So, welcome back to the second session of our today's lectures.

For those of you who do not have these templates, is there anyone who still needs that?

So I leave it here, maybe anyone else needs them as well.

So let me first recapitulate what we did this morning.

Here we have the weak form of the mechanical problem in 2 or 3D, here given in folk notation.

And we considered the approximation of the strain and of the symmetric gradient of the test function.

So we identified a certain pattern to do that.

After that we computed the stiffness matrix and the external force vector.

This is given here.

And then we did an example where we put all together and computed the ingredients of the stiffness matrix entries.

So this was this here and as a little homework you can try to compute based on the matrices that we have provided during the lecture, the final stiffness matrix.

After that we considered an example where we had a look at a system consisting of two triangular elements

with given nodal forces, no forces applied to the system via surface tractions or body forces.

And we already started to set up the system of equations.

This I copied to the nodes of the present section.

So this was the initial problem.

And as you see we already discussed what entries of the element stiffness matrices are associated with which node.

And since we have a two-dimensional system with two degrees of freedom for each node,

we have groups of two columns and two rows forming block matrices associated with specific nodes.

And here based on the connectivity matrix we already prepared the global node numbers here for the first element and here for the second element.

As far as the system of equations is concerned, maybe I copy that from the nodes directly such that I do not have this line break, a page break.

So this was what we ended with this morning.

And we already filled in the vector of the displacements.

And green are the displacements that are known because they are prescribed to the system.

Red or purple are those which are unknown.

Then we have the external force vector since we have just these point forces which are given,

we could directly fill them in without computing them from the body forces or the surface tractions.

And then the last vector is the vector of reaction forces.

And as you see wherever we have a prescript displacement we get a reaction force.

When the displacement is unknown then the reaction force is zero.

What we now want to do is to assemble the entire stiffness matrix based on that what we have prepared here.

But before I do that my question is, is there anything that we should discuss? Any doubts or questions from your side?

Nothing?

Okay, then let's start.

Maybe we start with some specific entries.

And let us have a look.

Where do I have to put this block matrix here?

This 50, 0, 0, 17.5 in the entire stiffness matrix.

Exactly the first block.

So this is 50, 0, 0, 17.5.

And maybe we can continue with this block here.

This minus 70.5, 17.5, 15 and minus 50. Where do I have to put this?

Second block row and which?

Are you sure?

If I'm asking like this there is some issue.

Which are the global nodes associated with this block entry here?

Which row?

Pardon? Sorry.

Yeah, row or column?

Second row?