Particularities of mathematical modeling of deformation processes for arched and panel designs of composites with large displacements and rotation angles

Abstract

In aerospace systems and automotive industry flexible elastic and thin-walled structures are widely used. The adequate mathematical models are in the process of development as well as numerical algorithms for examination of the features of processes of deformation of panel and arch designs with large displacements and arbitrary angles of rotation of the normal. For the discretization of the original continuum problem in spatial variables, the finite difference method can be used with the replacement of differential operators by finite-difference second-order approximations. The computational algorithm for solving a substantially nonlinear boundary-value problem is constructed on the basis of adaptation of the calculation method with construction of an explicit two-layer difference scheme in time of the second order of accuracy. The influence of the boundary conditions on the features of subcritical and supercritical behavior of the elastic arch structure under the influence of the surface load of the “tracking” type is considered.