Refined model of thermo-visco-elastic-plastic dynamic deformation of reinforced flexible shallow shell

A. P. Yankovskii

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 28 (2024) no. 3, pp. 562-585.

Résumé

The problem of thermo-visco-elastic-plastic deformation of reinforced shallow shells under dynamic loading is formulated. In this case, a refined theory of their bending is used, the simplest version of which is the Ambartsumyan theory. Geometric nonlinearity is taken into account in the Karman approximation. The inelastic behavior of the materials of the composition phases is described by the equations of the theory of plastic flow; their viscoelastic deformation is described by the relations of the Maxwell–Boltzmann model. Temperature in the transversal direction is approximated by high-order polynomials. Numerical integration of the coupled nonlinear thermomechanical problem is carried out using an explicit time-stepping scheme. The visco-elastic-plastic flexural behavior of a cylindrical fiberglass panel with an orthogonal 2D-reinforcement structure is studied. The structure is briefly loaded in the transverse direction with high-intensity pressure. A comparative analysis of calculations performed with and without taking into account the temperature response in a shallow shell is carried out. Additionally, cases of preheating the panel from one of the front surfaces are studied. It is shown that to calculate the thermo-visco-elastic-plastic behavior of fiberglass curved panels, a refined theory of bending should be used, rather than the traditionally used Ambartsumyan theory, which significantly distorts the shape of the calculated residual deflection and the field of residual deformations of the components of the composition. It is demonstrated that failure to take into account the temperature response in a shallow reinforced shell can lead not only to a quantitative, but also a qualitatively incorrect idea of the calculated form of its residual deflection. The presence of preheating of the fiberglass panel leads to a noticeable change in its residual deflection. In this case, an important role is played by the fact from which particular front surface additional heating or cooling of the thin-walled structure is carried out.

Détail

Keywords: shallow shells, geometric nonlinearity, fiber reinforcement, coupled thermo-visco-elastic-plasticity, refined bending theory, inelastic dynamics, residual state, explicit time step method

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