Optimization of the numerical algorithm for solving of elastoplastic deformation problem of rectangular plate under uniform transient thermal expansion

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¹Far Eastern Federal University, School of Natural Sciences, Vladivostok, Russia

² Far Eastern Federal University, Oriental Institute School of Regional and International Studies

Within the framework of the theory of small elastoplastic deformations we examined two-dimensional problem of the thin rectangular plate’s deformation with clamped upper and lower sides and the lateral face are free from external influence (Fig. 1). Changing of the stress-strain state of the plate connected with uniform increase in temperature field – the process of thermal expansion causes thermal stresses and deformations which are able to reach values sufficient to cause plastic flow regions.

The analysis of stress-strain state of the plate [2] shows that along the middle lines, which are marked on the graph, regardless of the temperature, values of some components of displacements and stresses are permanent (same):

The external boundary conditions and conditions in the inner sides (1) completely determine the boundary value of the problem for every single quarter of the plate. Obviously, using the method of finite differences in the two-dimensional case [3], the computation time of the problem can be reduced in several times at the expense of a fourfold reduction of grid points, which are aimed to define the displacement components.

If we firstly calculate the displacements and stresses in the upper left area of

and

, then build fields of displacements and stresses in the rest parts of the plate (top right index indicates a number of the area under consideration in accordance with (Fig. 1), we use the following formulas:

The obtained values of the parameters of the stress-strain state precisely coincide with the parameters when the problem is solved for the whole plate [2]. However, as it was shown by the results of the numerical experiment, the computation time was reduced by about 3 times.

1. Bykovtsev, G. I. Theory of Plasticity / G. I. Bykovtsev, D. D. Iclev. - Vladivostok: Dalnauka, 1998. - 528 p.

2. Gorshkov, S. A. Calculation of plane stress field under plastic flow and unloading/ S. A. Gorshkov, E. P. Dats, E. V. Murashkin // Vestnik Chuvash State Pedagogical University named after I.Y. Yakovlev. Series: mechanical limit state. - 2014. - №3 (21). – P. 169-175.

3. Samarskiy, A. A. Numerical Methods / A. A. Samarskiy, A. V. Gulin. - M.: Nauka, 1989. - 432 p.