BAsic doubt-1D element

[idly123]

1)How do i get the stiffness matrix of a 3 node one dimensional quadratic element( i have problem in integration).do i have to express the coordinate of interior node in terms of end nodes( non dimensionalize)

2)Can a combination of such elements be assembled to form a bigger one dimensional element. is the ususal assembly procedure valid. can i have 2- 3 noded id elements combined to form a structure with 5 nodes

please help me Raj

 

[brad]

A) If I didn't make a mistake, the matrix is:

[ 7 -8 1]
|-8 16 -8|
[ 1 -8 7]

Multiplied by AE/8L

B) I can't think why the usual assembly procedure woudn't hold.

The easiest way to find out is assembly it and compare your matrix answers with hand calcs for a variety of displacements vectors for which you can obtain a solution.
Brad

 

[brad]

That would be 1) and 2) instead of A) and B) respectively.

 

[idly123]

Thanks for response i shall check it up

shouldnt it have a square term of length.......u being quadratic
Raj

 

[idly123]

I forgot to ask what is L any way in the K u have written is it the whole length between first and 3rd node or is it between first and second node Raj

 

[brad]

Sorry,
Been on the road.
As defined, L is the total length (for my example, L is the length between node 1 and 3, with node 2 seated exactly in the middle).

I don't think that L is squared (there were 2nd order variables in the derivation, but they fall out).

The units as I described fall into place properly; hence I'm pretty sure that I didn't make a mistake (but please verify).
Brad

 

[idly123]

But why at all do we take a node at center ? why not at any other length in between
Raj