Modeling of Bending Non-Isothermal Viscoelasticviscoplastic Dynamic Deformation of Shallow Reinforced Shells. Part 1. Problem Formulation and Solution Method - Andrei P. Yankovskii (Механика машин, механизмов и материалов)
The problem of dynamic non-isothermal viscoelastic-viscoplastic deformation of flexible reinforced shallow shells and curved panels is formulated. Wave processes and poor resistance of such structures to transverse shear are modeled in terms of Ambartsumian’s non-classical bending theory. Transverse compression of composite shells is taken into account. The temperature field in the transverse direction is approximated by a high order polynomial. The geometric nonlinearity is taken into account in the Karman approximation. The viscoelastic behavior of the composition components is described by the Maxwell–Boltzmann body model. Inelastic deformation is described by the relations of the theory of plastic flow with isotropic hardening, and the loading functions of phase materials depend not only on the hardening parameter and temperature, but also on the intensity of the strains speed. Structural relationships of thermomechanics of composites are used, taking into account the complex stress-strain state (SSS) in all phase materials of the composition. These structural relationships make it possible to calculate the temperature fields and SSS in shallow shells not only with traditional “flat”-criss-cross, but also with spatial reinforcement structures. The reduced two-dimensional equations of the thermophysical component of the problem are written out, corresponding to the polynomial expansion of the temperature in the transverse direction of a thin-walled composite structure. In this case, the thermal boundary conditions of the general type on the front surfaces of the shallow shell and the thermal sensitivity of the materials of the components of its composition are taken into account. An explicit numerical scheme is used to integrate the formulated nonlinear coupled problem. The mechanical component of the dynamic problem is integrated using a “cross” type scheme on a three-point template in time; the thermal-physical component is integrated using an explicit scheme on a two-point template in time. A necessary condition for the stability of the numerical scheme is the Courant limitation on the time step.