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

$$q^{(e)}_{i}$$=axial displacement of element e at local node $$i$$ $$P^{(e)}_{i}$$=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: The relationships can be expressed in the form: $$q^{(e)}_{2x1}=T^{(e)}_{2x4}d^{(e)}_{4x1}$$
 * $$q^{(e)}_{2x1}$$ and $$d^{(e)}_{4x1}$$
 * $$P^{(e)}_{2x1}$$ and $$f^{(e)}_{4x1}$$

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

Insert figure 12-3

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