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Topic: Problem solving nonlinear equations with matrices
Replies: 4   Last Post: Dec 3, 2012 2:58 PM

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Joshua

Posts: 3
Registered: 12/1/12
Re: Problem solving nonlinear equations with matrices
Posted: Dec 2, 2012 3:09 PM
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"Nasser M. Abbasi" wrote in message <k9edki$v7d$1@speranza.aioe.org>...
> On 12/1/2012 12:12 PM, Joshua wrote:
> > Hello,
> >
> > I am working with the Finite Element Method using MATLAB and I
> > have run into a technical problem. For the basic finite element
> > procedure, a stiffness matrix K and a force vector F are created,
> >and the results we want to find are solved using
> >
> > d=K\F
> >
> > where K and F have no variables, only numbers. Now,
> >however, I am doing a vibration problem and need some help
> >to put a nonlinear equation into the matrix, or to solve it simultaneously.
> >
> > Here's my problem:
> >
> > I have a square matrix K of only numbers and my force vector F is zeros. I cannot just solve
> >
> > d=K\F
> >

>
> How can the load vector be zero?
>
> structure will either have external loads (loads, moments, etc..),
> and if not, there will still be reactions from the supports due to mass
> of structure.
>
> You can't have zero load vector. If it is zero, there nothing to
> solve. There is no stress and no deformation. HW is done. 100% grade.
>
> --Nasser


The load vector is zero due to a few reasons, but the solution is NOT zero. I am working with a vibrating membrane with clamped edges. There will be deformation in the middle, but not on the edges.. The load vector is zero due to the following reasons:

1) The problem formulation involves the divergence theorem. Therefore the load vector is entirely dependent on the boundary conditions at the edge of the membrane.

2) Since the displacements are all zero at the membrane edges, the load vector will contain only zeros.

The solution is not a vector of zeros due to the Mii*di^2=1 equation.



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