# Two-dimensional Shape Functions

(Difference between revisions)
 Revision as of 09:49, 4 November 2009 (view source)JMora (Talk | contribs)← Older edit Revision as of 09:49, 4 November 2009 (view source)JMora (Talk | contribs) Newer edit → Line 7: Line 7: − with $\quad p=\frac{(n+1)(n+2)}{2}$ + with:   $\qquad p=\frac{(n+1)(n+2)}{2}$   the number of terms.

## Revision as of 09:49, 4 November 2009

Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of nth order, these functions should include a complete polynomial of equal order.

That is, a complete polynomial of nth order can be written as:

$f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k \qquad j+k \le n$

with:   $\qquad p=\frac{(n+1)(n+2)}{2}$   the number of terms.

can only fit polynomial functions of pth order if they content a polynomial function

for any polynomial function of pth order it is enough to use p-1 integration points.

## References

1. Pascal's triangle