Solving the stability problem for a thin shell under impulsive loading
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 5-11
Voir la notice du chapitre de livre provenant de la source Math-Net.Ru
The stability problem for a thin shell under an axial impulsive load is considered. A new approach to building a mathematical model is presented, based on the Ostrogradskii–Hamilton principle of stationary action. It is shown that the problem reduces to a system of nonlinear differential equations that can be solved numerically and by using an approximate calculation algorithm developed by the authors. A formula that determines the dependence between the load intensity and the problem's initial conditions is derived. In the above formulation, the stability problem for a circular cylindrical shell is solved. To determine the critical value of the load impulse, the Lyapunov theory of dynamic stability is used.
Keywords:
shell, stability, impulse.
@article{UZKU_2014_156_1_a0,
author = {L. U. Bakhtieva and F. Kh. Tazyukov},
title = {Solving the stability problem for a~thin shell under impulsive loading},
journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
pages = {5--11},
publisher = {mathdoc},
volume = {156},
number = {1},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a0/}
}
TY - JOUR AU - L. U. Bakhtieva AU - F. Kh. Tazyukov TI - Solving the stability problem for a thin shell under impulsive loading JO - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki PY - 2014 SP - 5 EP - 11 VL - 156 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a0/ LA - ru ID - UZKU_2014_156_1_a0 ER -
%0 Journal Article %A L. U. Bakhtieva %A F. Kh. Tazyukov %T Solving the stability problem for a thin shell under impulsive loading %J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki %D 2014 %P 5-11 %V 156 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a0/ %G ru %F UZKU_2014_156_1_a0
L. U. Bakhtieva; F. Kh. Tazyukov. Solving the stability problem for a thin shell under impulsive loading. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 1, pp. 5-11. http://geodesic.mathdoc.fr/item/UZKU_2014_156_1_a0/