User:Eml4500.f08.echo.sell.cm/HW2

09.10.08
Global FD rel:  K d  =  F 

09.12.08
In compact Notation:

$$\begin{bmatrix}K_{ij}^{}\end{bmatrix}_{6x6} \left\{d_{ij}\right\}_{6x1} = \left\{F_{i}\right\}_{6x1}$$

In the more general form (nxn):

$$\sum_{j=1}^{6} K_{ij}d_{j}= F_{i}$$; i = 1, 2, ..., 6 $$K_{nxn} = \begin{bmatrix}K_{ij}^{}\end{bmatrix}_{nxn}$$ = global stiffness matrix $$d_{nx1} = \left\{d_{j}^{}\right\}_{nx1}$$ = global displacement matrix $$F_{nx1} = \left\{F_{i}^{}\right\}_{nx1}$$ = global force matrix

Recall Element Force-Displacement relationship:

$$k_{4x4}^{(e)} d_{4x4}^{(e)} = f_{4x1}^{(e)}$$ $$k_{4x4}^{(e)} = \begin{bmatrix}k_{ij}^{(e)}\end{bmatrix}_{4x4}$$ = element stiffness matrix $$d_{4x1}^{(e)} = \left\{d_{j}^{(e)}\right\}_{4x1}$$ = element displacement matrix $$f_{4x1}^{(e)} = \left\{f_{i}^{(e)}\right\}_{4x1}$$ = element force matrix

Use an assembly process to go from element matrices(stiffness, displacement, force) to global matrices.


 * Identify the correspondence between the element displacement degrees of freedom's and the global displacement degrees of freedom's.

Global Level: