The general nonlinear theory of thermoelastic shells

The general nonlinear theory of thermoelastic shells is created (1975 - 1984). The way of its construction fundamentally differs from all known versions of shell theories and can be easily extended to any shell-like constructions and other objects of continuum mechanics. Its key feature is that it allows studying shell-like objects of a complex internal structure, i.e. when traditional methods of construction of the theory of shells are not applicable [1 - 13]. For shells of constant thickness, made of isotropic material, the new method gives results that are in accordance with those of the classical methods and perfectly coincide with the results of three-dimensional elasticity theory for the case of any external forces, including point loads.
  1. Zhilin P.A. Two-dimensional continuum. Mathematical theory and physical interpretations // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1972. N 6. P. 207-208. (In Russian.)
  2. Modern handling of the theory of shells // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1974. N 4. (In Russian.)
  3. Zhilin P.A. Mechanics of Deformable Surfaces. The Danish Center for Appl. Math and Mech. Report N 89. 1975. P. 1-29.
  4. Zhilin P.A. Mechanics of Deformable Cosserat Surfaces and Shell Theory. The Danish Center for Appl. Math and Mech. Annual report, 1975.
  5. Zhilin P.A. Mechanics of deformable enriched surfaces // Transactions of the 9th Soviet conference on the theory of shells and plates. Leningrad, “Sudostroenie”. 1975. P. 48-54. (In Russian.)
  6. Zhilin P.A. Mechanics of Deformable Directed Surfaces. Int. J. Solids Structures. 1976. Vol. 12. P. 635-648.
  7. Zhilin P.A. General theory of constitutive equations in the linear theory of elastic shells // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1978. N 3. P. 190. (In Russian.)
  8. Zhilin P.A. A new method for the construction of theory of thin elastic shells // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1978. N. 3. (In Russian.)
  9. Zhilin P.A. Direct construction of the theory of shells basing on physical principles // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1980. N 3. P. 179. (In Russian.)
  10. Zhilin P.A. Basic equations of non-classical theory of shells // Dinamika i prochnost mashin (Dynamics and strength of machines.) Trudi LPI (Proceedings of Leningrad Polytechical Institute.) N 386. 1982. P. 29-46. (In Russian.)
  11. Altenbach H., Zhilin P.A. Eine nichtlineare Theorie duner Dreischichtschalen und ihre An-wendung aufdie Stabilitatsuntersuchung eines dreischictigen Streifens // Technische Mechanic. 1982. Bd. 3. Helt 2. S. 23-30.
  12. Altenbach H., Zhilin P.A. General theory of elastic simple shells // Advances in mechanics --- Warszawa, Polska. 1988. N 4. P. 107-148. (In Russian).
  13. Zhilin P.A. Applied mechanics. Foundations of shells theory. Tutorial book. St. Petersburg State Polytechnical University. 2006. 167 p. (In Russian.)