Computer Aided Engineering

Applications

4. Finite Element Analysis4.1 Introduction

4.2 FEA process

Engi 6928 - Fall 2014

4.2 FEA process

4.3 FEA Definitions

4.4 FEA Example

4.1 Introduction4.1 Introduction

• Engineering problems are approached using mathematical models (Approximations) of the physical system.

• The solution is found by solving the mathematical equations describing the system and the constraints.

• Finite Element Analysis is an effective discretization• Finite Element Analysis is an effective discretizationprocedure to numerically solve engineering problems.

• Powerful computer tools are available to perform FEA.

4.1 Introduction4.1 Introduction

Requirements

You can design your entry in any CAD software You can design your entry in any CAD software

as long as STEP or IGES file is submitted.

Material: Ti-6Al-4V

Service Temperature: 75 F

(wall thickness): 0.050 in.

- Assume yield strength is 131 ksi.

- Participants should target the lightest weight

designs.

4.1 Introduction4.1 Introduction

Your challenge

Material ABS M30

Max deflection at 100lbf < ½”

Fail between 100 and 200 lbf

Minimize Mass

Allow fixture with standard tools

4.2 4.2 FEA processFEA process

1. Problem Definition

2. Meshing - Subdivide the solution domain to nodes and

elements

• Assume element type and shape function

• Construct the global stiffness Matrix

3. Apply boundary conditions, loading

4. Solve the equations (i.e. Displacement of nodes,

Pre

-Pro

cess

ing

4. Solve the equations (i.e. Displacement of nodes,

temperature of nodes)

5. Obtain other information , Stresses, strain, heat flow

etc.

6. Model Refinement

Post-Processing

Solving

Tutorial Video : Formula 1 FEA Spindle design video series

Search string: open university Finite element analysis

https://www.youtube.com/playlist?list=PL30D4A9A59A75C20B

4.2 FEA process4.2 FEA process

4.2 FEA process4.2 FEA process

4.3 FEA definitions4.3 FEA definitions

Types of studies

• Linear Static structural analysis– Assumes gradual loading (no inertial, damping forces), small displacement, linear elastic response.

• Nonlinear - nonlinear elastic response, large displacement.displacement.

• Frequency – Analyse natural frequencies and mode shapes of a system.

• Dynamic – Considers inertial forces, damping forces.

• Buckling – Analyse buckling loads, mode shapes, Buckling load factor.

4.3 FEA definitions4.3 FEA definitions

Element Types» 2D/ 3D Truss element

• Node has 2 translational degrees of freedom for 2D.

• Transmits loads axially only

• Constant cross section of element

» 2D/3D Beam element

• Node has 2 translational and 1 rotation DOF for 2D• Node has 2 translational and 1 rotation DOF for 2D

• Transmits transverse loads and moments

» 2D/3D Shell element

• Node has 2 translational degrees of freedom

• Used in axi-symmetric studies, planar systems

» 3D tetrahedral element

• Each node of the element has 3 translational DOFs.

• Used for analysis of solid models

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4.3 FEA definitions4.3 FEA definitions

Shape Functions

Linear Quadratic Cubic

•Higher order shape functions improves the accuracy of results.

•Increasing the number of elements in a region improves the accuracy of results.

•Convergence analysis attempts to improve the accuracy of a study by adaptively

increasing the model complexity of areas with high stress concentration.

•P-adaptive convergence increases the number of elements to converge to accurate

results.

•H-adaptive convergence increases the order of the shape function to converge to

accurate results

4.3 FEA definitions4.3 FEA definitions

Types of constraints

Fixtures – Used to define geometric constraints of the model w.r.t. The

enviroment. i.e. Fixed, rollers, sliders.

Loads – Used to define gravity, external forces, torques and pressure

distributions acting on the mesh

Connectors- A connector simulates the behavior of a mechanism without

having to create detailed geometry. Ex. Walls, bolts, bearings, springshaving to create detailed geometry. Ex. Walls, bolts, bearings, springs

Load

Fixture

Connector

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4.3 FEA definitions4.3 FEA definitions

Types of result figures

FOS Plot

Ductile - Von misses criteriaStress plot (VonMissses)

Displacement plot

Ductile - Von misses criteria

Brittle - Mhor-coulomb criteria

Design insight

4.3 4.3 FEA definitionsFEA definitions

• Buckling failure of members under compression

• Buckling Load Factor:

4.4 FEA Example4.4 FEA Example

ReferencesReferences

• Saxena, Anupam, Sahay, Birendra, Computer Aided

Engineering Design, Chapter 11,

http://link.springer.com/book/10.1007%2F1-4020-3871-2

(Available @ MUN on Springer link)

• Saeed Moaveni, Finite Element Analysis Theory and • Saeed Moaveni, Finite Element Analysis Theory and

Application with ANSYS (3rd Edition).