Abstract—
The paper considers a sequence of solutions to the one-dimensional problem of irreversible deformation of a functionally graded material under conditions of uneven thermal expansion. Numerical solutions are obtained for the problems of heating an elastoplastic sphere, the material constants of which are linear functions of the radius, and exact solutions, in which the material constants are approximated by piecewise constant functions. It is shown that the deformation of a functionally graded elastoplastic material, in which the material constants are specified by piecewise-constant distributions, can be qualitatively described by numerical solutions, in which the material constants are continuous approximations of the corresponding piecewise-constant functions. The obtained numerical and analytical solutions of boundary value problems are graphically analyzed.
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Funding
The work was carried out within the framework of a state assignment (state registration no. АААА-А20-120011690132-4) and financially support of the Russian Foundation for Basic Research projects no. 20-01-00666 and by SA (NRF) / RUSSIA (RFBR) joint science and technology research collaboration (project no. RUSA180527335500/19-51-60001).
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Translated by M. Katuev
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Akinlabi, E.T., Dats, E.P., Mahamood, R.M. et al. On a Method of Temperature Stresses Computation in a Functionally Graded Elastoplastic Material. Mech. Solids 55, 800–807 (2020). https://doi.org/10.3103/S0025654420060023
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DOI: https://doi.org/10.3103/S0025654420060023