Open AccessEigenfunction Expansion for the Elastic Rectangle
Author(s) -
М. Д. Коваленко,
Irina V. Menshova,
Alexander P. Kerzhaev,
Gaoming Yu
Publication year - 2020
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1593/1/012008
Subject(s) - eigenfunction , rectangle , mathematics , boundary value problem , mathematical analysis , elasticity (physics) , geometry , eigenvalues and eigenvectors , physics , quantum mechanics , thermodynamics
In the paper, we construct an exact solution to a boundary value problem of the theory of elasticity for a rectangle in which the longitudinal sides are free, while normal and tangential stresses are given at the ends (even-symmetric deformation with respect to the central axes). The solution is represented in the form of series in Papkovich–Fadle eigenfunctions. The coefficients are determined explicitly by using functions biorthogonal to the Papkovich–Fadle eigenfunctions. We give the final formulas which have a simple appearance and can easily be used in engineering practice. The obtained solution is compared with the solution to the corresponding boundary value problem for a half-strip.