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July 30, 2009, 08:00 
How do I compute the normal vector to a surface with FEM

#1 
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I am trying to compute the normal vector to an inclined plate with the FEM.
Based on theory, the normal vector is given by n=(dz/dx,0,1) This is the normal to the top surface. There is no variation in the ydirection. Consider it as a 2D geometry. The plate has length L, and height H, and it is inclined with a slope equal to PHI, so that it's bottom right corner is located at (a,0) and it's top left corner is located at (b,1). If I use the FEM to compute the dz/dx derivative, I will find that it is equal to zero. Does this make sense? The only way to compute a nonzero value for the dz/dx derivative is to solve the problem where the domain was originally a rectangular which deformed to the one I have now. Is this the only way to compute the normal vector with FEM? 

July 31, 2009, 05:10 

#2 
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I am trying to calculate the normal on the outer surface of a circle. The circle lies in the yz plane.
I compute the value of the derivative dz/dy (which is equal to (yy0)/(zz0), if the equation for the circle is (zz0)^2+(yy0)^2=R^2 ), and there is no good agreement between FEM and theory. Any ideas why this is happening? 

July 31, 2009, 06:37 

#3 
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My mistake, I can not compute the normal vectors because both x and z are independent variables.


July 31, 2009, 07:59 

#4 
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So, how do I calculate the normal vectors in a moving boundary domain.
If we assume that x=f(X,Z) and z=h(X,Z) taking the derivative of dx/dZ will give me the rate of deformation. But, we need to compute quantities such as dx/dz. Does anybody has any idea about how to compute the normal vectors with FEM? 

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