## Coding by finite element method a truss

## Coding by finite element method a truss

(OP)

Hello,

I am coding the truss problem by finite element (figure below).I found difficulties at the level of the assembly of the stiffness matrices . Since the beams do not have the same materials, we will not have the same stiffness matrices. In the program , how to do the loop of assembly ? Any ideas please ?

I am coding the truss problem by finite element (figure below).I found difficulties at the level of the assembly of the stiffness matrices . Since the beams do not have the same materials, we will not have the same stiffness matrices. In the program , how to do the loop of assembly ? Any ideas please ?

## RE: Coding by finite element method a truss

each element has L/EA as a stiffness

then at each node assemble the member stiffness in global co-ords

suggest you start with a very simple one first, one you can hand calc.

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

You need to transform the element stiffnesses from local coordinates to global and then assemble in global stiffness matrix K.

E(ii)= Element Young's modulus

A(ii)=element area

L(ii)=element length

## RE: Coding by finite element method a truss

PS: goutam_freelance , I won't neglevt flexion in this example, so the matrix still like the one you showed me ?

## RE: Coding by finite element method a truss

you are asking very basic questions, so get some texts ... there are plenty on-line.

you assemble the global matrix from the grids/nodes/points.

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

different material is "only" an impact to local stiffness.

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

Engineers, think what we have done to the environment !https://www.linkedin.com/in/goutam-das-59743b30/

## RE: Coding by finite element method a truss

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

TTFN (ta ta for now)

I can do absolutely anything. I'm an expert! https://www.youtube.com/watch?v=BKorP55Aqvg

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## RE: Coding by finite element method a truss

Once you have seen and understood the basic procedure for combining the beam matrices into a global stiffness matrix your question will be answered, including why the beams having different lengths, angles and material properties is not a problem.

Regardless of the language you intend using in the end, I suggest setting up a simple problem on a spreadsheet and getting that to work.

The link below has links to a series of blog posts that work through that exercise, ending up with VBA and compiled code. The 3rd post addresses your question in this thread, but it is worth looking at the first two as well.

https://newtonexcelbach.com/2014/01/22/frame-analy...

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

Can you please tell me what is the size of stifness matrix of an inclined element if we consider traction , compression and flexion ? is it 4*4 or 6*6 ?

I have never saw a truss considering flexion problem....

## RE: Coding by finite element method a truss

I assume when you use the term "truss", you are using the standard interpretation that all members carry axial forces only, no shear forces or moments; hence node displacements are translations only, no rotations. (2 DOF per node in a 2D model, 3 DOF per node for a 3D model)

"Frame" members can carry axial forces, shear force, and bending moments, and node displacements include translations and rotations. (3 DOF per node in a 2D model, 6 DOF per node for a 3D model)

Hence a 2D truss element has a 4x4 element stiffness matrix; while a 3D frame element has a 12x12 element stiffness matrix.

http://julianh72.blogspot.com

## RE: Coding by finite element method a truss

There are 6 unrestrained nodes, so you need to find the magnitude of 12 deflections, so your stiffness matrix will be 12 x 12.

Numbering the freedoms in alphabetical order you will have 1,2 at Node E through to 11,12 at Node J. Each freedom number represents a row and column in the stiffness matrix, so for instance row and column 1 and 2 will combine the stiffness values from end 2 of elements AE and BE and End 1 of EF and EH.

If you want to include bending moments (assuming the nodes are fixed rather than hinged) there will be an additional freedom at each node, so your stiffness matrix will be 18 x 18.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

Yes, so you will have 17 matrices, each 6x6. Do you see how these are combined into a single 18x18 global matrix?

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Coding by finite element method a truss

Thank you so much 😊

## RE: Coding by finite element method a truss

Please ,should I find 17 or 18 forces in the postprocessing results ?

## RE: Coding by finite element method a truss

are your reaction points fixed or pinned ?

this is school work, no? please comply with site rules (about student posts).

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

I have 17 elements like shown in the picture I've put on the first comment. Yes AF and FD are elements so the total elements is 17. What is the difference between pinned and fixed ?

Like shown all displacement for A,B,C and D are 0

## RE: Coding by finite element method a truss

do the supports (A thru D) react moment (fixed) or just axial load (pinned) ?

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

## RE: Coding by finite element method a truss

Why do you think there will only be 17 or 18 forces?

You have 17 members, each with 2 ends, and each end has two forces and a moment.

You also have 17 6x6 member stiffness matrices, and the deflections and rotations at each end of each member, so you can find the 17x2x3 member actions by matrix multiplication.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Coding by finite element method a truss

with fixed ends you can anticipate that end member will have different loads at each end, different moments balanced by different shear forces.

sure in this specific case, you can invoke symmetry with your simple load.

another day in paradise, or is paradise one day closer ?

## RE: Coding by finite element method a truss

He's said several times that all the connections and supports are fixed rather than pinned.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Coding by finite element method a truss

another day in paradise, or is paradise one day closer ?