Development of two-dimensional theory of thick plates bending on the basis of general solution of Lamé equations https://doi.org/10.33108/visnyk_tntu2018.01.033
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Abstract
A theory of bending of the thick plate normally loaded on lateral surfaces, when its stress state
is not described by the hypothesis of Kirchhoff–Love or Tymoshenko, is suggested. Its three-dimensional stress-strain state is divided into symmetrical bend and compression. To describe the symmetrical bend, three harmonic
functions are used expressing the general solution of the Love equations and three-dimensional stress state of the plate. After integrating the stresses along the plate thickness, bending and torque moments and transverse stresses are expressed through three two-dimensional functions. Closed system of partial differential equations of the eighth order was developed on the introduced two-dimensional functions without the use of hypotheses about the geometric nature of the plate deformation. Three-dimensional boundary conditions are reduced to two-dimensional form.
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References
1. Ambartsumyan S.A. Theory of anisotropic plates, Moskva, Nauka, 1987, 360 pp. [In Russian].
2. Timoshenko S.P., Voynovsky-Krieger S. Plates and shells, Moscow, Nauka, 1966, 636 pp. [In Russian].
3. Kosmodamiansky A.S., Shaldirvan V.A. The Thick Multi-Connected Plates, Kiev, Naukova dumka, 1978, 240 pp. [In Russian].
4. Donnell L.H. Beams, plates and shells, Moskva, Nauka, 1982, 568 pp. [In Russian].
5. Lukasiewicz S. Local Loads in Plates and Shells. Monographs and Textbooks on Mechanics of Solids and Fluids, Alphen aan den Rijn, Sijthoff & Noordhoff, 1979, 570 pp.
https://doi.org/10.1007/978-94-009-9541-3
6. Noor A.K. Bibliography of Monographs and Surveys on Shells, Appl. Mech. Rev, 1990, Vol. 43, № 9, pp. 223 – 234.
7. Kobayashi H.A Survey of Books and Monographs on Plates, Mem. Fac. Eng., Osaka City Univ, 1997, Vol. 38, pp. 73 – 98.
8. Lebée A. and Sab K. A. bending gradient model for thick plates. Part I: Theory, Int. J. of Solids and Struct, 2010, Vol. 48, № 20, pp. 2878 – 2888.
9. Revenko V.P. Three-dimensional problem of the theory of elasticity for orthotropic cantilevers and plates subjected to bending by transverse forces, Materials Science, 2004, Vol. 40, No 2, pp. 215 – 222.
https://doi.org/10.1007/s11003-005-0042-9
10.Revenko V.P. Reduction of a three-dimensional problem of the theory of bending of thick plates to the solution of two two-dimensional problems, Materials Science, 2015, Vol. 51, № 6, pp. 785 – 792.
11. Revenko V.P. Solving the three-dimensional equations of the linear theory of elasticity, Int. Appl. Mech., 2009, Vol. 45, No. 7, pp. 730 – 741.