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Weak Form PDE

Posted 2011年1月4日 GMT-5 12:02 Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 4.0a 4 Replies

Elia Picault
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Hi everyone,

I'm just beginning to use Comsol so I hope somebody will be able to help me.

I'm trying to use a weak form PDE to solve the equation : variation(P)=0 where P is the potential energy of a beam (Hamilton's principle for statics) :

P = Int_over_1D_domain( Expression_1 ) + Expression_2

With : Expression_2 = F_X*(X(x=L)-L) - F_Y*Y(x=L) -C*theta(x=L) (x=L is the free end of the beam)

F_X, F_Y and C are constants defined in the section parameters.

X(x), Y(x) and theta(x) are my dependent variables.

And x is the spatial coordinate defined by Comsol for my 1D domain (i.e. the curvilinear abscissa of beam
which is not extensible).


Thus I built a 1D model, then added a PDE in weak form for the physics and entered test( Expression_1 ) in the weak field. So far no problem encountered (except for defining units but I worked out this one). I also defined initial values, appropriate Dirichlet boundary conditions and weak constraints with Lagrange multipliers (so that the beam is not extensible).

My problem is that I don't know where/how to define the other terms of P (i.e. those of Expression_2). Does anyone know how to do that?

Thanks a lot,

Elia





4 Replies Last Post 2011年1月6日 GMT-5 05:48
Elia Picault
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Posted: 1 decade ago 2011年1月6日 GMT-5 03:51
No one?
No one?
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago 2011年1月6日 GMT-5 04:55
Hi

I suppose if you upload your model it would be easier for us to really follow what you are doing, I have some problems understanding your equations just from the text ;)

--
Good luck
Ivar
Hi I suppose if you upload your model it would be easier for us to really follow what you are doing, I have some problems understanding your equations just from the text ;) -- Good luck Ivar
Elia Picault
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Posted: 1 decade ago 2011年1月6日 GMT-5 05:46
Good idea. So here they are.

First I 'm wondering if my two models are equivalent. In the first model, I used weak constraints to implement two constraints that must be verified by the solution. In the second model I implemented directly these constraints in the weak field of my PDE using two Lagrange multipliers that I defined as dependent variables. DO you think it is equivalent?

If they are not equivalent, the file Poutre_GD_statique_2.mph is the good one.

Second, when I run the model I get the following error : "Failed to find consistent initial values. Singular matrix.". Since the model lacks the terms I called Expression 2 in my first post, it's not surprising that the simulation does not work out.

My question is how do I add these terms to my model since I can't put them on the weak field of my PDE (since they do not need to be integrated over my 1D domain, thus are not part of the weak expression).

If something is not clear please ask me, I'll try to explain it in another way.

Thanks a lot.

Elia
Good idea. So here they are. First I 'm wondering if my two models are equivalent. In the first model, I used weak constraints to implement two constraints that must be verified by the solution. In the second model I implemented directly these constraints in the weak field of my PDE using two Lagrange multipliers that I defined as dependent variables. DO you think it is equivalent? If they are not equivalent, the file Poutre_GD_statique_2.mph is the good one. Second, when I run the model I get the following error : "Failed to find consistent initial values. Singular matrix.". Since the model lacks the terms I called Expression 2 in my first post, it's not surprising that the simulation does not work out. My question is how do I add these terms to my model since I can't put them on the weak field of my PDE (since they do not need to be integrated over my 1D domain, thus are not part of the weak expression). If something is not clear please ask me, I'll try to explain it in another way. Thanks a lot. Elia
Elia Picault
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Posted: 1 decade ago 2011年1月6日 GMT-5 05:48
The second model.
The second model.

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