Finite elements

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Welcome to this learning project about Finite elements!

Learning Project Summary[edit | edit source]

Content summary[edit | edit source]

This course will introduce you to the topic of finite element analysis. The course will cover linear finite elements and the analysis of simple solid mechanics and heat transfer problems.

Goals[edit | edit source]

This course aims to:

  • Introduce you to the finite element method
  • Show you how finite element formulations are arrived at
  • Show you how some engineering problems are solved numerically

Contents[edit | edit source]

Syllabus and Learning Materials[edit | edit source]

  1. Mathematical Preliminaries
    1. Set notation
    2. Functions
    3. Vectors
    4. Matrices
    5. Tensors
    6. Partial differential equations
    7. Variational calculus
  2. Tensor exercises and Physical Principles in Differential Form
    1. Quick indicial notation review
    2. Conservation of mass
    3. Conservation of linear momentum
    4. Conservation of angular momentum
    5. Conservation of energy
  3. Finite element basics in one-dimension
    1. An example: Axially loaded bar
    2. More examples: Some model problems
    3. A time-dependent problem: the heat equation

Assignments[edit | edit source]

Tests and Quizzes[edit | edit source]

Textbooks and References[edit | edit source]