Comparison of structural functions method approximations of the solution of a linear elastic layered plate bending problem
https://doi.org/10.22405/2226-8383-2022-23-4-211-232
Abstract
This paper comes to compare four different approximations of the solution to a layered linear elastic plate bending problem, obtained by the structural functions method. This method is in representation of a nonhomogeneous body displacement field as a weighted
sum of spatial derivatives of the so-called concomitant body displacements, the weighting coefficients are named structural functions of the nonhomogeneous body; the concomitant
body is a homogeneous one, subjected to the same loadings and boundary conditions, as the nonhomogeneous body; we come through the basic steps of structural functions method in this
paper. For the concomitant plate displacements, we consider two well-known approximations: the classical plate theory and the first-order shear deformation theory. We obtain the first- and the second-order structural functions of a layered plate. We derive direct formulae for the firstand second-order structural functions method approximations of the nonhomogeneous plate displacements, using both concomitant plate displacements approximations. For a set of sample plates, we compute the obtained structural functions method approximations, and compare the computation results with a known Pagano solution to the nonhomogeneous plate bending problem. The approximation, based on the first-order shear deformation theory approach to
the concomitant body displacements computation, gives an acceptable result in the considered cases.
About the Author
Lyubov Alexandrovna Kabanova
Lomonosov Moscow State University
Russian Federation
Russian Federation
junior researcher
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Review
For citations:
Kabanova L.A. Comparison of structural functions method approximations of the solution of a linear elastic layered plate bending problem. Chebyshevskii Sbornik. 2022;23(4):211-323. (In Russ.) https://doi.org/10.22405/2226-8383-2022-23-4-211-232
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