View by Category

The presentation will start after a short

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

(15 second) video ad from one of our sponsors.

Hot tip: Video ads won’t appear to registered users who are logged in. And it’s free to register and free to log in!

Loading...

PPT – Finite Element Method PowerPoint presentation | free to download - id: 17f609-NjYxY

The Adobe Flash plugin is needed to view this content

About This Presentation

Write a Comment

User Comments (0)

Transcript and Presenter's Notes

Finite Element Method

- Brian Hammond
- Ivan Lopez
- Ingrid Sarvis

Fundamental Concept of FEM

- A continuous field of a certain domain having

infinite degrees of freedom is approximated by a

set of piecewise continuous models with a number

of finite regions called elements. The number of

unknowns defined as nodes are determined using a

given relationship i.e.FKd.

Fundamental Concept of FEM

- Red line-Continuous field over the entire domain.
- Blue line-Finite number of linear approximations

with the finite number of elements

General Steps

- Discretize the domain
- a) Divide domain into finite elements using

appropriate element types (1-D, 2-D, 3-D, or

Axisymmetric) - 2) Select a Displacement Function
- a) Define a function within each element using

the nodal values - Define the Strain/Displacement and Stress/strain

Relationships - 4) Derive the Element Stiffness Matrix and

Equations - a)Derive the equations within each element

General Steps

- 5) Assemble the Element Equations to Obtain the

Global or Total Equations and Introduce Boundary

Conditions - a)Add element equations by method of

superposition to obtain global equation - 6) Solve for the Unknown Degrees of Freedom (i.e

primary unknowns) - 7) Solve for the Element Strains and Stresses
- 8) Interpret the Results

Applications

- Stress Analysis
- Truss and frame analysis
- Stress concentration
- Buckling
- Vibration analysis
- Heat transfer
- Fluid flow

Advantages of FEM

- Model irregularly shaped bodies
- Compute General load conditions
- Model bodies composed of different materials
- Solve unlimited numbers and kinds of boundary

conditions - Able to use different element sizes in places

where loads or stresses are concentrated - Handle non-linear behavior using linear

approximations - Reduce System Cost

FEM Packages

- Large Commercial Programs
- Designed to solve many types of problems
- Can be upgraded fairly easily
- Initial Cost is high
- Less efficient
- Special-purpose programs
- Relatively short, low development costs
- Additions can be made quickly
- Efficient in solving their specific types of

problems - Cant solve different types of problems

FEM Packages

- Algor
- ANSYS
- COSMOS/M
- STARDYNE

- IMAGES-3D
- MSC/NASTRAN
- SAP90
- GT-STRUDL

Note on Stiffness matrix

For a 1-D bar, the stiffness matrix is derived

from the stress/strain relationship in Hookes

law and the definitions of stress and strain. sx

Eex. sx P/A ex

du/dx (d2x d1x)/L By substitution -f1x

EA (d2x d1x)

L f1x EA (d1x d2x)

L Similarly for f2x f2x EA (d2x

d1x)

L Combining into matrix form, the stiffness

matrix is defined as

L

E

A

f2

f1

d1x

d2x

- -1
- -1 1

k EA

L

Note on the displacement function

- For a given set of nodes there exists a function

that approximates - the displacement at any position along the

bar. - This function, called the displacement function,

is derived from - Pascals Triangle.
- A new constant is introduced into the function

for every node in - the discretized domain.

For 1-D

u(x) a1 a2x a3x2

Note on the displacement function

If a 1-D bar is broken into 2 elements, the

displacement function would be

u(x) a1 a2x a3x2.

a1 a2 a3

Putting it into matrix notation u(x) 1 x

x2

By knowing the distances to the nodes and the

displacements at those nodes, the equation

becomes

u1 u2 u3

- 0 0
- 1 x2 x22
- 1 x3 x32

a1 a2 a3

, where

x1 0, x2 and x3 are the distances to the nodes

and u1, u2, and u3 are the displacements.

The coefficients are found by solving the

equation.

Example

E

2E

A A

P

a

b

L

L

Determine displacements of materials a and b if

the load P is applied to the end of the bar

given the above information.

