Download presentation

Presentation is loading. Please wait.

Published byCyrus Escott Modified over 2 years ago

1
5/1/2015 http://numericalmethods.eng.usf.edu 1 Finite Difference Method Civil Engineering Majors Authors: Autar Kaw, Charlie Barker http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates

2
Finite Difference Method http://numericalmethods.eng.usf.edu http://numericalmethods.eng.usf.edu

3
3 Finite Difference Method An example of a boundary value ordinary differential equation is The derivatives in such ordinary differential equation are substituted by finite divided differences approximations, such as

4
http://numericalmethods.eng.usf.edu4 Example Take the case of a pressure vessel that is being tested in the laboratory to check its ability to withstand pressure. For a thick pressure vessel of inner radius a and outer radius b, the differential equation for the radial displacement u of a point along the thickness is given by The pressure vessel can be modeled as, Substituting these approximations gives you,

5
http://numericalmethods.eng.usf.edu5 Solution Step 1 At node Step 2 At node Step 3 At node

6
http://numericalmethods.eng.usf.edu6 Solution Cont Step 4 At node Step 5 At node Step 6 At node

7
http://numericalmethods.eng.usf.edu7 Solving system of equations

8
http://numericalmethods.eng.usf.edu8 Solution Cont

9
http://numericalmethods.eng.usf.edu9 Solution Cont Using the approximation of and Gives you

10
http://numericalmethods.eng.usf.edu10 Solution Cont Step 1 At node Step 2 At node Step 3 At node

11
http://numericalmethods.eng.usf.edu11 Solution Cont Step 4 At node Step 5 At node Step 6 At node

12
http://numericalmethods.eng.usf.edu12 Solving system of equations

13
http://numericalmethods.eng.usf.edu13 Solution Cont

14
http://numericalmethods.eng.usf.edu14 Comparison of radial displacements Table 1 Comparisons of radial displacements from two methods ru exact u 1st order |єt||єt|u 2nd order |єt||єt| 50.0038731 0.00000.00387310.0000 5.60.00361100.00361651.5160×10 −1 0.00361151.4540×10 −2 6.20.00341520.00342222.0260×10 −1 0.00341591.8765×10 −2 6.80.00326830.00327431.8157×10 −1 0.00326891.6334×10 −2 7.40.00315830.00316181.0903×10 −1 0.00315869.5665×10 −3 80.0030769 0.00000.00307690.0000

15
Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://numericalmethods.eng.usf.edu/topics/finite_differ ence_method.html

16
THE END http://numericalmethods.eng.usf.edu

Similar presentations

OK

4/26/2015 1 LU Decomposition Civil Engineering Majors Authors: Autar Kaw Transforming.

4/26/2015 1 LU Decomposition Civil Engineering Majors Authors: Autar Kaw Transforming.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on water scarcity in south Ppt on personality development and communication skills Ppt on any one mathematician salary Best ppt on history of cricket Ppt on human body parts Ppt on social media in hindi Ppt on odisha culture of india Ppt on wildlife conservation Ppt on management information systems Ppt on fire extinguisher types