Geodesic
Mathematical models and algorithms for studying the strength and stability of shell structures
Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 53-65

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We describe several mathematical models of deformation of supported shell structures including those that take into account various properties of the material. We consider linear-elastic and physically nonlinear problems and also creep problems for structures of orthotropic and isotropic materials. All models are based on the functional of the total potential energy of the deformation of the shell. The geometric nonlinearity and transverse shifts are accounted for. Ribs are introduced as discretely as by the structural anisotropy method. We demonstrate three different algorithms for the study of the strength and stability of the shells under consideration each of which is most effective for its range of tasks.
Keywords: mathematical model, physical nonlinearity, creep, orthotropy, shell, strength, stability, algorithm, Ritz method, structural anisotropy method. 
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     author = {V. V. Karpov and A. A. Semenov},
     title = {Mathematical models and algorithms for studying the strength and stability of shell structures},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a5/}
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V. V. Karpov; A. A. Semenov. Mathematical models and algorithms for studying the strength and stability of shell structures. Sibirskij žurnal industrialʹnoj matematiki, Tome 20 (2017) no. 1, pp. 53-65. http://geodesic.mathdoc.fr/item/SJIM_2017_20_1_a5/