# University of Florida/Eml4500/f08.qwiki/Lecture 11

For a more thorough understanding of the Finite Element Method, it is wise to derive the element force displacement with respect to the global coordinate system.

Meeting 12

Recall from Page 6-1, ${\displaystyle k^{(e)}d^{(e)}=f^{(e)}}$ (Equation 1) Note to self; make sure these are 4x4, 4x1, 4x1

Note to self: insert diagrams (2) and the matrices for kq=P

${\displaystyle q_{i}^{(e)}}$=axial displacement of element e at local node ${\displaystyle i}$ ${\displaystyle P_{i}^{(e)}}$=axial force of element e at local node ${\displaystyle i}$

The overall goal is to derive equation 1 from equation 2(already derived in Meeting 4) We want to find the relationship between:

• ${\displaystyle q_{2x1}^{(e)}}$ and ${\displaystyle d_{4x1}^{(e)}}$
• ${\displaystyle P_{2x1}^{(e)}}$ and ${\displaystyle f_{4x1}^{(e)}}$

The relationships can be expressed in the form: ${\displaystyle q_{2x1}^{(e)}=T_{2x4}^{(e)}d_{4x1}^{(e)}}$

Consider the displacement of local node i, denoted by ${\displaystyle d_{i}^{(e)}}$: Note to self: make sure the i is enclosed by a square

Insert figure 12-3

${\displaystyle d_{[i]}^{(e)}=d_{1}^{(e)}i+d_{2}^{(e)}j}$