Modeling of Thermoelastic-Viscoplastic Dynamic Deformation of Flexible Cylindrical Reinforced Shells

Abstract

A mathematical model of thermoelastic-viscoplastic flexural dynamic deformation of thin circular cylindrical shells with complex reinforcement structures is developed. Weak resistance to transverse shear and wave processes in such composite structures are modeled in the framework of Ambartsumyan’s non-classical theory of bending. The geometric nonlinearity of the problem is taken into account in the Karman approximation. The composition materials are isotropic; their plastic deformation is described by the relations of the flow theory with a loading function that depends on temperature and strain rate. The connection between the thermal and mechanical components of the problem under consideration is taken into account. In the transverse direction of structures, the temperature is approximated by a 7th order polynomial. The formulated nonlinear two-dimensional initial-boundary value problem is numerically integrated using an explicit scheme of time steps. The elastic-viscoplastic and elastic-plastic dynamic behavior of fiberglass and metal-composite long cylindrical shells, which are orthogonally reinforced in the circumferential and longitudinal directions, is studied. Structures are loaded from the inside with pressure, which is similar to the pressure in an air blast wave. It is shown that flexible fiberglass shells during axisymmetric deformation can experience additional heating by 11…13 °C at certain points. Metal-composite structures similar in geometry and reinforcement structure — by 40…60 °C. Thermo-elastoplastic calculations lead to an overestimation of the maximum temperature values in fiberglass shells by 1.0…1.5 °C compared to thermoelastic-viscoplastic calculations, and for metal-composite structures, on the contrary, to an underestimation of these values by 20 °C. It is shown that the calculations of fiberglass shells can be carried out without taking into account the thermal response in them, and it is advisable to calculate the dynamics of metal-composite shells, taking into account the temperature response in them. The dynamic behavior of both metal-composite and fiberglass structures must be calculated taking into account the sensitivity of the plastic properties of their composition components to the strain rate.

Keywords

• flexible cylindrical shells
• complex reinforcement
• dynamic loading
• coupled thermoelasticviscoplasticity
• ambartsumyan’s bending theory
• explicit numerical scheme