136
N. A. Abrosimov et al.
vary slightly, and the greatest difference is observed for reinforcement angles of 90°.
For shells made from material with a weakly pronounced anisotropy, a slight effect
of the preliminary axial loading on the critical value of the dynamic external pressure
is observed, though a difference in buckling forms of a shell is noted.
Acknowledgements The method of calculating composite cylindrical shells under combined loads
was developed at a financial support of the Ministry of Science and Higher Education of the Russian
Federation (task 0729-2020-0054), and numerical analysis of loss of stability of shells was carried
out at a financial support of RFBR grants ((№ 18-08-01234, № 19-08-00828).
References
Abrosimov, N. A., & Bazhenov, V. G. (2002). Nonlinear Problems of dynamics of composite
structures. Nizhni Novgorod: Izd NNGU, 400 [in Russian].
Abrosimov, N. A., & Elesin, A. V. (2017). Numerical analysis of dynamic strength of composite
cylindrical shells under multiple-pulse exposures. Nizhni Novgorod, Problemy prochnosti i
plastichnosti, 79(4), 450–461 [in Russian].
Barchiesi, E., Spagnuolo, M., & Placidi L. (2018). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids.
Baskakov, V. N., Kostoglotov, A. I., & Shvetsova, L. A. (1982). Investigation of the dynamic stability
of smooth cylindrical shells. Problemy Prochnosti, 5, 31–33.
Bendyukov, V. V., & Deryushev, V. V. (1995) Dynamic short-wave instability of thin-walled
cylindrical shells at the local action of an external pressure pulse. Problemy Prochnosti, 4, 36–43.
Bisagni, C. (2005). Dynamic buckling of fiber composite shells under impulsive axial compression.
Thin-Walled Structure, 43, 499–514.
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: review of existing
models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topi-cal
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8).
dell’Isola, F., Cuomo, M., Greco, L., Della, Corte, A. (2017). Bias extension test for pantographic
sheets: Numerical simulations based on second gradient shear energies. Journal of Engineering
Mathematics.
dell’Isola, F., Della Corte, A., & Giorgio, I. (2016a). Higher-gradient continua: The legacy of Piola,
Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics
of Solids.
dell’Isola, F., Della Corte, A., Greco, L., & Luongo, A. (2016b). Plane bias extension test for
a continuum with two inextensible families of fibers: a variational treatment with Lagrange
multipliers and a perturbation solution. International Journal of Solids and Structures.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016c). Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical
examples of equilibrium. Proceedings of The Royal Society A, 472(2185).
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 63(6).
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al.
(2019a). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
N. A. Abrosimov et al.
vary slightly, and the greatest difference is observed for reinforcement angles of 90°.
For shells made from material with a weakly pronounced anisotropy, a slight effect
of the preliminary axial loading on the critical value of the dynamic external pressure
is observed, though a difference in buckling forms of a shell is noted.
Acknowledgements The method of calculating composite cylindrical shells under combined loads
was developed at a financial support of the Ministry of Science and Higher Education of the Russian
Federation (task 0729-2020-0054), and numerical analysis of loss of stability of shells was carried
out at a financial support of RFBR grants ((№ 18-08-01234, № 19-08-00828).
References
Abrosimov, N. A., & Bazhenov, V. G. (2002). Nonlinear Problems of dynamics of composite
structures. Nizhni Novgorod: Izd NNGU, 400 [in Russian].
Abrosimov, N. A., & Elesin, A. V. (2017). Numerical analysis of dynamic strength of composite
cylindrical shells under multiple-pulse exposures. Nizhni Novgorod, Problemy prochnosti i
plastichnosti, 79(4), 450–461 [in Russian].
Barchiesi, E., Spagnuolo, M., & Placidi L. (2018). Mechanical metamaterials: a state of the art.
Mathematics and Mechanics of Solids.
Baskakov, V. N., Kostoglotov, A. I., & Shvetsova, L. A. (1982). Investigation of the dynamic stability
of smooth cylindrical shells. Problemy Prochnosti, 5, 31–33.
Bendyukov, V. V., & Deryushev, V. V. (1995) Dynamic short-wave instability of thin-walled
cylindrical shells at the local action of an external pressure pulse. Problemy Prochnosti, 4, 36–43.
Bisagni, C. (2005). Dynamic buckling of fiber composite shells under impulsive axial compression.
Thin-Walled Structure, 43, 499–514.
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: review of existing
models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topi-cal
contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20(8).
dell’Isola, F., Cuomo, M., Greco, L., Della, Corte, A. (2017). Bias extension test for pantographic
sheets: Numerical simulations based on second gradient shear energies. Journal of Engineering
Mathematics.
dell’Isola, F., Della Corte, A., & Giorgio, I. (2016a). Higher-gradient continua: The legacy of Piola,
Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics
of Solids.
dell’Isola, F., Della Corte, A., Greco, L., & Luongo, A. (2016b). Plane bias extension test for
a continuum with two inextensible families of fibers: a variational treatment with Lagrange
multipliers and a perturbation solution. International Journal of Solids and Structures.
dell’Isola, F., Giorgio, I., Pawlikowski, M., & Rizzi, N. (2016c). Large deformations of planar extensible beams and pantographic lattices: Heuristic homogenization, experimental and numerical
examples of equilibrium. Proceedings of The Royal Society A, 472(2185).
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the shape
of Cauchy cuts in Nth gradient continua: approach “à la D’Alembert”. Zeitschrift für angewandte
Mathematik und Physik, 63(6).
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al.
(2019a). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.