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

 

[SothunN]

Hello, FEA way!

Thank you for your response.

Regards,
SoThun

 

[SothunN]

Hello, rb1957!

Thank you for your response. I am using both Ansys Mechanical and ABAQUS to model the porous medium with a fracture domain. There is water inside that domain in a static state so I want to know the behavior of traction forces exerted by water or how they vary along the interface of that solid domain. And I have tried to look at both the Ansys Mechanical and ABAQUS manuals, but I still could not find any helpful information.

Regards,
SoThun

 

[rb1957]

apologies, but are you saying you can't follow the math to calculate a surface from a set of points ? and then the normal of that surface at a point ? This is (in my day) 1st or 2nd year uni.

I'd go back to basic math texts if this is the case.

But aren't you interested in ... fluid pressure ?

I wonder how FE models water ? I mean, water doesn't "strain" ... or does it ??

Or are you asking how to do a hand calc to verify the FEA solution ??

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

 

[SothunN]

Hello rb1957!

I wonder how FE models water? I mean, water doesn't "strain"... or does it?? Yes, you are right; it does not. But it is not the problem and what I want to know is just how the traction vector calculates and imposes on the interface of a 10-node quadratic tetrahedron solid element? And I also want to do a hand calc to verify the FEA solution.

Regards,
SoThun

 

[rb1957]

"what I want to know is just how the traction vector calculates and imposes on the interface of a 10-node quadratic tetrahedron solid element" ... this is
"simple" FEA ... the face force is the sum of calculated nodal forces (based on the calculation at the integration points). Th nuance of this is each FE code will likely have a different calculation, but a standard calculation should be available in an FEA text book based on deflections at the integration points from which deflections at the nodes are inferred and then strain and stress at the nodes and then forces.

As for a hand calc, you'll have to describe your problem much better for us (me?) to understand it.

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

 

[SWComposites]

SothunN - you need to call Abaqus tech support to maybe get the answer you need. Its a very obscure question.

 

[SothunN]

Hello SWComposites!

Thank you so much.

Regards,
SoThun

 

[SothunN]

Hello rb1957!

I want to determine the elastic coefficient of a porous medium with a fracture that contains the fluid in a static state inside. Let's say we just ignore the fluid phase and think there are traction forces exerted on the interface of the solid phase. Then I want to define the normal vectors of the traction forces on each element's face of the solid phase in order to calculate the traction forces for the next step. And for the solid phase, I used the C3D10 element (a 10-node quadratic tetrahedron element).

Regards,
SoThun

 

[centondollar]

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).

Just to chime in, this is not strictly speaking the case. Stiffness matrices, mass matrices, damping matrices and other matrices (related to other physics) as well as force vectors are calculated by numerical integration which utilizes integration points, but the solution (e.g., deflection) is determined for the nodes. Then, the solution or gradients (of various orders) of the solution are evaluated in the element (e.g., at integration points) using the shape functions - so nodal results are used to infer other results.

 

[centondollar]

Porous medium with a fracture, coupling of fluid dynamics and solid mechanics - sounds very complicated. How are you expecting to verify the result by a hand calculation? If you doubt the correctness of the implementation of the element in question (things more likely incorrect are user input and parameters used for the fluid), you should probably start with a much simpler problem.

I am not familiar with the details of the C3D10 element, but keep in mind that order of geometry approximation and shape function are not necessarily identical- the geometry of an element face can be locally flat even though the shape function is quadratic and vice versa.

 

[SothunN]

Hello centondollar!

Thank you so much for sharing. Actually, the real RVE of that element's face is curved but in FEA software, it is not really curved; even though I tried to increase the mesh, by using the shape function, I can determine the real curved shape of the surface. And the thing is, I just have no idea how to calculate and determine the directions of those traction vectors caused by fluid on solid (fluid-solid interface) and it is also a type of boundary that I have to impose. So after that, maybe I can define the effective elastic coefficients of a saturated porous medium with fractures of varying aperture as the final result.

Regards,
SoThun

 

[rb1957]

I don't know this specific element but I'd be surprised if the "thickness" faces are generally curved, as one convex element would require the next element to be concave (as they nest together) ... so why not flat faces (and the mid-side node allows for a parabolic stressstrain distribution, unlike the linear stressstrain distribution of a 6 node brick).

The inner and outer faces can be curved.

But the element probably prefers to be a cubic brick, and there'd be limits on the "non-cubic" shape parameters.

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

 

[SothunN]

Hello rb1957!

Thank you so much for your explanation.

Regards,
SoThun