I want to compute nodal displacements from nodal stresses.
This is my approach:
I implemented an FEA using force as the boundary condition. And I obtained displacements D1. With my displacements, I computed the stress (sigma xx, sigma yy and sigma xy) acting on each of the node. Now, I want to do the reverse: I want to use the nodal stresses (used as force) acting on each of the node as the boundary condition to compute the displacements of the model (D2).
I am using sigma xx as the force in the x-direction and sigma yy as the force in the y-direction but I am yet to discover how to apply sigma xy. So I leave sigma xy out. But D1 and D2 are not agreeing.
In summary, in Finite Element Analysis, having used the nodal displacements to compute the nodal stresses. how can the nodal stresses be used to recover the same nodal displacements?
nodal stresses are not directly calculated from nodal displacements. We calculate element stresses {s} then to find nodal displacements use {r}=inv(K)*Transpose(B)*{s}
where K is the stiffness matrix and B strain displacement matrix and {s} element stresses.
I used the equation:
{r}=inv(K)*Transpose(B)*{s}
where K is the stiffness matrix and B strain displacement matrix and {s} element stresses.
But my result is not agreeing with the displacement I used initially to obtain the element stresses.
This is what I did:
My nodal strain displacement matrix for each node is a 3 x 8 matrix. I arranged the nodal displacement matrix for all the four nodes to have 12 x 8 matrix which I used as B
K is the element stiffness matrix
Each of my node has three stresses (3 x 1 matrix). I arranged the four to have a 12 x 1 matrix which I used as s.
When I calculated r, the result is different from the displacements.
Please Sir, Kindly help me figure out what I am doing wrong.
Thank you.
In standard FEM, there is no way to get exact values of strain or stress on the nodes. Even when you get it with global or local smoothing methods, these values are just approximations, mainly for post processing.
I think what you want to get is actually not stress (Unit N/m2), but force (Unit N).
To get force, you should integral over the whole element and allocate the total force back to the nodes.
Thank you so much, Yiming Zhang. Please, kindly explain how to do that. Thank you.
I code FEM program myself and don't have much experience about commercial FEM software. I don't know what software you used. Maybe you could try to search help documents with keywords nodal force and stress/strain on Gauss points.
Yes, I also do coding. What is your email address? Let's converse on email. My email address: [email protected]
Thank you so much, Mohammad Sarhil. Can we chat on email. Mine email is [email protected].
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