126
N. A. Abrosimov et al.
Bendyukov and Deryushev 1995; Skurlatov 1972; Dubrovin 2015). In (Manevich
et al. 1977), results of an experimental–theoretical study on the buckling instability
of a steel cylindrical shell under pulsed loading by external pressure in combination
with external (or internal) static pressure are presented. In (Baskakov et al. 1982),
the results of experimental investigations into the effect of internal static pressure
and loading rate on the stability of aluminum cylindrical shells subjected to pulsed
loadings by external pressure are given.
An experimental analysis of buckling of thin-walled cylindrical shells under
local pulsed loading at various values of axial static compression is presented in
(Bendyukov et al. 1995). In (Skurlatov 1972), the results of investigation into the
stability of cylindrical shells subjected to axial static forces and an incident in the
longitudinal axial direction pressure wave are given.
Experimental and theoretical investigations into the processes of deformation
and loss of stability of composite structural elements under dynamic loading were
considered in (Smirnov and Lamzin 2018; Volkov et al. 2018; Jansen 2005; Bisagni
2005; Rahman et al. 2011).
At the same time, the nonlinear 3D problems on the dynamic deformation and
loss of stability of preliminary loaded composite cylindrical shells have not been
investigated carefully enough (Smirnov and Lamzin 2018). The aim of the present
work was to develop a technique of numerical research into nonlinear nonstationary
deformation and loss of stability of cylindrical shells of composite materials under
combined quasi-static and dynamic loading conditions.
It is also worth to mention about one of the most interesting subjects in modern
continuum mechanics and engineering regarding composite materials (Placidi et al.
2015). This is the development of newly (scientifically) conceived materials (‘metamaterials’) with mechanical properties that cannot be found in nature (Barchiesi and
Spagnuolo 2018; Del Del Vescovo and Giorgio 2014). Metamaterials are macroscopic composites whose properties are mainly determined by their periodic cellular
microstructure rather than by the chemical and physical properties of the material
constituting them.
An example of mechanical metamaterials are pantographic structures (dell’Isola
et al. 2016a, b, c, 2017, 2019b; Placidi et al. 2016, 2017; Rahali et al. 2015).
In order to account for multiscale mechanical interactions, which taking place for
metamaterials, higher order gradient continuum theories can be a choice (dell’Isola
et al. 2012, 2015, 2016, 2019a; Sciarra et al. 2007).
9.2 Problem Formulation and Solution Method
Let us consider a cylindrical shell formed by angle-ply winding of a unidirectional
composite material in the orthogonal curvilinear system of coordinates α i (i = 1, 3),
coinciding with lines of the principal curvatures and the external normal to the internal
surface of the shell. The Lamé coefficients of the shell are H 1 = 1, H 2 = 1 +
N. A. Abrosimov et al.
Bendyukov and Deryushev 1995; Skurlatov 1972; Dubrovin 2015). In (Manevich
et al. 1977), results of an experimental–theoretical study on the buckling instability
of a steel cylindrical shell under pulsed loading by external pressure in combination
with external (or internal) static pressure are presented. In (Baskakov et al. 1982),
the results of experimental investigations into the effect of internal static pressure
and loading rate on the stability of aluminum cylindrical shells subjected to pulsed
loadings by external pressure are given.
An experimental analysis of buckling of thin-walled cylindrical shells under
local pulsed loading at various values of axial static compression is presented in
(Bendyukov et al. 1995). In (Skurlatov 1972), the results of investigation into the
stability of cylindrical shells subjected to axial static forces and an incident in the
longitudinal axial direction pressure wave are given.
Experimental and theoretical investigations into the processes of deformation
and loss of stability of composite structural elements under dynamic loading were
considered in (Smirnov and Lamzin 2018; Volkov et al. 2018; Jansen 2005; Bisagni
2005; Rahman et al. 2011).
At the same time, the nonlinear 3D problems on the dynamic deformation and
loss of stability of preliminary loaded composite cylindrical shells have not been
investigated carefully enough (Smirnov and Lamzin 2018). The aim of the present
work was to develop a technique of numerical research into nonlinear nonstationary
deformation and loss of stability of cylindrical shells of composite materials under
combined quasi-static and dynamic loading conditions.
It is also worth to mention about one of the most interesting subjects in modern
continuum mechanics and engineering regarding composite materials (Placidi et al.
2015). This is the development of newly (scientifically) conceived materials (‘metamaterials’) with mechanical properties that cannot be found in nature (Barchiesi and
Spagnuolo 2018; Del Del Vescovo and Giorgio 2014). Metamaterials are macroscopic composites whose properties are mainly determined by their periodic cellular
microstructure rather than by the chemical and physical properties of the material
constituting them.
An example of mechanical metamaterials are pantographic structures (dell’Isola
et al. 2016a, b, c, 2017, 2019b; Placidi et al. 2016, 2017; Rahali et al. 2015).
In order to account for multiscale mechanical interactions, which taking place for
metamaterials, higher order gradient continuum theories can be a choice (dell’Isola
et al. 2012, 2015, 2016, 2019a; Sciarra et al. 2007).
9.2 Problem Formulation and Solution Method
Let us consider a cylindrical shell formed by angle-ply winding of a unidirectional
composite material in the orthogonal curvilinear system of coordinates α i (i = 1, 3),
coinciding with lines of the principal curvatures and the external normal to the internal
surface of the shell. The Lamé coefficients of the shell are H 1 = 1, H 2 = 1 +