User:Eml4500.f08.RAMROD.F/HW4

 Wednesday October 15 

Justification of assembly of element stiffness matrices into global stiffness matrix K. $$K^{(e)} \; \; e=1, ... ,n_{el}\;$$

Consider the 2 bar truss example. Recall Force displacement equation.

$$ K^{(e)}_{4x4} \cdot d^{(e)}_{4x1} = F^{(e)}_{4x1}$$

You then can use the Euler cut method to establish the equilibrium of global node 2

Using the free body diagram of element one and of element 2 you can describe the elements degrees of freedom $$d^{(e)}_2 $$

$$d_2=d_2^{(1)}$$

$$d_3=d_3^{(1)}=d_1^{(2)} $$

$$d_4=d_4^{(1)}=d_2^{(3)}$$

$$d_5=d_3^{(2)}$$

$$d_6=d_4^{(2)}$$

Equilibrium of node 2





$$\sum{F_x}=-f_3^{(1)}-F_1^{(2)}=0$$

$$\sum{F_y}=P-f_4^{(1)}-F_2^{(2)}=0$$

Then you would use element force displacement relation $$K^{(e)}_{4x4} \cdot d^{(e)}_{4x1} = F^{(e)}_{4x1}$$