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B.3.1 Tetrahedron


linear interpolation:

\resizebox{5.0cm}{!}{\includegraphics{/iue/a39/users/radi/diss/fig/shape/lin3D_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$      


shape functions:
N1($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = 1 - $\displaystyle \xi$ - $\displaystyle \eta$ - $\displaystyle \zeta$  
N2($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \xi$  
N3($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \eta$  
N4($\displaystyle \xi$,$\displaystyle \eta$,$\displaystyle \zeta$) = $\displaystyle \zeta$  

next up previous
Next: B.3.2 Hexagon Up: B.3 Three-Dimensional Shape Functions Previous: B.3 Three-Dimensional Shape Functions
Mustafa Radi
1998-12-11