h Theory of shells

Elimination of a paradox in the problem of bending deflection of a round plate

The exact analytical solution is given (1982) for the problem of final displacements of a round plate [1, 2]. The solution explains a well-known paradox which was described in handbooks and assumed that the deflection of a membrane, i.e. a plate with zero beam stiffness, was less than the deflection calculated with non-zero beam stiffness taken into account. (The problem considers a round plate with its edges fixed and loaded by transversal pressure, whose magnitude makes the application of the linear theory incorrect. The latter one overestimates the deflection approximately 25 times). Later the idea of works [1, 2] was used for calculation of an electrodynamic gate [3].
  1. Zhilin P.A. Axisymmetric bending of a flexible circular plate under large displacements // Vichislitelnie metodi v mekhanike i upravlenii (Numerical methods in mechanics and control theory). Trudi LPI (Proceedings of Leningrad Polytechical Institute.) N 388. 1982. P. 97-106. (In Russian.)
  2. Zhilin P.A. Axisymmetrical bending of a circular plate under large displacements // Izvestiya AN SSSR, Mekhanika tverdogo tela (Transactions of the Academy of Sciences of the USSR, Mechanics of Solids). 1984. N 3. P. 138-144. (In Russian.)
  3. Venatovsky I.V., Zhilin P.A., Komyagin D.Yu. Inventor's certificate N 1490663 with priority from 02.11.1987. (In Russian.)