CIE 633 FINITE ELEMENT ANALYSIS

1. CIE 633 FINITE ELEMENT ANALYSIS KALPESH P PARIKH

2. OVERVIEW • Introduction • Buckling Analysis - Eigenvalue Buckling Analysis - Non Linear Analysis • Modal Analysis • Transient Dynamic Analysis

3. Introduction • Beam with Cross Section I shape • Geometry Information

4. Introduction Material Properties • ASTM Designation: A992 Steel Section • Modulus of Elasticity: E =30000 Ksi • Poisson ratio =0.3 • Density of Steel= 490 lb/ft3 • Yield Strength Fy= 50 ksi • Tensile Strength Fu = 65 ksi

5. Buckling Analysis • Analysis- Eigenvalue and Non Linear Analysis • Element used Beam 4, Beam 188, Beam 189,Shell 63 and Shell 93. • Boundary Condition Cantilever , Simply Supported, Fixed and pinned. • Loading Condition - Axial Loading - Lateral Loading

6. Buckling – Eigenvalue Analysis • Euler’s Buckling Load Formula was used for different Boundary condition and Loading Condition • Result’s as Tabulated Below

7. Buckling – Eigenvalue Analysis

8. Buckling – Eigenvalue Analysis

9. Buckling – Eigenvalue Analysis

10. Buckling – Eigenvalue Analysis Observation • Model Imperfection in shell 63 and shell 93. • Effect of number of modes does not change the result. • Behavior of the I section Changes like Web Crippling and Flange Yeilding are noticed. • Buckling is about weak axis.

11. Buckling – Non Linear Analysis

12. Buckling – Non Linear Analysis • Buckling Loads are approximate ones. • We calculate Euler’s Buckling Load (Theoretically) and Put in the Command fmax and then we simulate. • Model Becomes Unstable shows Non Linear Behavior.

13. Modal Analysis • What is modal analysis? • A technique used to determine a structure’s vibration characteristics: • Natural frequencies • Mode shapes • Mode participation factors (how much a given mode participates in a given direction) • Most fundamental of all the dynamic analysis types.

14. Modal Analysis • Gives an idea of how the design will respond to different types of dynamic loads. • I tried a case of Cantilever Beam with two masses and noticed the response based on that. • Geometry remains same W 10 x 26. • Element used Beam 4 and Mass 21 • Method used Subspace Method.

16. Transient Dynamic Analysis • Here Study was done for the Same Problem for the Modal analysis but now the at each Time the displacement is noted at the tip and Middle. • Method used is Superposition Method. • Review of Result • Displacement at Tip and mid is plotted against time

18. Transient Dynamic Analysis • Two Concentrated masses are affixed to a cantilever Beam a third mass is resting on the beam . A Hammer strike is applied at free end a Study of Hop of the third mass. • Element used-contact 12, Spring element, combin14, Mass 21 and Beam4. • Hammer Load is applied at t=0.01 and removed at t= 0.02.

19. Transient Dynamic Analysis

21. Transient Dynamic Analysis • When Block Falls and strike a beam. • Element used Beam 4, Plane 42, Contact 171, Target 169 • To see the Dynamic Response of the Beam when Block Falls on the Beam Displacement is noted . • Below Graph shows a Clear Picture.

24. Vision of the Future Thank You! Rene Magritte, Clairvoyance, 1936