Modeling of elastic-plastic deformation of work material along multielement piecewise zig-zag linear trajectories

Mathematical simulation of 45 steel elastic-plastic deformation processes which takes place in Ilyushin's vector space and goes along a flat multielement trajectory. Each trajectory consists of four rectilinear piecewise broken segments with its simultaneous stretching or compression with torsion. In the simulation, a mathematical model of the theory of processes for plane trajectories with refined approximations of the process functionalities was used which contains all the necessary parameters for the complex loading for plane trajectories. The basic equations of the mathematical model are reduced to the Cauchy problem, the Runge-Kutta method of the accuracy fourth order was used for the numerical solution and the calculation results. A technique is given for determining the material parameters of approximations in the expressions for the functionals by processing the experimental data on basic trajectories of the "displaced fan" type of two-link trajectories. The experimental test on the SN-EVM testing complex has been carried out in mechanical laboratories in Tver State Technical University. Cylinder thin-walled shells from steel 45 in the condition of delivery were used as physical models for researching on the SN-EVM testing complex. The results of the theoretical numerical calculations are compared with the experimental data to assess the validity of the mathematical models of the processes under complex loading for these types of trajectories of deformation. The offered mathematical model of the theory of processes yields adequate results which are correspond well to the experimental data on material scalar and vector properties. It confirms the reliability of the settlement data which is sufficient for practical issues and accuracy of the constructed approximations of processes’ functionalities related to the used mathematical model of the theory of processes.