How do I compute the normal vector to a surface with FEM

Vasilis · July 30, 2009, 08:00

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 y-direction. 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 non-zero 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?

Vasilis · July 31, 2009, 05:10

I am trying to calculate the normal on the outer surface of a circle. The circle lies in the y-z plane.

I compute the value of the derivative dz/dy (which is equal to (y-y0)/(z-z0), if the equation for the circle is (z-z0)^2+(y-y0)^2=R^2 ), and there is no good agreement between FEM and theory.
Any ideas why this is happening?

Vasilis · July 31, 2009, 06:37

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

Vasilis · July 31, 2009, 07:59

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?

July 30, 2009, 08:00	How do I compute the normal vector to a surface with FEM	#1
Vasilis New Member Join Date: Apr 2009 Posts: 17 Rep Power: 17	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 y-direction. 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 non-zero 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?

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July 31, 2009, 05:10		#2
Vasilis New Member Join Date: Apr 2009 Posts: 17 Rep Power: 17	I am trying to calculate the normal on the outer surface of a circle. The circle lies in the y-z plane. I compute the value of the derivative dz/dy (which is equal to (y-y0)/(z-z0), if the equation for the circle is (z-z0)^2+(y-y0)^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
Vasilis New Member Join Date: Apr 2009 Posts: 17 Rep Power: 17	My mistake, I can not compute the normal vectors because both x and z are independent variables.

July 31, 2009, 07:59		#4
Vasilis New Member Join Date: Apr 2009 Posts: 17 Rep Power: 17	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?