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Lecture Notes: Introduction to Finite Element Method

Chapter 5. Plate and Shell Elements

Examples:

A square plate with four edges clamped or hinged, and under a uniform load q or a concentrated force P at the center C.

z

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

y

 

 

 

 

 

 

 

 

 

 

C

 

 

 

 

L

x

L

 

 

Given: E, t, and ν = 0.3

For this simple geometry, Eq. (10) with boundary condition (11) or (12) can be solved analytically. The maximum deflections are given in the following table for the different cases.

Deflection at the Center (wc)

 

Clamped

Simply supported

 

 

 

Under uniform load q

0.00126 qL4/D

0.00406 qL4/D

 

 

 

Under concentrated

0.00560 PL2/D

0.0116 PL2/D

force P

 

 

 

 

 

in which: D= Et3/(12(1-v2)).

These values can be used to verify the FEA solutions.

© 1997-2002 Yijun Liu, University of Cincinnati

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