ORLOV G.A. Ural Federal University

Spoluautoři POLYAKOV A.A.

The urgency of a problem of calculation of the indicators of stress state is considered. The analysis the known methods of calculating the stress in the theory of metal forming was performed. An improved method for calculating the stresses on the basis of finite elements method and the principle of virtual stress is proposed. The process of isothermal axisymmetric deformation is considered. Material adopted isotropic, incompressible, rigidly-visco-plastic. Тhe stress approximated polynomials within the triangular finite element. Unknown coefficients of the polynomials were determined for each element of the solution of systems of the corresponding linear equations. Functional of the Castigliano principle was submitted after the numerical integration of a function of many variables - voltage values at the nodes of elements in a given time. The functional minimization carried out on the computer method of conjugate gradients. Transition to the next step in time were made by the calculation by the equations of the communication components strain rate tensor on average over the cells with subsequent determination of flow velocity and displacement in the element nodes using formulas of numerical differentiation and current forming. The algorithm of the calculation in the axially symmetric deformation considered. The method illustrated by compression of cylinder. The comparison of the results with known data shows.

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