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Old   May 3, 2001, 13:27
Default FEM/Linear algebra question
  #1
clifford bradford
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Hi I have a question:

Suppose I have a Finte element problem which is in the form of a system of linear equations: [K]{u}={F} where [K] is the sparse symmetric stiffness matrix, {u} is the solution vector of DOFs and {F} is the load vector. Is it possible to solve uniquely for [K] if we know what {u} and {F} are? What if I had the node connectivity (ie the grid), would it be possible then?
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Old   May 3, 2001, 14:29
Default Re: FEM/Linear algebra question
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Peter Attar
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Unless K is diagonal you have too many unknowns to uniquely determine the coefficients.....if you have the grid then you could find K just by assembling it in the normal finite element method manner..assumming you have all the other constants that you need.
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Old   May 3, 2001, 17:05
Default Re: FEM/Linear algebra question
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clifford bradford
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yeah i thought that'd be the answer. It seems strange though that that should be the case. The way I figured was if you knew the grid then you know which entries in the matrix are non-zero and reduce the problem that way. I was thinking of a sort of inverse problem where you didn't quite know the material properties so you could reconstruct the stiffness matrix via the solution. Oh well.
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Old   May 3, 2001, 17:16
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Peter Attar
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You could conceivably construct a stiffness matrix using impulse responses/green's function type method..however I don't think it would be worth the effort.
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Old   May 3, 2001, 20:53
Default Re: FEM/Linear algebra question
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Adrin Gharakhani
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Curious, why you'd want the matrix if you already have the solution? Is the idea: you have "one" solution vector, you want to construct the matrix for possible follow up problems?

Anyway, the answer is already given. Can't do it

Adrin Gharakhani
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Old   May 4, 2001, 23:33
Default Re: FEM/Linear algebra question
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clifford bradford
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yeah that's it. Suppose you didn't have the stiffness matrix but needed it for subsequent calculations... My thinking was that the stiffness matrix is essentially a linear transformation so if you know the solution and the force vector then you might be able to recreate the stiffness matrix. But it was probably wishful thinking.
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Old   May 4, 2001, 23:34
Default Re: FEM/Linear algebra question
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clifford bradford
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can you explain or give references?
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Old   May 4, 2001, 23:47
Default Re: FEM/Linear algebra question
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Peter Attar
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In Meirovitch's Principles of Vibrations there is a decent explanation of construction of a stiffness matrix via Green's function/kernel approach for a linear self-adjoint elastic structure. You may want to do a google search under influence function approach as well.This method of deriving approximate systems of equations from experimental data has been around for a while and was used a lot in aeroelasticity back in the day..
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