buckling

I have an eigenvalue solver, subspace iteration, that can get only positive eigenvalues. I have a problem (K - lambda M)u=0 that has pairs of eigenvalues +/- lambda. How can I transform the eigenvalue problem for the solver to search for lambda^2 rather than lambda?

Can buckling and instability of a structure be affected by Eshelby forces?

Submitted by Davide Bigoni on Mon, 01/27/2014 - 18:05

Can buckling and instability of a structure be affected by Eshelby forces?

We provide a positive answer to this question, see http://www.ing.unitn.it/~bigoni/blade.html

Educational iPad app on structural mechanics

Submitted by Julian J. Rimoli on Fri, 12/06/2013 - 16:18

I would like to share with fellow mechanicians an educational iPad app I recently developed. The name of the app is Truss Me! and the main goal is to help students, all the way from high school to college, to build intuition on how truss structures behave. The video below highlights some features of the app:

The app utilizes state of the art simulation techniques to provide the most realistic behavior for the structures.

Buckling of an elastically restrained column

Submitted by rajnishmallick on Fri, 11/29/2013 - 07:10

elastically restrained boundary condition

How to find a response for a pinned-(pinned+ torsion spring) column with sinusoidal axial load?

I am unable to decouple the equations in space and time using variable separable method, with one end pinned-other end pinned with torsion spring as boundary conditions.

Can anyone please help.

Good day.

Rajnish

Subspace Iteration eigenvalues and eigenvectors--efficient implementation?

Submitted by Echeban on Sat, 10/19/2013 - 22:08

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buckling

ANSYS Subspace Mode Extraction

bifurcation buckling

Anyone knows an efficient implementation of the subspace iteration method to compute a few lower eigenvalues and eigenvectors of a generalized problem KG*u=lambda*KS*u or any similar method? i.e., to compute the buckling loads and modes.

I'd like to use something optimized to Intel or amd64 processors or similar, like MKL, etc.

This is for bifurcation buckling analysis. KG is the stiffness matrix. KS is the geometric stress matrix. Both constructed from a FEM discretization.

Math Kernel Library MKL

Submitted by Echeban on Mon, 10/14/2013 - 22:08

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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?