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Weak constraint in PDE for linear solid mechanics
Posted 19 sept. 2018, 07:22 UTC−4 Structural & Acoustics, Structural Mechanics, Equation-Based Modeling Version 5.1 1 Reply
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Hi,
I am currently doing my PhD studies and I have a problem understanding the weak constraint/weak contribution in the Weak Form PDE toolbox. I'm trying to implement an RVE (Representative Volume Element) in 2D using Weak Form PDE. Everything worked great until I tried to implement a constraint equation.
The equation I need to implement as a constraint is in the following form:
vint(u*x) = 1
That is, I want to constraint the volume integral (in the whole domain) of u*x (where u is the displacement field in x-direction and x is just the nodal x-coordinates) to a constant value, here 1. I've tried using the Weak constraint node, but get singular matrix. The pointwise constraint works better, but the results are completely wrong (and give a great error).
Is there a way to implement such a constraint in Comsol, and how?
Thanks for any help!
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Hi,
If you are using a Weak Constraint node, it seems like you apply it to a domain (that is for each mesh node).
But since you already use a volume integral, there is only a single constraint with a single Lagrange multiplier. So it is the tools under Global... you should use. There you will find a Pointwise Constraint (which you would write something like "intop1(u*x)-1".
There is no predefined weak global constraint. If you really need that one, you will have to write it yourself, like "test(lm)*(intop1(u*x)-1)+lm*test(intop1(u*x))". Here 'lm' is your scalar Lagrange multiplier, to be defined in a Global Equations node.
Regards,
Henrik
Henrik Sönnerlind
COMSOL