Open AccessON THE BENDING OF RECTANGULAR PLATES WITH CLAMPED EDGES
Author(s) -
Hu Hai-Chang
Publication year - 1955
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.11.19
Subject(s) - isotropy , orthotropic material , power series , convergent series , boundary value problem , series (stratigraphy) , mathematical analysis , differential equation , bending , bending of plates , physics , perturbation (astronomy) , materials science , geometry , mathematics , composite material , optics , thermodynamics , finite element method , quantum mechanics , paleontology , biology
The problem of bending of orthotropic rectangular plates with clamped edges on elastic foundation may be reduced to the following differential equation and boundary conditions (?4w)/(?x4)+2λ(?4w)/(?x2?y2)+(?4w)/(?y4)+kw=q/D. w=0, (?w)/(?x)=0 at x=±a, w=0, (?w)/(?y)=0, at y=±b. In the case of isotropic plates, λ = 1. In this paper a perturbation method is proposed for the solution of this problem fay expanding w in power series of λ: w=w0+w1λ+w2λ2+……. It is proved that this series is convergent when -1 ≤λ≤1.