User:Eml4500.f08.a-team.melvin/Lecture 22

Justification of assembly of $$ \underbrace{ element \ stiffness \ matrix }_{\underline{k}^{(e)} } $$ into  $$ \underbrace{ global \ stiffness \ matrix }_{\underline{K}} $$

e = 1,...,n (# of elements)

Consider the example of a two-bar truss.

Recall element FD relation: k(e) d(e) = f(e)

p.11-3: Euler cut principle, method 2 (equilibrium of global node 2)

p.4-2, 4-3: FBDs of element 1 and element 2, element dofs. d(e)

p.8-3: For node 2, identify global dofs to element dofs for both element 1 and 2.



$$ \sum Fx = 0 $$ = -f3(1) - f1(2) = 0

$$ \sum Fy = 0 $$ = P - f4(1) - f2(2) = 0

Next, use element FD relation k(e) d(e) = f(e)