic problems of the mathematical theory of elasticity. Berlin: Springer.Google Scholar
  73. 73.
    Kovalenko, A. D. (1970). Fundamentals of thermoelasticity. Kiev: Naukova Dumka (in Russian).Google Scholar
  74. 74.
    Nowacki, W. (1970). Theory of micropolar elasticity. New York: Springer.zbMATHGoogle Scholar
  75. 75.
    Ilyushin, A. A. (1978). Continuum mechanics. Moscow: Moscow University Press (in Russian).Google Scholar
  76. 76.
    Prigogine, I. (1978). Time, structure, and fluctuations. Science, 201(4358), 777–785.Google Scholar
  77. 77.
    Gyarmati, I. (1970). Non-equilibrium thermodynamics. Field theory and variational principles. Berlin: Springer.Google Scholar
  78. 78.
    Sedov, L. I. (1971). A course in continuum mechanics. Wolters-Noordhoff Publishing.Google Scholar
  79. 79.
    Lomakin, V. A. (1976). The elasticity theory of inhomogeneous solid. Moscow: The Moscow University (in Russian).Google Scholar
  80. 80.
    Danilovskaya, V. I. (1950). Thermal stresses in elastic half-space resulting from a sudden heating of its surface. Applied Mathematics and Mechanics, 14(3), 316–318 (in Russian).Google Scholar
  81. 81.
    Tanigawa, Y. (1995). Some basic thermoelastic problems for nonhomogeneous materials. Applied Mechanical Review, 48, 287–300.Google Scholar
  82. 82.
    Biot, M. A. (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27, 240–253.MathSciNetzbMATHGoogle Scholar
  83. 83.
    Podstrigatch, Y. S., Lomakin, V. A., & Kolyano, Yu. M. (1984). Thermoelasticity of bodies of heterogeneous structure. Moscow: Nauka (in Russian).Google Scholar
  84. 84.
    Kozlov, V. I. (1972). Thermoelastic vibrations of rectangular plates. Applied Mechanics, 8(4), 445–448 (in Russian).Google Scholar
  85. 85.
    Day, W. A. (1981). Cesaro means and recurrence in dynamic thermoelasticity. Mathematics, 28(2), 211–230.MathSciNetzbMATHGoogle Scholar
  86. 86.
    Day, W. A. (1981). On the status of the uncoupled approximation within quasistatic thermoelasticity. Mathematics, 28(2), 286–294.MathSciNetzbMATHGoogle Scholar
  87. 87.
    Rogacheva, N. N. (1980). Free thermoelastic shells. Applied Mathematics and Mechanics, 44(3), 516–522.MathSciNetzbMATHGoogle Scholar
  88. 88.
    Kupradze, V. D., Hegel, T. G., Basheleishvili, M. O., & Burchuladze, T. V. (1976). Three dimensional problems of mathematical theory of elasticity and thermoelasticity. Moscow: Nauka (in Russian).Google Scholar
  89. 89.
    Smirnov, M. N., Mikhaylovskaya, I. B., & Novik, O. B. (1977). On the mathematical description of wave phenomena in a dissipative media. University News: Geology and Intelligence, 8, 128–133.Google Scholar
  90. 90.
    Dafermos, C. M., & Hsiao, L. (1982). Global smooth thermomechanical processes in one-dinesional nonlinear thermoviskoelectricity. Nonlinear Analysis: Theory of Mathematics and Applied, 5, 435–454.zbMATHGoogle Scholar
  91. 91.
    Dafermos, C. M. (1982). Solvable “in general” smooth solutions of the initial-boundary value problem for one-dimensional nonlinear equations of thermoviscoplastic. SIAM Journal of Mathematical Analysis, 13(3), 397–408.zbMATHGoogle Scholar
  92. 92.
    Lord, H., & Shulman, Y. (1967). A generalized dynamical theory of thermoelasticity. Journal of the Mechanics and Physics of Solids, 15(5), 299–309.zbMATHGoogle Scholar
  93. 93.
    Dhaliwal, R., & Sherief, H. (1980). Generalized thermoelasticity for anisotropic media. Quarterly Applied Mathematics, 38, 1–8.MathSciNetzbMATHGoogle Scholar
  94. 94.
