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FEM Theory question

Posted 5 apr 2012, 18:28 GMT-4 Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 4.2a 2 Replies

Marco Chrappan
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I remember from my FEM course at university that systems equations to find displacement like:

[K][u]=[F]

cannot be solved if the body is free (no boundary conditions). Matrix K becomes singular and cannot be inverted. Solutions cannot be found. Is this right?

If rigid body displacements are permitted there isn't a single solution to equilibrium problem. Now what happens in COMSOL if I put a harmonic load on a body with no boundary conditions (no constraints) and perform a frequency response analysis? Will it converge to a solution? Will it give me an error? Or does COMSOL output a solution in some way (even if that has little or no sense)?

Marco
2 Replies Last Post 7 apr 2012, 07:51 GMT-4
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago 6 apr 2012, 00:31 GMT-4
If rigid body displacements are permitted there is no single solution as you said, but only in static analysis. In dynamic analyses (transient or harmonic) there is a unique solution. In that case the effective [K] matrix is not singular, due to the contribution from the inertia term.

Nagi Elabbasi
Veryst Engineering
If rigid body displacements are permitted there is no single solution as you said, but only in static analysis. In dynamic analyses (transient or harmonic) there is a unique solution. In that case the effective [K] matrix is not singular, due to the contribution from the inertia term. Nagi Elabbasi Veryst Engineering
Marco Chrappan
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Posted: 1 decade ago 7 apr 2012, 07:51 GMT-4
Yes. The equation will be then like:

[M][a]+[K][u]=[F]

where a is d2u/dt2 (in absence of a better notation here...) and F is a vector of harmonic loads.

But this kind of boundaries/constrains give good results, or maybe the matrixes become bad conditioned?

Yes. The equation will be then like: [M][a]+[K][u]=[F] where a is d2u/dt2 (in absence of a better notation here...) and F is a vector of harmonic loads. But this kind of boundaries/constrains give good results, or maybe the matrixes become bad conditioned?

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