# 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, $k^{(e)}d^{(e)}=f^{(e)}$ (Equation 1) Note to self; make sure these are 4x4, 4x1, 4x1

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

$q_{i}^{(e)}$ =axial displacement of element e at local node $i$ $P_{i}^{(e)}$ =axial force of element e at local node $i$ The overall goal is to derive equation 1 from equation 2(already derived in Meeting 4) We want to find the relationship between:

• $q_{2x1}^{(e)}$ and $d_{4x1}^{(e)}$ • $P_{2x1}^{(e)}$ and $f_{4x1}^{(e)}$ The relationships can be expressed in the form: $q_{2x1}^{(e)}=T_{2x4}^{(e)}d_{4x1}^{(e)}$ Consider the displacement of local node i, denoted by $d_{i}^{(e)}$ : Note to self: make sure the i is enclosed by a square

Insert figure 12-3

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