Normal vectors

[SothunN]

Hello everyone!

Is there anyone can explain me on how normal vectors are computed for both flat and curved surfaces of the elements?

regards, 

Sothun

 

[rb1957]

which "normal" are you asking about ? "Normal Force" is an in-plane normal to the edge of the element. Pressure is a load normal to the surface of the element.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SWComposites]

For a three nodes triangle element it is trivial to calc the normal vector.

For a four noded shell, the normal vector is probably the average of the four normals calculated using each of the 4 sets of 3 nodes of the element (its probably in a FE text book somewhere; and I recall its in the Nastran theory manual somewhere).

 

[sdm919]

Different codes may have different definitions, but the following is probably typical.

For a 4 node shell element (quad), compute the mid-points of each side. Connect the mid-points on opposite sides with vectors. These 2 vectors are in general not perpendicular to each other, but they do define a plane which is taken to be the element x-y plane. The cross product of those 2 vectors defines the element normal (element z-axis). One of the in-plane vectors becomes the element x-axis. Finally, cross the x-vector with the z-vector to get the orthogonal y-axis. (The second mid-point vector was just an intermediate step).

Also note that for non-planar quad elements, the 4 corner nodes will not lie in the average mid-plane as defined above. 2 of the corner nodes will be above that plane by a certain distance, and 2 of them will be below by the same distance. This defines the "warping" of the element. Too much warp is bad. To minimize warping, it is best to define the mesh so that it "follows" the surface contours. For example, if you mesh a cylindrical surface with rows of nodes running axially and hoop-wise, the elements will be flat (no warp). But if the node lines run +/-45 degrees to the axial direction, the quads will be warped.

 

[SothunN]

Hello rb1957!
Thank you for your answer. Here I want to talk about the traction forces exerted on the surfaces of an element, especially on the curved surfaces of the element.

 

[SWComposites]

what FE code?
what element types?
do you mean applied forces or calculated forces?

 

[SothunN]

Hello SWComposites!
Thank you for your answer. I use the quadratic tetrahedron element, but I have chosen only the surface of that element to study the traction force. And to do that, I have to calc the normal vector first, so I do not know how to do that. And I also want to know the location of those vectors (at the centre of the element or on every node of that element's face?)

 

[SothunN]

Hello sdm919!
Thank you for your answer. I want to impose the traction forces on my quadratic tetrahedron element's surface. And on one face of that element is a curved face and I want to calc the normal vectors of those forces and define the location of the normal vector, whether they are on the center or on each node of that curved face. So first I need to find a way to calc those normal vectors and then I can find the traction force on that element's face.

 

[rb1957]

I guess "traction forces" describes the in-plane normal force along the edge of a surface (or face of a solid).

Since you've said you're using solid elements then the answer is much easier. You are applying a force normal to the face (surface) of the element. So position you nodes so that the face is planar. Then the normal to the plane is easy to establish, Since this sounds like research, I'd start with very simple 3D elements, a cube, and work up to more complicated elements. Are you using 6 node, or 20 node, bricks ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SothunN]

Hello rb1957!
I am using a 10-node quadratic tetrahedron solid element and there is only one curved face of that element on which I want to study the behavior of traction forces exerted on that face (surface traction). But for me to determine those traction forces, first I need to know how to calculate and define the normal vectors, which can help me get the final result of traction forces.

 

[SWComposites]

If the face is curved, then the normal vector is different at every point on the face.

Fit an equation thru the 6 node points on the face, and from that determine the normal at any point.

 

[rb1957]

ok, just because you've a 10 node brick doesn't mean the thickness faces aren't flat, but maybe they are. There is still a "simple" equation to these points, to the face that FeMap knows ... I think you should be able to extract this, but maybe FeMap is hiding it's secrets ?

I think you need to work through how the element actually works, where the integration points are, how does it determine the element normal force from these.

I think it'd be interesting to figure out how accurate are generally non-cubic elements (how element shape and element loading affect the element results).

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[SothunN]

Hello SWComposites!
Of course, you are right. And the problem is that I could not find those kinds of equations but if you know, please let me know about that too.

Regards,
SoThun

 

[SothunN]

Hello rb1957!

I have tried to look at those things but I still cannot figure out how they calculate and determine the normal vectors on a flat or curved surface. If you have any ideas about that, please let me know, because it will help me solve the problem.

Regards,
SoThun

 

[SWComposites]

A Google search will bring up several examples of how to determine normal vectors for 2 and 3 D equations.

 

[SothunN]

Hello SWComposites!

I have been looking at some of them but I have found that they are not helpful to me in applying them to my problem. Because I need to compare it with what I have done with the numerical method. So I wonder is normal vector imposed at the center of an element's face or on each node of an element's face?

Regards,
SoThun

 

[FEA way]

Apart from general FEM textbooks, you could check the source codes of some open-source FEA software.

 

[rb1957]

the face has 9 nodes defined on it, use these co-ords to define the surface. I'd assume a parabolic surface (parabolic in x and y) ... Ax2+Bx+C+Dy2+Ey.

As your uni math will remind you this is under-defined, so use the "sum of squares" best fit ... google can remind you of the math.

But the program knows this (the equation of the surface) already ... it didn't put those points in space. Maybe ask the help desk ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[rb1957]

"So I wonder is normal vector imposed at the center of an element's face or on each node of an element's face?"

the answer is "both". FEA works with nodes, so results are calculated at nodes (ok, I know they're not, they are calculated at integration points within the element and then the nodal results are inferred). The normal force at a node is a portion of the element's normal force for the face of the element. This is summed, yes all the different directions are taken into account, this should be explained in a FEM text on 3D elements. At a node you can also get the summed normal force (from all the elements that share that node).


"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[rb1957]

what FE code are you using ?

You being civil, is this RC ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.