A refined model of viscoelastic-plastic deformation of flexible spatially-reinforced cylindrical shells

A model of viscoelastic-plastic deformation of flexible circular cylindrical shells with spatial reinforcement structures is developed. The instant plastic behavior of the materials of the composition is determined by flow theory with isotropic hardening. The viscoelastic deformation of the components of the composition is described by the equations of the Maxwell–Boltzmann body model. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The relations used make it possible to calculate with varying degrees of accuracy the residual displacements of the points of the construction and the residual deformed state of the components of the composition. In this case, a possible weak resistance of the reinforced shell to transverse shear is simulated. In the first approximation, the equations used, the initial and boundary conditions, are reduced to the formulas of the nonclassical Ambardzumyan theory.

The numerical solution of the formulated initial boundary-value problem is constructed according to the explicit “cross” scheme. Elastoplastic and viscoelastic-plastic dynamic deformation of thin fiberglass shells under the influence of internal pressure of an explosive type is investigated. Two reinforcement structures are considered:

1) orthogonal reinforcement in the longitudinal and circumferential directions;
2) spatial reinforcement in four directions.

It is shown that even for relatively thin composite shells the Ambardzumyan theory is unacceptable to obtain adequate results of calculations of their viscoelastic-plastic dynamic deformation. It has been demonstrated that a calculation according to the theory of elastoplastic deformation of reinforced structures does not allow even an approximate estimate of the residual states of composite shells after their dynamic loading. It is shown that even for a relatively thin and long cylindrical shell, the replacement of the traditional “flat”-cross-reinforcement structure with a spatial structure can significantly reduce the residual strain of the binder material. In cases of relatively thick and especially short shells, the positive effect of such a replacement of the reinforcement structures is manifested to a much greater extent.