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Expansions in terms of Papkovich–Fadle eigenfunctions in the problem for a half‐strip with stiffeners
Author(s) -
Kovalenko Mikhail D.,
Menshova Irina V.,
Kerzhaev Alexander P.,
Yu Guangming
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.202000093
Subject(s) - eigenfunction , elasticity (physics) , boundary value problem , mathematics , mathematical analysis , transverse plane , bending moment , bending of plates , flexural strength , bending , geometry , structural engineering , eigenvalues and eigenvectors , materials science , physics , engineering , composite material , quantum mechanics
We have constructed an exact solution to the boundary value problem in the theory of elasticity for a half‐strip with identical stiffeners along its long sides and a load acting at its end (even‐symmetric deformation). The solution is represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from closed formulas. The solution includes two easily variable parameters that characterize the relative tensile‐compressive and flexural rigidities of the stiffeners. The final formulas for the stresses and displacements in the plate as well as for the longitudinal and transverse forces and bending moment in the stiffeners are simple and can be easily used in engineering.