User:Eml4500.f08.a-team.robinson/Lecture 9/5/08

Steps to solve simple truss system:

1. Global picture (description) -At structure level: *global d.o.f.’s (displ. d.o.f’s) --> unknowns in general *global forces -Actually --> displ. d.o.f.’s are partitioned into: *a known part: e.g. fixed d.o.f.’s, constraints *an unknown part: solved using FEM -Similarly for the global forces: *a known part: applied forces *an unknown part: reactions

2. Element Picture -Element d.o.f.’s and element forces:
 * either in global or local coordinate system

3. Global FB relation -Element stiffness matrices in global coordinates -Element force matrices in global coordinates -Assembly of element stiffness matrix and element force matrix into global FB    relation:  K * d = F  “free-free system” (unconstrained)  K=singular
 * K --> N x N
 * d --> N x 1
 * F --> N x 1

4. Elimination of known d.o.f.’s to reduce the global FB relation -Stiffness matrix non-singular --> invertible -K * d = F     *K --> M x M      *d --> M x 1			M < N      *F --> M x 1 -M = number of unknown displ. d.o.f.’s -N = number of both known & unknown d.o.f.’s -K is non-singular --> K(-1) exists *d = K(-1) * F

5. Compute element forces from now known d --> elem. stresses

6. Compute reactions (unknown forces)

Specific example to see how method works:

Numbering the displ. d.o.f.’s: -Follow order of global node number -For each node, follow the order of global coord. axes, number displ d.o.f.’s for that node -Global forces --> same thing