📖 Finite Element Method

Welcome! This section serves as a personal knowledge hub 🔧 for the theoretical foundation of the Finite Element Method (FEM). Whether you're refreshing the basics or diving deep into variational mechanics, here you'll find hand-picked notes, examples, and insights.

🎓 Lecture Series

📘 Lecture 1: Mathematical Notation
📘 Lecture 2: Variational Principles and Weak Formulation
📘 Lecture 3: Galerkin Method and Ritz Approximation
📘 Lecture 4: Shape Functions and Element Discretization
📘 Lecture 5: Interpolation Schemes and Gauss Integration Points
📘 Lecture 6: Element Stiffness Matrix and Residual Evaluation
🛠️ Lecture 7: Shear Locking – Causes and Remedies
🛠️ Lecture 8: Volumetric Locking and Its Mitigation

🧪 Example Cases

🔍 Example 1: B-Bar for Volumetric Locking
🔍 Example 2: FEA for Wave Propagation in Porous Media (Matlab)
🔍 Example 3: Uinter for Dugdale Model (Abaqus and Fortran)
🔍 Example 4: FEA for Motz problem and Poisson Equation in L-shape (Matlab)
🔍 Example 5: FEA for 1D cylindrical Helmothoz Equation (Python)
🔍 Example 6: UEL for 2D Continuum Beam Element (Fortran)
🔍 Example 7: Vumat for McCormick ( Abaqus and Fortran)
🔍 Example 8: Mathematica for Central Hole (Mathematica)

📚 Supplemental Topics

📐 Sup 1: CNN and Michelson Interferometer
🎯 Sup 2: PINNs and Elastic Modulus Identification

🧠 More coming soon... Stay curious, stay sharp!