    Green, A. E., & Lindsay, K. A. (1972). Thermoelasticity. Journal of Elasticity, 2, 1–7.zbMATHGoogle Scholar
  95. 95.
    Suhubi, E. S. (1964). Longitudinal vibrations of a circular cylinder coupled with a thermal field. Journal of the Mechanics and Physics of Solids, 12(2), 69–75.MathSciNetzbMATHGoogle Scholar
  96. 96.
    Green, A. E., & Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31, 189–208.MathSciNetzbMATHGoogle Scholar
  97. 97.
    Straughan, B. (2011). Heat waves. Berlin: Springer.zbMATHGoogle Scholar
  98. 98.
    Chadrasekariah, D. S. (1986). Thermoelasticity with second sound: A review. Applied Mechanics Review, 39, 355–376.Google Scholar
  99. 99.
    Tzou, D. Y. (1995). A unified field approach for heat conduction from macro-to microscales. Journal of Heat Transfer-T ASME, 117, 8–16.Google Scholar
  100. 100.
    Hetnarski, R. B., & Ignaczak, J. (1999). Generalized thermoelasticity. Journal of Thermal Stresses, 22, 451–476.MathSciNetzbMATHGoogle Scholar
  101. 101.
    Hetnarski, R. B., & Ignaczak, J. (1996). Soliton-like waves in a low temperature nonlinear thermoelastic solid. International Journal of Engeenerig Sciences, 33, 1767–1787.MathSciNetzbMATHGoogle Scholar
  102. 102.
    Hetnarski, R. B., & Ignaczak, J. (2000). Nonclassical dynamical thermoelasticity. International Journal of Solids and Structures, 37, 215–224.MathSciNetzbMATHGoogle Scholar
  103. 103.
    Kobzar, V. N., & Fil’shtinskii, L. A. (2008). The plane dynamic problem of coupled thermoelasticity. Journal of Applied Mathematics and Mechanics, 72(5), 611–618.Google Scholar
  104. 104.
    Bagri, A., & Eslami, M. R. (2008). Generalized coupled thermoelasticity of functionaly graded annular disk considering the Lord-Shulman theory. Journal of Composite Structures, 83, 168–179.Google Scholar
  105. 105.
    Yang, Y. C., & Chu, S. S. (2001). Transient coupled thermoelastic analysis of an annular fin. Journal of International Communications in Heat Mass Transfer, 28, 1103–1114.Google Scholar
  106. 106.
    Bahtui, A., & Eslami, M. R. (2007). Coupled thermoelasticity of functionally graded cylindrical shells. Mechanical Research and Communications, 34, 1–18.zbMATHGoogle Scholar
  107. 107.
    Hosseini-Tehrani, P., & Eslami, M. R. (2000). BEM analysis of thermal and mechanical shock in a two-dimensional finite domain considering coupled thermoelasticity. Engeeniering Analysis with Boundary Elements, 24, 249–257.zbMATHGoogle Scholar
  108. 108.
    Aubin, J.-P. (1972). Approximation of elliptic boundary-value problems. New York: Wiley-Interscience.zbMATHGoogle Scholar
  109. 109.
    Lions, J. L., & Magenes, E. (1961). Problemi ai limiti non omogenei, III. Annali Scuola Norm. Sup. Pisa, 15, 41–103.MathSciNetzbMATHGoogle Scholar
  110. 110.
    Fichera, G. (1974). Existence theorems of elasticity theory. Moscow: World Press (in Russian).Google Scholar
  111. 111.
    Searle, F. (1992). The mathematical theory of elasticity. Moscow: Mir (in Russian).Google Scholar
  112. 112.
    Haug, E. J., Choi, K. K., & Komkov, V. (1986). Design sensitivity analysis of structural systems. New York: Academic Press.zbMATHGoogle Scholar
  113. 113.
    Gallagher, R. H. (1975). Finite element analysis: Fundamentals. London: Prentice-Hall.Google Scholar
  114. 114.
    Amiro, I. Ya., & Zarutskiy, V. A. (1980). Methods for calculating shells. Theory of ribbed shells (Vol. 2). Kiev: Naukova Dumka (in Russian).Google Scholar
  115. 115.
    Bolotin, V. V., & Novichkov, Yu. N. (1980). Mechanics of multilayer structures. Moscow: Mashinostroenie (in Russian).Google Scholar
  116. 116.
