Finite element analysis node displacement

[mertcan]

Hi, I would like to ask why center of element displacement is always estimated with polynomial equation involving nodes displacement (like in attachment/picture)? Also I know that if nodes' number increase for an element then displacement of center of element is estimated with higher order polynomial, why do we always include polynomial equation to estimate center of element?? why don't we use logarithmic or exponential function or other kind of function to model the displacement of center of element?? Does the application of polynomial equation to estimate the displacement of center of element give better real results ?? if it gives then why ??

 

[mertcan]

Hi everyone I have been waiting for 2 days but nobody has responded to my question is there a in comprehensible situation in thread?

 

[timthereaper]

My FEA is a bit rusty so maybe others will have to chime into confirm or deny what I'm saying, but I'm replying for the sake of starting the discussion.

In classical finite element theory (really the Galerkin method), we discretize the geometry by placing nodes and connecting them with elements. We are calculating the displacement of the nodes under certain boundary conditions and elements are there to restrict the nodes to be displaced consistent with physical experiment. In the end, the only result we get back are the displacement at the nodes. We have to interpolate to get the displacement at what we're calling the center of the element. In your above image, this just looks like a formulation of a point in barycentric coordinates. I think the exact formulation for interpolation needs to be consistent with the basis functions used for the FEA calculation.

(Note for FEA gurus: this is a really simplistic explanation and not intended to be thorough, so be gentle when ripping this apart :-) )

 

[mertcan]

thanks for return @timthereaper , but whenever I want to learn how the center of element displacement is estimated what I see is always it is estimated involving polynomial functions not other functions, so I am really eager to know why only polynomial function is used?