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eigenvalue

Bathe's subspace iteration, how to find the largest eigenvalue/mode?

Does anyone know how to modify Bathe's subspace iteration eigensolver to compute the highest eigenvalue instead of the smallest ?

Math Kernel Library MKL

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I want to use Intel Math Kernel Library (MKL) to calculate the bifurcation loads and modes in my custom FE program. MKL has many algorithms and I want to use the most efficient one.
Basically, I need to find a few eigenvalues lambda_i and eigenvectors u_i for the problem
KG * u = lambda * KS * u
where KG is the stiffness matrix and KS is the geometric stiffness matrix, also called stress-displacement matrix.
Is KG supposed to be positive definite?

AliADawood's picture

Bifurcation Analysis in Abaqus

Hello Everyone,

Im relatively new to Abaqus and I have to carry out a bifurcation analysis of a pipe. Once that is done I need to add the imperfection wavelength and amplitude calculated to the pipe and carry out further simulations.

 

Ive been trying very hard to get a direction as to where to start with it. Can anyone please help me with it? I know that you need to carry out a buckle analysis that will give you a wrinkle pattern on the pipe. This inturn will add up to the bifurcation scheme that you get.

 

Wanted: Fast FEA Solvers...

Summary:

I am thinking of informally conducting a specific case-study concerning the FEA solvers. The reference problem is a very simple but typical problem from stress analysis, leading of course to the linear systems: Ax = b and Ax = Lx.

I seek advice as to what software libraries currently available in the public domain would be best to use---the ones that would be fastest in terms of execution time for the reference problem.

I have a personal and longer-term research interest with certain issues related to the solvers technologies.

bifurcation buckling using ABAQUS

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The following is taken from the book Concepts and applications of Finite element methods by Cook, Malkus and Plesha.

 For bifurcation buckling, we have the following eigenvalue problem:

(K+Lambda Ksigma)delta d= 0 

principal directions for 4th order tensor

Is it possible to find eigenvalues and principal directions for a 4th order tensor? How?

For a zero order tensor? for a first order tensor? for a third order tensor.........

many thanks

lqkhai's picture

Find eigenvalues of the coupled differential equations by Finite Difference Method.

Hello everybody,

The coupled differential equations need to solve as following:

Could you help me to discretize this systems and find the eigenvalue λ  numerically using finite difference method?

 

Thanks in advance,

 

lqkhai 

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