Calculation of the plate plane stress in polar coordinate system on the basis of Lamé equation general solution https://doi.org/10.33108/visnyk_tntu2018.03.056
Article Sidebar
Main Article Content
Abstract
The mathematical model describing plane stress-strain state of plane elastic bodies in polar coordinate system is offered. To describe its three-dimensional stress state, three harmonic functions expressing
the general solution of Lamé equations in cylindrical coordinate system are used. After stresses integration on the thickness of the plate normal and tangential efforts are expressed through two two-dimensional harmonic
and biharmonic functions. The closed equation system in partial derivatives is developed on the introduction of two-dimensional functions without using hypotheses about the geometric nature of plate deformation. Threedimensional
boundary conditions are reduced to two-dimensional form. The example of stress-strain state of disk is given.
Article Details
Issue
Section
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
1. Timoshenko S.P., Voynovsky-Krieger S. Plates and shells. Moscow, Nauka, 1966, pp. 636 [In Russian].
2. Kosmodamiansky A.S., Shaldirvan V.A. The Thick Multi-Connected Plates. Kiev, Naukova dumka, 1978, pp. 240 [In Russian].
3. Donnell L.H. Beams, plates and shells. Moskva, Nauka, 1982, pp. 568 [In Russian].
4. Lukasiewicz S. Local Loads in Plates and Shells. Monographs and Textbooks on Mechanics of Solids and Fluids. Alphen aan den Rijn, Sijthoff & Noordhoff, 1979, pp. 570.
https://doi.org/10.1007/978-94-009-9541-3
5. Kobayashi H.A. Survey of Books and Monographs on Plates. Mem. Fac. Eng., Osaka City Univ, 1997, Vol. 38, pp. 73 – 98.
6. Chen H., Cai L.X. Unified ring-compression model for determining tensile properties of tubular materials. Materials Today Communications, 2017, Vol. 13, pp. 210 – 220.
https://doi.org/10.1016/j.mtcomm.2017.10.006
7. Wang W., Shi M.X. Thick plate theory based on general solutions of elasticity. Acta Mechanica, 1997, Vol. 123, pp. 27 – 36.
https://doi.org/10.1007/BF01178398
8. 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.