Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structure. ІІ. Model Problems

For axisymmetrically loaded annular plates rigidly fixed on one edge and statically loaded on the other edge and for rectangular elongated plates subjected to cylindrical bending, we propose a simplified version of the refined theory (model problems) for which the complexity of realization is comparable with the complexity of the Reissner and Reddy theories. Specific calculations are performed for the case of thermoelastoplastic bending of these plates for different levels of thermal action. It is shown that, for relatively thick plates, neither the classical theory, nor the traditional nonclassical Reissner and Reddy theories guarantee the possibility of getting reliable results in finding deflections even under the conditions of rough accuracy equal to 10%. It is shown that, under the conditions of bending of layered metal-composite plates carried out at elevated temperatures in the vicinity of their supporting edges, we observe the appearance of edge effects characterizing the phenomenon of shear of these structures in the transverse direction. The traditional theories characterized by the low orders of approximation of transverse shears do not enable one to detect these local effects, which explains their quite rough accuracy. It is shown that, for the adequate analysis of thermoelastoplastic bending of relatively thin and relatively thick plates for which the materials of the phases of their compositions are linearly elastic, it is sufficient to apply the Reddy theory.

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Correspondence to А. P. Yankovskii.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 2, pp. 111–123, April–June, 2018.

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Yankovskii, А.P. Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structure. ІІ. Model Problems. J Math Sci 253, 122–135 (2021). https://doi.org/10.1007/s10958-021-05217-5

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Keywords

  • composite plate
  • regular structure
  • thermoelastoplasticity of the deformation type
  • bent plate
  • Reissner theory
  • Reddy theory
  • refined theory of bending