FEM-Stiffness matrix 3

[HomerWelsh]

Hi everyone,

I am very new to the FEM. I have been doing some basic linear analysis using the COSMOS application within Solidworks. However, I find my colleagues accept the post-processed results as the 'truth'. I am not saying I don't believe it's output but I am from a more traditional background so I wish to check the analysis with some hand calculations. The part in question I can assume as a single element.

Please forgive my ignorance but I have consulted the two available texts on the FEM and neither explain the formulation of the stiffness matrix, K. I see the A*E/L is from deflection theory. It is the construction of the stiffness matrix with 'ones' and 'zeros' I cannot presently understand. I have attached a word document with a simple example from wikipedia and the associated K matrix.

Thanks in advance to the experts who can answer this.

Best Regards,
H.

 

[ferryscott]

Some uni notes I found online:

http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/num/midkiff/theory.html

I would normally steer clear of wikipedia where possible. The notes above are ok, there's plenty more to be found online though (this was just a quick search).

I'd recommend getting yourself on a course to be honest.

I went on a NAFEMS one a few months back (UK based) 'Practical Stress Analysis and the Finite Element Method'. It was particularly good in showing you how to validate your modelling/analysis, which I guess is what you're after.

 

[IDS]

You might find this series of posts from my blog useful:

http://newtonexcelbach.wordpress.com/2009/01/31/frame-analysis-with-excel-1-single-beam/

I build up a frame analysis program in Excel starting from basics (a single beam), through sloping beams, continuous beams etc. Follow the links in the comments for the next relevant post, or search the blog on frame analysis.

The matrix in your link is just saying:

(ux1 - ux2)AE/L = fx1
(-ux1 + ux2)AE/L = fx2

where ux1, ux2 are the horizontal deflections at end 1 and end 2 and fx1, fx2 are the axial forces at end 1 and 2.

The other matrix elements are zero because the memeber is horizontal and a truss element, so transverse forces, bending and shear, don't come into it. An example stiffness matrix for an inclined beam, including bending is shown here:

http://newtonexcelbach.files.wordpress.com/2009/02/beam2-1.jpg

(Which might or might not prove useful!)

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[chris9]

A good practical FEA book I recommend is 'Building Better Products with Finite Element Analysis'. It's a bit old but still relevent. The Nafems courses are also very good.

Chris

http://www.value-design-consulting.co.uk