Analytical study of the bending of isotropic plates, inhomogeneous in thickness
DOI:
https://doi.org/10.15587/1729-4061.2016.75052Keywords:
theory of elasticity, isotropic bodies, nonhomogeneous materials, bending of plates, stresess and deformationsAbstract
A threedimensional problem of bending the plate, in which the parameters of elasticity of the material vary by thickness and are arbitrary integrable functions, was examined. And the plate itself is exposed to the action of mass forces while the action of surface loads is studied as a separate case.
An analytical solution to the boundary problem by the operator methods was obtained in a case when the boundary conditions are satisfied exactly on the flat surfaces of the plates and on the lateral surface – in the Saint Venant approximation.
It was theoretically proved that the exact, in the sense of Saint Venant, analytical solutions may be obtained if the plate is exposed to the action of the mass and surface forces, distributed on the plate and on its surface by the twodimensional polyharmonic law. In this case, the thinner the plate, the more exact the solution will be, since the corresponding solutions represent the series that contain a finite number of members.
It was demonstrated that the obtained formulas for the calculation of bending the thin plates in the case of homogeneous material transfer to the classic formulas of the theory of bending thin plates.
The obtained solutions allow using them as the approximate, “technical” theory for engineering calculations of the stressed and deformed state of nonhomogeneous plates.References
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Copyright (c) 2016 Vоlоdymyr Plevako, Volodymyr Potapov, Viktor Kycenko, Ighor Lebedynecj, Iryna Pedorych
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