WELCOME ALL !!
Dr Airil Yasreen Mohd Yassin is offering a free online Finite Element Method (FEM) course designed to build strong foundations in numerical methods and computational mechanics. Starting on 3 June, classes will be held every Wednesday, 9:00–11:00 PM, over approximately 12 weeks. The course begins from first principles, making it suitable for beginners, and follows the team’s FEM textbooks. It also provides a pathway to more advanced topics, including meshless methods, NURBS, and the Numerical Derivation Method (NDM).
1️⃣ For those who have not registered yet
Please complete your registration using the following link:
[https://forms.gle/ArsRx4a35TpcSkum7]
2️⃣ Join the WhatsApp Group
Please join the WhatsApp group for updates and discussions using the following link:
[https://chat.whatsapp.com/DqS4h7eJdVJ8LazYPR4sM5?s=cl&p=i&ilr=4]
3️⃣ Download the Red Book & Blue Book
The PDF books can be downloaded from the following link:
[https://github.com/msnm-official/fem_books]
WEEK 01
Introduction to numerical methods
03 JUNE 2026
We have learned the basics of numerical methods and their application in solving mechanics problems governed by differential equations. Since computers and programming languages primarily operate with matrix systems, these governing equations must be transformed into matrix form. This can be achieved using methods such as the collocation method and the weighted residual method. The collocation method satisfies the governing equation at specific points, whereas the weighted residual method minimizes the overall error across the domain. As a result, the weighted residual method is less likely to overlook local regions with high gradients within the domain, leading to improved accuracy and a more representative solution.
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WEEK 02
Galerkin WRM approach & FEM
10 JUNE 2026
We successfully learned the Galerkin Weighted Residual Method (WRM) and its application in the Finite Element Method (FEM). The session emphasized the derivation of the weak form through integration by parts (IBP), where natural boundary conditions appear naturally within the formulation. We also explored the importance of the Kronecker delta property of finite element shape functions, which allows essential boundary conditions to be imposed directly. In addition, we studied the formulation of elemental equations and their assembly into a global system, providing a strong foundation for accurate and efficient numerical solutions to engineering problems.
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WEEK 03
Higher-Order FEM for Bar Element + Beam Problem
17 JUNE 2026
We first discussed the formulation of the bar problem and considered its p-refinement using quadratic elements. We then learned how the Finite Element Method (FEM) can be naturally extended from bar elements to beam problems using the same discretization philosophy, element formulation procedure, and matrix assembly process. By introducing beam elements with both displacement and rotational degrees of freedom, we observed that the resulting system of matrices closely resembles those of bar elements. This demonstrates the power and versatility of FEM as a unified framework for solving diverse engineering problems while maintaining a strong connection to the underlying mechanics and physics.
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WEEK 04
Derivation of Differential Equations – 1D and 2D Applications
24 JUNE 2026
Now we have learned how differential equations are derived from engineering and physical systems. Students will derive Ordinary Differential Equations (ODEs) for bar and beam problems, as well as Partial Differential Equations (PDEs) for two-dimensional heat transfer phenomena. As consistently emphasized in previous classes, understanding the underlying physics and mechanics is essential for developing accurate mathematical models and becoming a true engineer. Furthermore, this foundation is crucial for pursuing advanced studies in mechanics and contributing to new discoveries and innovations in academic research.
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WEEK 05
Application of 1D FEM to Buckling and Vibration
WILL BE ON 01 JULY 2026
Building on the finite element formulations for bar and beam problems, we will apply 1D FEM to buckling and vibration analyses. Students will learn how geometric stiffness and mass matrices are used to formulate eigenvalue problems for predicting critical buckling loads and natural frequencies, reinforcing the connection between mechanics and numerical modeling…
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Note (Week 05)
Recorded Video (Part 1)
Recorded Video (Part 2)