Two-dimensional Shape Functions
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| − | Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of | + | Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of n<sup>th</sup> order, these functions should include a complete polynomial of equal order. |
| − | That is, a complete polynomial of | + | That is, a complete polynomial of n<sup>th</sup> order can be written as: |
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| + | :<math>f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k \qquad j+k \le n</math> | ||
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| + | with <math>p=frac{(n+1)(n+2)}{2}</math> | ||
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can only fit polynomial functions of p<sup>th</sup> order if they content a polynomial function | can only fit polynomial functions of p<sup>th</sup> order if they content a polynomial function | ||
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:
with p = frac(n + 1)(n + 2)2
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.
