I have a square-shaped finite element ABCD. I have x-displacement and y-displacement for each of its 4 nodes (x1,y1), (x2,y2), (x3,y3), (x4,y4). I created a finer mesh. As a result, my finite element ABCD now have 9 nodes. I need a MATLAB code to compute the x-displacement and y-displacement for each of its 5 intermediate nodes (x5,y5), (x6,y6), (x7,y7), (x8,y8) and (x9,y9). I am working in 2 dimensional plane. Thank you.
You need to interpolate your displacement field and get the values in correspondence of the new nodes. There are many options, I would personally try with radial basis function:
https://en.wikipedia.org/wiki/Radial_basis_function
I am sure there is something already implemented and available on matlab exchange .
maybe this is too simplistic, but suppose we re-meshed before the displacement
x5 = (x1+x2)/2, x6 = (x1+x3)/2, .... etc
so now after displacement we have x1', x2', x3', and x4'
would it make sense to say x5' = (x1'+x2')/2, x6' = (x1'+x3')/2, ....
the one example that might require finesse is x7' since there appear to be two ways to arrive there (x6' and x8') and (x5' and x9'); if these gave different answers you could average them again
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