Two-dimensional Shape Functions

From KratosWiki
(Difference between revisions)
Jump to: navigation, search
 
Line 1: Line 1:
 +
Shape functions are selected to fit as exact as possible the Finite Element Solution. If this solution is a combination of polynomial functions of  p<sup>th</sup> order, these functions should include a complete polynomial of equal order.
  
 +
That is, a complete polynomial of p<sup>th</sup> order can be written as:
 +
 +
 +
:<math>f(x,y)=\sum_{i=1}^p \alpha_i x^j y^k; \qquad j+k \le p</math>
 +
 +
can only fit polynomial functions of p<sup>th</sup> order if they content a polynomial function
 +
 +
 +
for any polynomial function of pth order it is enough to use p-1 integration points.
 +
 +
 +
 +
 +
 +
 +
== References ==
 +
 +
# [http://en.wikipedia.org/wiki/Pascal%27s_triangle Pascal's triangle]
  
  
 
[[Category: Shape Functions]]
 
[[Category: Shape Functions]]

Revision as of 09:47, 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 pth order, these functions should include a complete polynomial of equal order.

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


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

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
Personal tools
Categories