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A question about RPIM shapefunction

Submitted by 11hours on
I am solving a simple solid mechanics problem by meshless method.  use RPIM to  calculate shape function.

when i calculate the derivatives of shape function, i found the derivative is not close to zero at the compute point, when the point is on the boundry of problem domain. 
 
My question is, should the derivative be zero if the node is on the boundry?
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11hours

fig.1 derivatives of shape function respect to x when the point for computing is in domain.

 the derivative at the comput point is very close to zero.

 Fig.2 derivatives of shape function respect to Y when the point for computing is on the lower boundry of domain.

   the derivative at the comput point is not close to zero.

 also, the derivative at the comput point is much bigger than zero.

Fri, 03/01/2013 - 03:51 Permalink
zahur_ullah

You are right, if the node is inside the domain then the shape function
derivative is zero at the node but if the node is on the boundary then
the derivative of the shape function is not zero at the node. If you
plot the shape function and look at its slope you will also see this and
the reason is that the shape function is symmetric about a node when it
is inside the domain but this is not true for a node on the boundary.

 

Fri, 03/01/2013 - 17:17 Permalink
11hours

 Thank you zahoorswati!
 
I see your point. The shape function derivative is discontinuous on the normal direction of boundary.

My compute result shows that, I can get the right displacement and stress inside the domain, but can't get them on the boundary. So I thought may be the shape function has some problem.

I will check on my code. 
Sat, 03/02/2013 - 03:29 Permalink