Exploring Finite Elements: A Practical Approach for Engineers

[tomcenjerrym]

Hi,

I am taking FINITE ELEMENT METHOD and NUMERICAL METHOD in this semester of my college and I am looking for any ONLINE COURSE on them, if available, at reasonable price (or student price). If anybody here can suggest me about it then it would be appreciated so much. I wonder if there available any online course of them, well-organized, sort, comfort, like I was learning in my boyhood.

Please advance

 

[Astronuc]

Search Google with "MIT","OCW","finite element method" or "MIT","OCW","numerical methods"

MIT offers several options in their online courseware.

 

[tomcenjerrym]

Search Google with "MIT","OCW","finite element method" or "MIT","OCW","numerical methods"

MIT offers several options in their online courseware.

I know, but, the mathematic level is too high for me. Thanks for the reply.

 

[Astronuc]

Finite element method is a numerical method for solving partial differential equations! If one is doing FEM, one needs exposure to differential equations and calculus.

What is one's background?

 

[tomcenjerrym]

Finite element method is a numerical method for solving partial differential equations! If one is doing FEM, one needs exposure to differential equations and calculus.

What is one's background?

I’m not sure when you’re saying “What is one's background?”.
However, I already studied differential equations, calculus, and linear algebra in my college and I am an undergraduate student of Mechanical Engineering myself.

 

[Astronuc]

I’m not sure when you’re saying “What is one's background?”.
However, I already studied differential equations, calculus, and linear algebra in my college and I am an undergraduate student of Mechanical Engineering myself.

You indicated that the math level was too high. So I wondered what level one had achieved.

Normally in learning numerical methods, one is exposed to solving differential equations and integrals numerically, e.g. Euler method or Runge-Kutta for diffEQ's ( http://en.wikipedia.org/wiki/Numerical_ordinary_differential_equations ) or trapezoidal rule, Simpson's rule for numerical integration ( http://en.wikipedia.org/wiki/Numerical_integration ).

Then there are systems of equations -

Much effort has been put in the development of methods for solving systems of linear equations. Standard direct methods i.e. methods that use some matrix decomposition are Gaussian elimination, LU decomposition, Cholesky decomposition for symmetric (or hermitian) and positive-definite matrix, and QR decomposition for non-square matrices. Iterative methods such as the Jacobi method, Gauss-Seidel method, successive over-relaxation and conjugate gradient method are usually preferred for large systems.

One can look at this
http://en.wikipedia.org/wiki/Numerical_partial_differential_equations

which leads to
16.920J / 2.097J / 6.339J Numerical Methods for Partial Differential Equations (SMA 5212), Spring 2003
http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/16-920JNumerical-Methods-for-Partial-Differential-EquationsSpring2003/CourseHome/index.htm

http://ocw.mit.edu/OcwWeb/Aeronautics-and-Astronautics/16-920JNumerical-Methods-for-Partial-Differential-EquationsSpring2003/LectureNotes/index.htm

 

[tomcenjerrym]

I already download that courses before and read the files within the folder. Still too high of mathematics levels to me. Actually, I am looking a kind of interactive online course. Thanks.

 

[Astronuc]

Besides MIT's program there is

Numerical Methods for Partial Differential Equations: an Overview and Applications
http://www.lifelong-learners.com/pde/
http://www.lifelong-learners.com/pde/SYL/node1.php

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
http://www.caam.rice.edu/~caam452/

Search Google for "Online","Course","Numerical Methods For Partial Differential Equations" and there are alternatives to MIT's course.

 

[AlephZero]

There are two ways into understanding finite elements. The "modern" way is to treat FE as an general method for finding piecewise-continuous approximate solutions to partial differential equations (which tends to look more like pure maths than engineering).

The more traditional way is to focus on specific, fairly simple, practical problems (e.g. stress analysis of frame structures) and show how all the parts of the FE method fit together in practice, without trying to generalize or worry to much about WHY it works. Maybe you want the second type of approach rather than the first.

I don't know about online courses, but there are some short books by Hinton and/or Owen (published by Pineridge Press) that talk mainly about engineering and computer programming, not about Hilbert spaces.