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Next: Bibliography Up: B.3 Three-Dimensional Shape Functions Previous: B.3.1 Tetrahedron

B.3.2 Hexagon


linear interpolation:

\resizebox{5.0cm}{!}{\includegraphics{/iue/a39/users/radi/diss/fig/shape/lin3Dq_2.eps}}

interpolating polynomial function:

u($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$$\displaystyle \xi$ + $\displaystyle \alpha_{3}^{}$$\displaystyle \eta$ + $\displaystyle \alpha_{4}^{}$$\displaystyle \zeta$ +      
$\displaystyle \alpha_{5}^{}$$\displaystyle \xi$$\displaystyle \eta$ + $\displaystyle \alpha_{6}^{}$$\displaystyle \xi$$\displaystyle \zeta$ + $\displaystyle \alpha_{7}^{}$$\displaystyle \eta$$\displaystyle \zeta$ + $\displaystyle \alpha_{8}^{}$$\displaystyle \xi$$\displaystyle \eta$$\displaystyle \zeta$      


shape functions:

N1($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = (1 - $\displaystyle \xi$)(1 - $\displaystyle \eta$)(1 - $\displaystyle \zeta$)  
N2($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \xi$(1 - $\displaystyle \eta$)(1 - $\displaystyle \zeta$)  
N3($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \xi$$\displaystyle \eta$(1 - $\displaystyle \zeta$)  
N4($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \eta$(1 - $\displaystyle \xi$)(1 - $\displaystyle \zeta$)  
N5($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = (1 - $\displaystyle \xi$)(1 - $\displaystyle \eta$)$\displaystyle \zeta$  
N6($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \xi$(1 - $\displaystyle \eta$)$\displaystyle \zeta$  
N7($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \xi$$\displaystyle \eta$$\displaystyle \zeta$  
N8($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \eta$(1 - $\displaystyle \xi$)$\displaystyle \zeta$  


next up previous
Next: Bibliography Up: B.3 Three-Dimensional Shape Functions Previous: B.3.1 Tetrahedron
Mustafa Radi
1998-12-11