Example cont.

1) Discretize the domain with appropriate

elements.

Element a

Element b

f3 P

f1

2

3

1

u1

u2

u3

f21

f22

2

2

3

f1

f3 P

1

u1

u2

u3

u2

Example cont.

2) Select a displacement function

There will be new term for each element, and the

terms are

derived from Pascals triangle.

1

2

3

u1

u2

u3

u(x) a1 a2x a3x2

Example cont.

3) Define stress/displacement and stress/strain

relationships

sx Eex

ex du/dx

4) Derive the element stiffness matrix and

element equations

F kd k stiffness

matrix

- -1
- -1 1

k EA

F Force

L

d displacement

a

b

1 -1 -1 1

EA

f1 f21

u1 u2

2 -2 -2 2

EA

f22 f3

u2 u3

,

L

L

Example cont.

- Construct Global equation and introduce boundary
- conditions and known variables.

- -1 0
- -1 3 -2
- 0 -2 2

f1 f21f22 f3

EA

u1 u2 u3

Global Equation

L

B.C. (x 0) u1 0 Known variables f3

P and f2 f21f22 0

Example cont.

6) Solve for unknowns.

- -1 0
- -1 3 -2
- 0 -2 2

f1 0 P

EA

0 u2 u3

L

f1 -EAu2 L

0 EA(3u2-2u3) L

P EA(2u3-2u2) L

u2 PL EA

u3 3PL 2EA

f1 -P

Example cont.

7) Solve for the element strains and stresses.

ea P u2 EA L

sa Eea P A

eb 3P u3 2EA L

sa 2E eb P 3 A

8) Interpret the Results

- After solving for the displacements, the

coefficients of the - displacement function can be determined.

Bibliography

- Logan, Daryl L. A First Course in the Finite

Element Method Using Algor. Brooks/Cole,

Pacific Grove, CA. 2001 - http//www.finite-element-method.info
- http//www.eng.fsu.edu/chandra/courses/eml4536/
- http//urbana.mie.uc.edu/yliu/FEM-525/FEM_Lecture_

Notes_Liu_UC.pdf

About PowerShow.com

PowerShow.com is a leading presentation/slideshow sharing website. Whether your application is business, how-to, education, medicine, school, church, sales, marketing, online training or just for fun, PowerShow.com is a great resource. And, best of all, most of its cool features are free and easy to use.

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

You can use PowerShow.com to find and download example online PowerPoint ppt presentations on just about any topic you can imagine so you can learn how to improve your own slides and presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

presentations for free. Or use it to find and download high-quality how-to PowerPoint ppt presentations with illustrated or animated slides that will teach you how to do something new, also for free. Or use it to upload your own PowerPoint slides so you can share them with your teachers, class, students, bosses, employees, customers, potential investors or the world. Or use it to create really cool photo slideshows - with 2D and 3D transitions, animation, and your choice of music - that you can share with your Facebook friends or Google+ circles. That's all free as well!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

For a small fee you can get the industry's best online privacy or publicly promote your presentations and slide shows with top rankings. But aside from that it's free. We'll even convert your presentations and slide shows into the universal Flash format with all their original multimedia glory, including animation, 2D and 3D transition effects, embedded music or other audio, or even video embedded in slides. All for free. Most of the presentations and slideshows on PowerShow.com are free to view, many are even free to download. (You can choose whether to allow people to download your original PowerPoint presentations and photo slideshows for a fee or free or not at all.) Check out PowerShow.com today - for FREE. There is truly something for everyone!

Recommended

«

/ »

Page of

«

/ »

Promoted Presentations

Related Presentations

Page of

Page of

CrystalGraphics Sales Tel: (800) 394-0700 x 1 or Send an email

Home About Us Terms and Conditions Privacy Policy Contact Us Send Us Feedback

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

Copyright 2016 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

The PowerPoint PPT presentation: "Finite Element Method" is the property of its rightful owner.

Do you have PowerPoint slides to share? If so, share your PPT presentation slides online with PowerShow.com. It's FREE!

Committed to assisting Fsu University and other schools with their online training by sharing educational presentations for free