The Exact Solution of Unequal Thickness Plate Problem

  • Cong Zun Li
Conference paper


Plate equation is
$$ \text{D}\frac{\text{d}} {{\text{dr}}}\left[ {\frac{{\text{ld}}} {{\text{rdr}}}\left( {\text{r}\frac{\text{d}} {{\text{dr}}}\text{w}} \right)} \right] + \frac{\text{d}} {{\text{dr}}}\text{D}\left( \frac{{\text{d}^2 }} {{\text{dr}^2 }}\text{w} + \frac{\text{v}} {\text{r}}\frac{\text{d}} {{\text{dr}}}\text{w} \right) = \frac{1} {2}\text{qr} $$
in which \( \text{D} = \frac{{\text{Eh}^3 \left( \text{r} \right)}} {{12\left( {1 - \text{v}^2 } \right)}} \) q=evenly distributed load, h(r)thickness of the plate, a function of r. To solve these problems, generally use numerical solution method. In this paper, we assume that h(r) is continuously differentiable sectionally. According to Weierstrass theorem, it can be uniformly approximated by using multinomial, we can thus obtain the analytic expression of the solution. This method is more facilitated for analytizing problems.


Exact Solution Balance Equation Textile Engineer Variable Thickness Thickness Plate 
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  1. 1.
    S. Timoshenko, S. Woinowsky-Krieger: Theory of Plates and Shells (second edition) McGraw-Hill Book Company, Inc (1959)Google Scholar
  2. 2.

Copyright information

© Springer Japan 1986

Authors and Affiliations

  • Cong Zun Li
    • 1
  1. 1.Tianjin Textile Engineering InstituteHedong District, TianjinChina

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