CIE 633 FINITE ELEMENT ANALYSIS

KALPESH P PARIKH

OVERVIEW

• Introduction• Buckling Analysis - Eigenvalue Buckling Analysis - Non Linear Analysis• Modal Analysis• Transient Dynamic Analysis

Introduction

• Beam with Cross Section I shape• Geometry Information

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

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

Buckling – Eigenvalue Analysis

• Euler’s Buckling Load Formula was used for different Boundary condition and Loading Condition

• Result’s as Tabulated Below

Buckling – Eigenvalue Analysis

Buckling – Eigenvalue Analysis

Buckling – Eigenvalue Analysis

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.

Buckling – Non Linear Analysis

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.

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.

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.

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

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.

Transient Dynamic Analysis

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.

Rene Magritte, Clairvoyance, 1936

Vision of the FutureThank You!