On some aspects of implementation of boundary elements method in plate theory

Authors

  • A. H. Kutsenko National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • O. G. Kutsenko National University of Life and Environmental Sciences of Ukraine image/svg+xml
  • V. V. Yaremenko National University of Life and Environmental Sciences of Ukraine image/svg+xml

DOI:

https://doi.org/10.31548/machenergy2021.03.107

Keywords:

plate theory, deflection, boundary elements method, Sapondzyan`s paradox

Abstract

The article deals with the problem arising in the construction of a numerical scheme of the first-order boundary element method for plate theory. During construction of such a scheme, the initially smooth boundary of the plate is replaced by a polygonal chain. Due to this replacement the deviation of the numerical results from the actual distribution of deflections and other characteristics is arisen. The reason for this deviation lies in the so-called Sapondzyan's paradox. According to it, the deflection of a plate bounded by a regular polygon does not converge to the deflection of a circular plate with increasing of the polygon sides number. In the paper, on the basis of an analytical consideration of Sapondzyan's problem, the components of the numerical scheme of the boundary element method, which are responsible for the mentioned deviation, are pointed out. The modification of the boundary element method scheme that allows to eliminate given problem is presented. This approach is tested on the example of solving two pairs of problems for elliptical and rectangular plates. The results of numerical solution of those problems confirmed the adequacy of the proposed modification.

References

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Published

2022-01-16

Issue

No. 12(3) (2021)

Section

Статті

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