Discussion Forum

you can find the answer in this ppt: alphard.ethz.ch/Hafner/Workshop/ComsolContact2009.pdf

Hi,

The structural mechanics equations are implemented using the so-called weak PDE formulation. In version 3.5a, click the Weak tab in the Subdomain Settings - Equation System dialog box to see the equations that COMSOL solves.

Best regards,
Magnus Ringh, COMSOL

I can see the weak terms and time dependent weak terms in my subdomain settings - equation system window. However, I don't understand how these fit into equations which are solved for displacement (u).

More generally, I am trying to understand how COMSOL is solving my problem. Here is what I see:

In the weak terms window:
thickness_smps*(-ex_smps_test*sx_smps-ey_smps_test*sy_smps-2*exy_smps_test*sxy_smps)
I don't really understand the physical meaning of this term, other than that it contains stresses and strains.

In the dweak terms window:
rho_smps*thickness_smps*(u_test*utt+v_test*vtt)
This looks like Newton's second law, which I would expect for a structural mechanics problem.

How are these terms assembled into an equation which is solved for displacement? And where is the force term? I have no body force defined, but I do have contact pairs.

Hi

probably what confuses you (and what gave me problems in the beginning) is to understand all the steps COMSOL has taken before reducing the equations to the one above, and also, more important the implicit integrations from COMSOL's way of presenting the data.

From what I have learned (I'm not COMSOL;)
1) the full equations are reduced and simplified analytically, as your input fields might be =0, =1, scalars, functions or even fields of type f(x,y,z,t), which mean that several terms might be dropped, or simplified, or taken out of the integration path
2) the eqautions are per elementary volume "dx*dy*dz" (in your case the integration over dz reduces to the" thickness" as I assume your are in 2D) so you need to imagine these expressions are integrate them over the relevant Domains
3) all expressions are remade such that the final integration are expressed as =0 (for the right term, hence some signs +/- that are not always as first expeced)
3) the weak form expression is established, (this has also implication on the units, test functions might have units too)
4) these equations shown are to be integrated, and then equated to "0"
5) also given constant terms are dropped, if possible before the integration

so the first expression you state is the remaining stess times strain product, while the second is mainly Newton law showing up in the energy conservation expression. But as these expressions are to be integrated, they have units units of densities (per m^3) or fluxes (per m^2) casted into the correct dimensions.
Note COMSOL always consider 3D even when you decide to go for 1D, then everything is expresse as "per m^2" so when you express a variable along a path and integrate over ds, COMSOL adds internally the section A[m^2] that ou have defined in the main node

Hope this helps, COMSOL proposes in their "book" chapter (more in the doc too) a few good math books that also talks about the weak form (i.e Edsberg, or Pepper or Baker's books)

--
Good luck
Ivar

All of the terms in the weak expression should be defined as variables so you can check for example how a term like “sx_smps” relates to displacements and material constants. The equations provide a “standard” solid mechanics weak form which is well explained in many FE text books. There is a good explanation of the weak form in the COMSOL manuals too but in its general form (not specific to solid mechanics).

Nagi Elabbasi
Veryst Engineering

Thanks to everyone for your help! This is starting to make some sense. I don't know what I would do without the forum.

Ryan

Just to close on this thought, is the following equation the one which COMSOL solves for displacement in a transient structural mechanics problem?



Of course, this is the equation in the general form, before COMSOL converts it to the weak form to solve... correct?

Hi

Almost, it's the development of Sigma, the stress tensor, that might vary depending on the material property you are choosing (and or including geometrical non-linearities). Check the doc and the latest literature (i.e. Tadmor & Miller Modelling Materials I&II)

--
Good luck
Ivar

Ivar,

Could you elaborate on this topic? Do you mean the stress tensor will change because it contains the Elastic modulus value for your material? Also, going through the derivation of the equation above in the doc, it looks like "c" is the elastic modulus. Is this true?

Thanks.

Ryan