Finite Element Method - Example | Complete Linear Analysis in Mathematica

Finite Element Method - Example | Complete Linear Analysis in Mathematica

Thanks for Watching :)

Theory Videos:
Gaussian Integration:

Introduction: (0:00)
Parameters: (2:53)
Constitutive Laws: (10:56)
Stiffness Matrix - Shape Functions: (15:01)
Stiffness Matrix - Coordinate Mapping: (17:34)
Stiffness Matrix - N Matrix: (23:33)
Stiffness Matrix - Jacobian Matrix: (28:39)
Stiffness Matrix - B Matrix: (33:08)
Stiffness Matrix (Full Gauss Integration): (41:42)
Nodal Forces - Concentrated Loads: (46:52)
Nodal Forces - Body Forces (Gravity): (48:08)
Nodal Forces - Traction Vectors (Distributed Loads): (50:59)
Nodal Forces Vector: (55:08)
Solving the System - Nodal Displacements: (56:10)
Solving the System - Reaction Forces: (1:02:34)
Displacement Field: (1:05:14)
Strain Field: (1:06:51)
Stress Field: (1:07:43)
Results: (1:08:33)

[유튜브초보-dx]

It is amazing FEM Example. I am sometimes using the ABAQUS program. However I almost forgot what happen in ABAQUS background. Almost 20 years past since I graduated from graduate school. Your Video makes me awaken of FEM Theory which I almost disappear in my brain. Great Well, Thank you for very kind explanations.

[jaboust]

Thank you Clayton! I followed your very nice lecture and reproduced the results using MATLAB. It helped me understand the theory formulation better!

[smileall]

Hey Clayton, what changes would have to be made in the code if this were a Linear Rectangular Element and not just a quadrilateral? Thanks.

[yachallenge]

Thank you so much. That's amazing!

[FEM_UserAC]

Thank you so much for this lecture video. It was extremely helpful. I have a question for you: Is there any chance you made a mistake in the Jacobian matrix definition? Equation showed is [dx/dXi dx/dEta ; dy/dXi dy/dEta] but, shouldn't it be [dx/dXi dy/dXi ; dx/dEta dy/dEta]? In advance, thank you for your answering.

[mohamedorsod]

thank u very much for amazing FEM example. I have inquires did the code in MATLAB and i got nice K matrix. Now iam trying to divided the elements into multiple elements and combined them together . do u know i ican combine them

[qwm]

I've got same results for plane stress, then decided to change the C-matrix to plane strain and compare results with Abaqus. And my results for the plane strain case is different from ABAQUS plane strain. Could someone suggest why could be so?

[adirhori]

Hello my friend.
can you please send me this code in MATLAB format ?
OR this code in TEXT file?
thank you :)