We formulate the problem of quasistatic thermoelastoplastic bending of layered plates with regular structures in the geometrically linear statement. The mechanical behavior of isotropic layers is described by the deformation-type relations of thermoelastoplasticity with regard for their different tensile and compression resistances. The linearized governing relations of layered media are deduced with the help of the method of variable parameters of elasticity. The obtained equations enable us to describe, with different degrees of accuracy, the stress-strain state of these plates by taking into account their weakened resistance to transverse shears. Note that the relations of traditional nonclassical Reissner and Reddy theories follow from these equations as particular cases. Within the framework of the proposed refined theories and Reddy theory, the force boundary conditions for tangential stresses are satisfied on the front surfaces. The boundary conditions for normal stresses are not satisfied on these surfaces. The variations of deflections across the thickness of the structures are not taken into account. The threedimensional equilibrium equations and the boundary conditions imposed on the end surface of the plate are reduced to two-dimensional relations by the method of weighted residuals. As weight functions, we use homogeneous polynomials in the transverse coordinate.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 1, pp. 116–129, January–March, 2018.
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Yankovskii, А.P. Refined Model of Thermoelastoplastic Bending of Layered Plates with Regular Structures. I. Statement of the Problem. J Math Sci 249, 446–461 (2020). https://doi.org/10.1007/s10958-020-04952-5
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DOI: https://doi.org/10.1007/s10958-020-04952-5