This paper deals with refined beam, plate, and shell theories which are based on the reduction of the three-dimensional elasticity theory by assuming an approx imation of the displacements through the thickness. Conditions which should be imposed on this approximation to provide the consistency of the theory are obtained. For brevity's sake the derivation is performed for a beam, the results being further generalized for plates and shells. A thick isotropic plate is considered as an example.
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References
1.
Whitney, J.M.1989. "Stress Analysis of the Double Notch Shear Specimen," Proc. Amer. Soc. Comp. Fourth Techn. Conf., Blacksburg, VA, Oct. 3-5, 1989 , Lancaster, PATechnomic Publishing Co., pp. 325-333
2.
Krein, S. G., ed. 1964. Functional Analysis (in Russian. Moscow: Nauka .
3.
Grigorenko, J.M., A.T. Vasilenko and N.D. Pankratova .1985. Statics of Anisotropic Thick-Walled Shells (in Russian) Kiev. Visha Shkola.
