## Simple Finite Element noob question

## Simple Finite Element noob question

(OP)

Hi,

I am new to FEM theory, and I have a small issue with a very simple example.

It's a square in x/y as shown below. "Bottom" nodes, (0) and (3), are fixed.

There is a 10000 kN down force at node (1) and a horizontal force of 11000 kN at node (1).

Simple 2D mesh.

Nodes (0) and (3) are fixed.

All sides equal length and k values.

length = 1000 mm

k = 10000 kN/mm^2

Here are the stiffness matrices for each beam one at the time, and finally the sum.

As the last step, the rows/columns representing the fixed nodes are removed.

However, I end up with an unsolvable matrix.

What am I doing wrong?

I am new to FEM theory, and I have a small issue with a very simple example.

It's a square in x/y as shown below. "Bottom" nodes, (0) and (3), are fixed.

There is a 10000 kN down force at node (1) and a horizontal force of 11000 kN at node (1).

#### CODE -->

y ^ | | Fy | | | beam 1 | (2) v (1) +----------+--->Fx | | | | beam 2 | | beam 0 | | | | +----------+ ------> x (3)^ beam 3 ^(0)

Nodes (0) and (3) are fixed.

All sides equal length and k values.

length = 1000 mm

k = 10000 kN/mm^2

Here are the stiffness matrices for each beam one at the time, and finally the sum.

As the last step, the rows/columns representing the fixed nodes are removed.

However, I end up with an unsolvable matrix.

What am I doing wrong?

#### CODE -->

beam 0 stiffness matrix 0 1 2 3 0 1 2 3 0 1 2 3 F [N] 0 0 0 0 0 0 0 x 1 0 10000 0 -10000 0 y 1 2 0 0 0 0 -11000 x 3 0 -10000 0 10000 -10000 y 2 4 x 5 y 3 6 x 7 y beam 1 stiffness matrix 0 1 2 3 0 1 2 3 0 1 2 3 F [N] 0 0 x 1 y 1 2 10000 0 -10000 0 -11000 x 3 0 0 0 0 0 y 2 4 -10000 0 10000 0 0 x 5 0 0 0 0 0 y 3 6 x 7 y beam 2 stiffness matrix 0 1 2 3 0 1 2 3 0 1 2 3 F [N] 0 0 x 1 y 1 2 x 3 y 2 4 0 0 0 0 0 x 5 0 10000 0 -10000 0 y 3 6 0 0 0 0 0 x 7 0 -10000 0 10000 0 y beam 3 stiffness matrix 0 1 2 3 0 1 2 3 0 1 2 3 F [N] 0 0 10000 0 -10000 0 0 x 1 0 0 0 0 0 y 1 2 x 3 y 2 4 x 5 y 3 6 -10000 0 10000 0 0 x 7 0 0 0 0 0 y Main (summed) stiffness matrix 0 1 2 3 0 1 2 3 0 1 2 3 F [N] 0 0 10000 0 0 0 0 0 -10000 0 0 x 1 0 10000 0 -10000 0 0 0 0 0 y 1 2 0 0 10000 0 -10000 0 0 0 -22000 x 3 0 -10000 0 10000 0 0 0 0 -10000 y 2 4 0 0 -10000 0 10000 0 0 0 0 x 5 0 0 0 0 0 10000 0 -10000 0 y 3 6 -10000 0 0 0 0 0 10000 0 0 x 7 0 0 0 0 0 -10000 0 10000 0 y Constrained (fixed) nodes removed stiffness matrix 1 2 2 3 0 1 F [N] 1 2 10000 0 -10000 0 -22000 3 0 10000 0 0 -10000 2 4 -10000 0 10000 0 0 5 0 0 0 10000 0

## RE: Simple Finite Element noob question

## RE: Simple Finite Element noob question

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: Simple Finite Element noob question

The link below works through setting up a 2D frame analysis on a spreadsheet starting with a single beam.:

https://newtonexcelbach.com/2009/01/31/frame-analy...

There is a link to the next post in the series at the bottom of each post.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Simple Finite Element noob question

you say "stiffness = ..." ... axial stiffness ? (you'd think so) ... but your frame requires bending stiffness to work ... you need to specify a diagonal member (say 1-3).

looking at beam "0" ("odd" that number !)

node "0" is fixed in x (zero deformation) but has deformation in y (finite k)

node "1" is also fixed in x, deformable in y

... that seems very "odd" ...

is this homework ? (doesn't look like "real" work)

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

## RE: Simple Finite Element noob question

And no, it’s not “homework”. I am implementing some basic FEM in software and I am in the process of adding some basic unit tests, where this came up.

With one or two diagonals, I get a solvable stiffness matrix.

... and I guess this is trusses? Sorry for the confusion.

## RE: Simple Finite Element noob question

node "0" should not deflect under X or Y loads.

node "1" should only deflect under Y loads (as far as beam "0" is concerned, and deflect under X loads as far as beam "1" is concerned.

There are plenty of texts out there on this.

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

## RE: Simple Finite Element noob question

I bought a copy and it has been one of the best FEA books I have.

https://www.amazon.com/Introduction-Finite-Element...