[miraboreasu]

Hello
A spherical is meshed by many little triangles. Suppose the triangle is made of elastic material, and Young's modulus is E. . A time-dependent pressure (p=10*t) is equally applied to the inner surface of a spherical. After t1=0.1s, the spherical is broken, and each little triangle is disconnected.
The data I have is the nodes locations (m) of each little triangle like
point1 2.48309 2.51276 2.45388
point2 2.4875 2.50415 2.45103
point3 2.47773 2.50283 2.45452
and velocity (m/s) of each node
v1 -11.352 4.68846 -58.9501
v2 -10.2788 -1.54017 -60.6666
v3 12.043 6.94501 -34.1632
and displacement (m) of each node
d1 0.000131475 -0.000706995 0.000754736
d2 6.02E-05 -0.000662299 0.000711364
d3 0.000147876 -0.000661116 0.000729507


I calculated the areas of each triangle from the edge vectors
I think I can use the pressure times area to get the force, then times displacement.
But I have the displacement for three nodes, how to make them the same direction as my force?

How can I calculate the work has been done by pressure p
I think we need to ignore the work done by the interaction of each triangle

[FMDenaro]

Use the definition for the reversible part of mechanical work:


Int[S] n.v p dS


then you can define linear shape function and integrate.

[miraboreasu]

Originally Posted by FMDenaro

Use the definition for the reversible part of mechanical work:


Int[S] n.v p dS


then you can define linear shape function and integrate.

Thanks, but I didn't get it, can you please explain more? My idea is to use pressure times cavity volume, but I don't know how to get the volume from the locations of the three nodes

[FMDenaro]

Originally Posted by miraboreasu

Thanks, but I didn't get it, can you please explain more? My idea is to use pressure times cavity volume, but I don't know how to get the volume from the locations of the three nodes

The definition I wrote requires only surface values.

[miraboreasu]

Originally Posted by FMDenaro

The definition I wrote requires only surface values.

Can I ask how to get the normal vector n in your equation to perform a dot product with the velocity vector? And how to do the integral? Just times intact surface area?

[FMDenaro]

Originally Posted by miraboreasu

Can I ask how to get the normal vector n in your equation to perform a dot product with the velocity vector? And how to do the integral? Just times intact surface area?

There are simple formula for the integrals of shape functions in a FEM manner

[miraboreasu]

Originally Posted by FMDenaro

There are simple formula for the integrals of shape functions in a FEM manner

I really appreciate your time, but I want more explanations on how to calculate the work.

[LuckyTran]

To get the normal vector take the cross product of any two sides of the triangle. Normalize as you like.


You need said vectors also to calculate the area of the triangles.

[miraboreasu]

Originally Posted by LuckyTran

To get the normal vector take the cross product of any two sides of the triangle. Normalize as you like.


You need said vectors also to calculate the area of the triangles.

Thanks, what is said vector?

[LuckyTran]

You have 3 points and 3 edge vectors from point 1 to 2, 2 to 3, and 1 to 3. To obtain the vector going from 1 to 2, take the (x,y,z) coordinates of point 2, and subtract the (x,y,z) coordinates of point 1. Do the same to get the other edge vectors. Repeat for all faces.

[miraboreasu]

Originally Posted by LuckyTran

You have 3 points and 3 edge vectors from point 1 to 2, 2 to 3, and 1 to 3. To obtain the vector going from 1 to 2, take the (x,y,z) coordinates of point 2, and subtract the (x,y,z) coordinates of point 1. Do the same to get the other edge vectors. Repeat for all faces.

Thanks, LuckyTran, I got the area of my problem which is 4.84e-05
I think I will use pressure times the area to get the force.

I also have the displacement as a vector of each node in the dataset, how to use three displacement vectors to times the force?



BTW, I got the cross product, to get the triangle area. I use 0.5 times the 2-norm of the cross-product result. The idea from here
https://www.youtube.com/watch?v=hQMbD2JT-qA