Modeling of Thermoelastic-Visco-Plastic Deformation of Flexible Reinforced Plates

A model of thermoelastic-visco-plastic deformation of a composite material cross reinforced with continuous fibers in arbitrary directions has been developed. The materials of the components of the composition are isotropic; their plastic deformation is described by the flow theory with isotropic hardening. The dependences of the loading functions on temperature and strain rate of these materials are taken into account. A mathematical model of thermoelastic-visco-plastic bending behavior of reinforced plates has been constructed. The weak resistance to transverse shears of such thin-walled structures is taken into account in the framework of Ambarcumian’s theory. Geometric nonlinearity is taken into account in the Karman approximation. The relation of the mechanical and thermophysical components of the problem of dynamic inelastic deformation of composite plates is taken into account. The temperature over the thickness of the constructions is approximated by polynomials of various orders. An explicit numerical scheme is used to solve the formulated two-dimensional problem. The thermoelastic-visco-plastic behavior of two-dimensionally and spatially reinforced fiberglass and metal-composite plates, dynamically bent under the action of an air blast wave, has been investigated. It is shown that in order to adequately determine the temperature in such structures, it must be approximated by polynomials of the 6th or 7th order over the thickness of the plates. It has been demonstrated that relatively thin composite plates heat up by 15…30°C, and relatively thick ones by 1.5…2.5°C. Due to such a low level of heating of reinforced constructions, their dynamic calculation under the action of loads such as an air blast wave can be carried out without taking into account the thermal effect if there are no additional heat sources of non-mechanical origin. In this case, it is necessary to take into account the sensitivity of the plastic properties of the components of the composition to the rate of their deformation.