Modeling of non-isothermic viscoelastic-plastic behavior of flexible reinforced plates

Based on a step-by-step procedure over time, a numerical-analytical model of the nonisothermal viscoelastic-plastic behavior of crisscrossed-reinforced material is constructed. The components of the composition are isotropic; their viscoelastic deformation is described by the Maxwell - Boltzmann model of the body, and instantaneous inelastic behavior is described by the relations of the theory of elastoplastic deformation with isotropic hardening. In this case, the temperature dependence of the loading function and material constants is taken into account. The conditions of the viscoelastic deformation, the beginning of unloading, neutral and active viscoelastic-plastic loading of the thermosensitive materials of the composition are formulated. Relationship between the mechanical and thermophysical characteristics of the composite material is taken into account. The structural relationships of the thermophysical component of the problem are presented. The developed mathematical model is focused on the use of explicit schemes for the numerical integration of viscoelastic-plastic and thermophysical problems. The initial-boundary problem of nonisothermal viscoelastic-plastic bending deformation of fibrous plates is formulated. The poor resistance of such thin-walled constructions to transverse shear is described in the framework of Ambardzumyan's theory. The geometric nonlinearity of the problem is taken into account in the Karman approximation. In the transverse direction, the temperature is approximated by a second-order polynomial. To reduce the three-dimensional heat conduction problem to two-dimensional relations, the method of additional boundary conditions is used. The dynamic bending of a flat-crisscrossed-reinforced fiberglass plate under the influence of an air blast wave is investigated. It is shown that in the absence of external thermal heating in the process of oscillations, this structure heats by only 2-3ºС. In such cases, the calculation can reasonably be carried out without taking into account the temperature effect. In the presence of intense thermal loading of the structure, the heat sensitivity of the materials of the composition must be taken into account. It has been demonstrated that in the presence of a temperature field inhomogeneous over the thickness of the plate, the shape and magnitude of the residual deflection significantly depend on which face surface an external dynamic load is applied to.