Geodesic
A~finite-variation method in the nonlinear shell mechanics
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 3, pp. 329-340

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A numerical algorithm is proposed for calculating the coefficients of the first and second order variations of the strain energy of a nonlinear finite element model of a shell, which are necessary to determine the equilibrium states of a shell and investigate their stability. Several numerical schemes based on various finite difference approximations are considered. For these schemes, the accuracy, convergence, and computation time are studied using popular geometrically-nonlinear problems of elastic plates and shells. 
@article{SJVM_2008_11_3_a6,
     author = {V. V. Kuznetsov and S. V. Levyakov},
     title = {A~finite-variation method in the nonlinear shell mechanics},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {329--340},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2008_11_3_a6/}
}
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V. V. Kuznetsov; S. V. Levyakov. A~finite-variation method in the nonlinear shell mechanics. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 11 (2008) no. 3, pp. 329-340. http://geodesic.mathdoc.fr/item/SJVM_2008_11_3_a6/