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B.1 One-Dimensional Shape Functions


linear interpolation:

\resizebox{5.0cm}{!}{\includegraphics{/iue/a39/users/radi/diss/fig/shape/lin1D.eps}}

interpolating polynomial function:

u($\displaystyle \xi$) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$$\displaystyle \xi$
 
 
  

shape functions:

N1($\displaystyle \xi$) = 1 - $\displaystyle \xi$  
N2($\displaystyle \xi$) = $\displaystyle \xi$  

 
 

quadratic interpolation:

\resizebox{5.0cm}{!}{\includegraphics{/iue/a39/users/radi/diss/fig/shape/lin1D_2.eps}}

interpolating polynomial function:

u($\displaystyle \xi$) = $\displaystyle \alpha_{1}^{}$ + $\displaystyle \alpha_{2}^{}$$\displaystyle \xi$ + $\displaystyle \alpha_{3}^{}$$\displaystyle \xi^{2}_{}$
 
    

shape functions:

N1($\displaystyle \xi$) = (1 - $\displaystyle \xi$)(1 - 2$\displaystyle \xi$)  
N2($\displaystyle \xi$) = - $\displaystyle \xi$(1 - 2$\displaystyle \xi$)  
N3($\displaystyle \xi$) = 4$\displaystyle \xi$(1 - $\displaystyle \xi$)  

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Next:B.2 Two-Dimensional Shape FunctionsUp:B. Shape functionsPrevious:B. Shape functions
Mustafa Radi

1998-12-11