Abstract
A system of equilibrium equations for the deflection of thick transversely isotropic plates with constant thicknesses is derived by expanding the stress and displacement components as Fourier series in Legendre polynomials of the thickness coordinate. A method for constructing a general solution of this system is described. It is made up of three types of solutions: biharmonic, potential, and rotational.
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REFERENCES
I. Yu. Khoma, “Representation of the solutions of the equilibrium equations for non-thin transversely isotropic plates, ” Teor. Prikl. Mekh., No. 30, 3–12 (1999).
I. N. Vekua, Some General Methods for Constructing Different Variants of the Theory of Shells [in Russian], Moscow (1982).
I. Yu. Khoma, Generalized Theory of Anisotropic Shells [in Russian], Kiev (1986).
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Khoma, I.Y. Representation of Solutions of the Deflection Equilibrium Equations for Thick Transversely Isotropic Plates. Journal of Mathematical Sciences 103, 306–313 (2001). https://doi.org/10.1023/A:1011349809289
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DOI: https://doi.org/10.1023/A:1011349809289