Stryhun R. Numerical research of dynamic geometrically nonlinear elastoplastic deformation of axissymmetric solids by semi-analytical finite element method.

The advanced variant of semi-analytical finite element method is developed to simulate dynamic geometrically nonlinear elastoplastic deformation of axissymmetric solids taking into account time-varying condition of contact interaction. To describe the dynamic deformation of the body of the survey, the initial relations of the spatial problems of the theory of elasticity in the curvilinear coordinate systems are used. By the limit of elasticity, the relationship between stresses and deformations taken into accordance with the equation of the theory plastic flow under the condition of the current time for the isotopically varying material. The description of stress-strain state based on the use of initial, trancient and final configuration and considered within the framework of the current scheme of physical components. To simulate interacting contact system, used a spetial contact element that provides mutual opacityof the individual elements of the design. The most effective approach to solve the problem is to use an administrative variant of methodological approaches that occupy a place among mathematical and computational methods. The approximation based on the decomposition of unknown and given functions of the finite-element model along a system of continuous smooth functions and finite-element sampling in the region of the cross section of a finite element. Software implementation and testing with reference examples are provided. New results of solving practical construction problems were obtained. The regularities of intensive elastic-plastic deformatoin characterizing the evolutionary processes of steam turbine rotor fabrication have been established. Features of technological processes of impulse metal processing are revealed.