1. F = 10,000 lb A = 2 in2 E = 30 x 106 psi L = 10 ft θ = 45°
Finite Element Method (FEM) Finite Element Analysis (FEA) Computer Aided Engineering (CAE) 2
F = 10,000 lb
A = 2 in2
E = 30 x 106 psi
L = 10 ft
θ = 45° 3 L θ 1 4 F L

2. Element 1 l and m are direction cosines E Modulus of Elasticity
A Cross Sectional Area
L Length of the Truss Element

3. Element 1 1x 1y 2x 2y 2 1x 1y L 2x 2y 1 F

4. Element 1 1x 1y 2x 2y 2 1x 1y L 2x 2y 1 F

5. Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

6. Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

7. Element 2 1x 1y 3x 3y 3 1x 1y 3x 3y θ 1 F

8. Element 2 1x 1y 3x 3y 1x 3 1y 3x 3y θ 1 F

9. Element 3 1x 1y 4x 4y 1x 4 1 1y F 4x L 4y

10. Element 3 1x 1y 4x 4y 1x 4 1 1y F 4x L 4y

11. Total Stiffness Matrix1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

12. Total Stiffness Matrix1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

13. Total Stiffness Matrix1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

14. Total Stiffness Matrix1y 2x 2y 3x 3y 4x 4y 1x 1y 2x 2y 3x 3y 4x 4y

15. Force and Displacement Vectors

16. Expand the matrix and reorganize the information
{F}=[K]{d}
Expand the matrix and reorganize the information

17. {F}=[K]{d}
Create A matrix Create B matrix Recall that AX=B X=A-1B Find the inverse using Microsoft Excel Calculate X X= {D1x , D1y , F2x , F2y , F3x , F3y , F4x , F4y}

18. Solution X = {D1x , D1y , F2x , F2y , F3x , F3y , F4x , F4y}

19. Displacement and Stress Results

20. Mechanical Simulation

21. Mechanical Simulation Results