Basics of FEA-I

🎉 Mastering the Fundamentals of FEA with Samanwita Bag 🎉

Course Title: Basics of FEA - Matrix Algebra, Differential Equations & Their Solutions, and FEM-Weighted Residue Approach

Headline: Unlock the Secrets of FEA through Mathematical Mastery!

Introduction to the Course: This comprehensive course serves as an entrypoint into the fascinating world of Finite Element Analysis (FEA), where you will delve into the core concepts of Matrix Algebra, Differential Equations, and their solutions with a focus on the FEM-Weighted Residue Approach. Designed for students with a foundational understanding of basic mathematics, this course is your stepping stone to mastering complex numerical methods used in ANSYS and other simulation software.

📚 What You Will Learn:

• Introduction to FEA: Gain insights into the strengths, limitations, and real-world applications of Finite Element Analysis.

  • Advantages and Disadvantages of FEA
  • Applications across various industries

• Matrix Algebra: Master the essentials of Matrix Algebra with a focus on:

  • Matrix Operations & Properties
  • Solving Linear Systems using Gauss Elimination Method
  • Finding Inverses of Matrices

• Differential Equations: Explore the realm of Differential Equations by learning:

  • The Exact Method for solving linear differential equations
  • Techniques to calculate solutions accurately and efficiently

• FEM-Weighted Residue Approach: Understand and apply the FEM-Weighted Residue Approach through:

  • Seven methods to solve Linear Differential Equations
  • The role of Taylor's series in Finite Difference Method (FDM)
  • Comparing numerical solutions with the exact method for validation and accuracy assessment

• FEM Methods: Study various FEA methods including:

  • Weak Form & Non-Weak Form type methods (Sub-domain, Galerkin, Petrov-Galerkin, Collocation, Least Square, Rayleigh Ritz)

Course Structure:

1. Introduction to FEA:

   • Understanding the role of FEA in engineering and design
   • Learning about the advantages, limitations, and key applications

2. Matrix Algebra Fundamentals:

   • Mastering Matrix Operations & Properties
   • Applying Gauss Elimination Method to solve systems of equations
   • Learning how to find matrix inverses with higher-order matrices

3. Differential Equations Explored:

   • Diving into the basics of linear differential equations
   • Mastering the Exact Method for finding solutions
   • Solving real-world problems using exact methods

4. FEM-Weighted Residue Approach:

   • Understanding the FEM-Weighted Residue Approach
   • Implementing seven different methods to solve Linear Differential Equations
   • Validating numerical solutions with exact solutions for accuracy checks

5. Finite Element Method (FEM) Techniques:

   • Exploring various FEA methods such as Weak and Non-Weak form type methods
   • Learning practical applications of the Sub-domain, Galerkin, Petrov-Galerkin, Collocation, Least Square, and Rayleigh Ritz methods

Why Take This Course?

• Foundation for Advanced FEA: Lay a solid mathematical foundation to tackle more complex problems in FEA.
• Understanding ANSYS Solutions: Learn to check the accuracy of ANSYS solutions using exact solutions.
• Versatile Applications: Apply your knowledge across various fields such as mechanical, civil, electrical engineering, and more.

Prerequisites: A basic understanding of mathematics is essential for grasping the concepts covered in this course.

Join Samanwita Bag on this educational journey and transform your grasp of Finite Element Analysis! 🎓✨