The Finite Element Method (FEM) | Part 4: Truss Elements (1)

In this video, we will be checking out chapter 3 of the book "A first course in the finite element method". Learn the fundamentals of truss elements in tutorial. We'll cover the stiffness matrix, displacement function, and shape functions with a step-by-step example to help you understand the concepts better. Don't forget to check the timestamps below for easy navigation!

Whether you're a beginner or an experienced engineer, this tutorial will provide you with a solid understanding of the direct stiffness method and how to apply it to solve structural analysis problems. So, sit back, relax, and let's get started!

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Timestamps:
0:00 Introduction
1:39 Deriving The Stiffness Matrix of Truss Elements
14:41 Example
24:55 The Displacement Function
30:12 Shape Functions / Interpolation Functions
35:53 Outro

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[donaldkhanye]

Hello Dr CEE

Thank you for the shout-out. Wow, that was quite a very nice and detailed explanation from 24:54 of the displacement function (and the associated “mixing functions”) for the current element; outstanding work Dr CEE, really good stuff right there. I also appreciate that you throw in hints to show how deep the rabbit hole goes.

05:16 The relationship AE*du/dx = T make sense. Whilst I understand that if one further differentiates both sides of this relationship, they would get what is referred to here as the “…. governing differential equation for a bar element….”, my question is: Isn’t the relationship AE*du/dx = T sufficient for defining and exploring the relationships between the applied forces on the bar and the resulting displacements of the bar as it is? Why would it be necessary to further differentiate this relationship on both sides as opposed to using it as it is?

I have truly enjoyed this video and I am looking forward to the next videos on the series.

Keep well.
DK

[yousafhassan]

Please contiinue uploading more videos on FEM of all the chapters of this book.
Thank You soo much

[FetiSelmani]

Excellent explanation of the subject matter!

[eslamahmed]

I'm a MSc student in California State University and I really love the Finite Element Course because of you ♥
You energy is everywhere around me, thanks Dr. CEE ♥

[niisarpei]

Thank you soo much Dr CEE and the rest of the team, CEE editor and CEE TA.

This is indeed a powerful lecture. However, it’s so obvious that the spring and truss have same stiffness formulation, with only the addition of member and material properties(EA/L)

Would the case of the beam and the truss be to change the EA/L to EI/L for a simple beam element?

Thank you for your good works
God bless you.