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rpim shape function

A question about RPIM shapefunction

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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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