The Flamant problem for an orthotropic half-plane
UDC
531.39DOI:
https://doi.org/10.31429/vestnik-20-1-27-32Abstract
Modern mechanical engineering very often sets tasks for the calculation of thin-walled structures with mutually exclusive properties: on the one hand, the studied structures must combine high reliability and strength, and on the other, lightness and economy. For a successful combination of the above properties, it seems quite justified to use orthotropic materials and plastics in structures.
It is known that there are mathematical analogies that allow solving problems of strength, stability and vibrations to effectively use solutions for the same type of isotropic structures to predict the behavior of the same structures made of orthotropic material. The article demonstrates the possibility of using mathematical analogies and the integral Fourier transform to solve the Flamant problem for an orthotropic half-plane by reducing it to two isotropic problems.
The transformation of the equations of the plane problem of the theory of elasticity of an orthotropic body made it possible to lower the order of the equations. The transformed systems of equations differ only in signs, so the integration of equations can be carried out for one half-plane. Due to this, the amount of computational work has significantly decreased compared to the solution of the original system of equations.
Keywords:
mechanics, mathematical analogies, the Flamant problem, orthotropic plates, integral Fourier transformAcknowledgement
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