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strains from the given Displacements with given X Y values by Radial Basis Function Thin Plate Spline in MATLAB

Zuhaib Nazir's picture

Dear Researchers 

I have attach a text file with this message in which I have written all my code. I have applied the Radial Basis Function (interpolation) to find approximated displacements.

f = RBF(r)*a

f = given values e-g displacements to be approximate

RBF(r)= Radal Basis function (Thin Plate spline)

a= Radial Basis Function coefficient

X= x distance from the origin (given) (first column of disppoints)

Y= y distance from the origin (given)(second column of disppoints) For example as below

X    Y    f(U)

1    5    4

7    4    3

1    7    6

4    8    7

1    7    9        

I have found the approximated displacements f(approx) and from these displacements I want to find the strains E.

forexample if I approximate U1 here which is f(approx) then strain   E11=delta U1/delta X

If I approximate U2 then then E22 = delta U2/Delta Y

If U1 U2 approximated then shear strain      E12 = 1/2[Delta U1/Delta Y + Delta U2/ Delta X].

Can anybody tell me how I implement this in Matlab to find strains by using these formulas as we know all the values on right hand side.

Should I apply For Loop by making another function of strains?

Kindly reply me I will be very thankful to you.

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Plain text icon disppoints.txt14.78 KB
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