Geodesic
Numerical implementation of method of subsequent perturbation of~parameters for computation of~stress-strain state of a shell rigidly fixed on the boundaries
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 74-79.

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The Karman model for a shell rectangular in the plan with rigid fixation of the boundaries is considered. An orthonormalized system of basis functions satisfying the boundary conditions of the problem is obtained. Linearization of the problem is given and the solution is obtained by the method of subsequent perturbation of parameters due to Vladlen V. Petrov. The solutions including supporting intermediate results for the shell made of rolled duralumin are discussed. 
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L. V. Bessonov. Numerical implementation of method of subsequent perturbation of~parameters for computation of~stress-strain state of a shell rigidly fixed on the boundaries. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 1, pp. 74-79. http://geodesic.mathdoc.fr/item/ISU_2015_15_1_a10/

[1] Petrov V. V., Method of successive loadings in nonlinear theory of plates and shells, Saratov Univ. Press, Saratov, 1975, 118 pp. (in Russian)

[2] Kuznecov V. V., Petrov V. V., “Using the method of perturbed region of integration in the solution of nonlinear boundary value problems of the theory of flexible plates and shells”, Izvestiia Akademii Nauk SSSR. Mekhanika tverdogo tela, 1985, no. 2, 176–178 (in Russian)

[3] Petrov V. V., Ovchinnikov I. G., Inozemcev V. K., The deformation of the structural elements of nonlinear runmodule heterogeneous material, Saratov Univ. Press, Saratov, 1988, 160 pp.

[4] Shabanov L. E., Issues of numerical implementation of the method consistent perturbation parameters when calculating shell designs, Dr. phys. and math. sci. diss., Saratov, 2005 (in Russian)

[5] Kuznecov V. N., The method of successive perturbations of the parameters in the application to the calculation of dynamic stability of thin-walled shell structures, Dr. techn. sci. diss., Saratov, 2000 (in Russian)

[6] Bessonov L. V., “Numerical realization of algorithm of spectral criterion of local buckling of shell structures”, Interuniversity collection of scientific papers, Research in algebra, number theory, functional analysis and related issues, 7, Saratov Univ Press, Saratov, 2012, 3–9

[7] Pisarenko G. S., Jakovlev A. P., Matveev V. V., The reference resistance of materials, Naukova dumka, Kiev, 1988, 734 pp.