    Kolpakov, A. G. (1995). Asymptotic of the problem of thermoelasticity of beams. Applied Mechanics and Technical Physics, 36(5), 135–143.MathSciNetzbMATHGoogle Scholar
  117. 117.
    Grigorenko, Ya. M., & Vasilenko, A. T. (1998). About some of the approaches to the solution of problems of statics of shells of structures. International Journal of Applied Mechanics, 34(10), 42–49.Google Scholar
  118. 118.
    Aldoshina, I. A., & Nazarov, S. A. (1998). Asymptotically exact conditions of the fillet at the junction of plates with very different characteristics. Journal of Applied Mathematics and Mechanics, 62(2), 272–282 (in Russian).Google Scholar
  119. 119.
    Evensen, D. A. (1974). Nonlinear vibrations of circular cylindrical shells. In Y. C. Fung & E. E. Sechler (Eds.), Thin walled structures: Theory, experiment and design (pp. 133–155). Englewood Cliffs: Prentice-Hall.Google Scholar
  120. 120.
    Sathyamorthy, M., & Pandalai, K. A. (1972). Large amplitude vibrations of certain deformable bodies. Part I: disc, membranes and rings. Journal of the Aeronautical Society of India, 24, 409–414.Google Scholar
  121. 121.
    Sathyamorthy, M., & Pandalai, K. A. (1973). Large amplitude vibrations of certain deformable bodies. Part II: plates and shells. Journal of the Aeronautical Society of India, 25, 1–10.Google Scholar
  122. 122.
    Leissa, W. (1993). Vibration of shells. Acoustical Society of America, 26, 385–400.Google Scholar
  123. 123.
    Amabili, M., Pellicano, F., & Paidoussis, M. P. (1998). Nonlinear vibrations of simply supported circular cylindrical shells, coupled to quiescent fluid. Journal of Fluids and Structures, 12, 883–918.Google Scholar
  124. 124.
    Marguerre, K. (1939). Theorie der Gekrummten Platte Grosser Formanderung. New York: Willey.zbMATHGoogle Scholar
  125. 125.
    Kármán, T. L., & Tsien, H. S. (1941). The buckling of thin cylindrical shells under axial compression. Journal of the Aeronautical Sciences, 8(8), 303–312.MathSciNetzbMATHGoogle Scholar
  126. 126.
    Godoy, L. A., & Batista-Abreu, J. C. (2012). Buckling of fixed-roof aboveground oil storage tanks under heat induced by an external fire. Thin-Walled Structures, 52, 90–101.Google Scholar
  127. 127.
    Godoy, L. A. (2016). Buckling of vertical oil storage steel tanks: Review of static buckling studies. Thin-Walled Structures, 103, 1–21.Google Scholar
  128. 128.
    Naj, R., Sabzikar-Boroujerdy, M., & Eslami, M. R. (2008). Thermal and mechanical instability of functionally graded truncated conical shells. Thin-Walled Structures, 46(1), 65–78.Google Scholar
  129. 129.
    Li, G. Q., Han, J., & Lou, G. B. (2016). Predicting intumescent coating protected steel temperature in fire using constant thermal conductivity. Thin-Walled Structures, 98, 177–184.Google Scholar
  130. 130.
    Yang, G. T., & Bradford, M. A. (2016). Thermal-induced buckling and postbuckling analysis of continuous railway tracks. International Journal of Solids and Structures, 97–98, 637–649.Google Scholar
  131. 131.
    Zeng, J. (1998). Nonlinear oscillations and chaos in a railway vehicle system. Chinese Journal of Mechanical Engineering, 11, 231–238.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vadim A. Krysko
    • 1
  • Jan Awrejcewicz
    • 2
    Email author
  • Maxim V. Zhigalov
    • 1
  • Valeriy F. Kirichenko
    • 1
  • Anton V. Krysko
    • 3
  1. 1.Department of Mathematics and ModelingSaratov State Technical UniversitySaratovRussia
  2. 2.Department of Automation, Biomechanics and MechatronicsLodz University of TechnologyLodzPoland
  3. 3.Department of Applied Mathematics and Systems AnalysisSaratov State Technical UniversitySaratovRussia

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