/fea_lectures

Beginner's Lectures on Finite Element

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Lectures on Finite Element Analysis for Beginners

Hand writted PDF lecture Notes By Dr. Shahzad Rehman based on Textbook: Concepts and Applications of Finite Element Analysis by Robert D. Cook , D.S. Malkus , M.E. Plesha. Revised by David S. Malkus and Michael E. Plesha

Course Content:

  1. Lecture 01: Overview
  2. Lecture 02: Method of Weighted Residual
    1. Galerkin
    2. Collocation
    3. Least Method
    4. Examples
  3. Lecture 03: Derivation of FE Equation and Principle of Virtual Work
  4. Lecture 04: Development of Stiffness Method for Beam, Two Dimensional Elasticity Problems
    1. Constant Strain Triangle (CST)
    2. Rectangular Element (PSR)
    3. Interpolation Formulae
    4. Coordinate System (Local, Global, and Natural)
  5. Lecture 05: Isoparametric Elements
    1. 8 Noded - Serendipity Element Q8
    2. 9 Noded Q9 Quardratic Lagrangian
    3. Numerical Integration
    4. Newton-Cotes formual for 1D integration
    5. Gauss Quadrature
  6. Lecture 06: Example Problems on Numerical Integration
    1. Isoparametric Triangular Element (3 and 6 noded)
    2. Area Coordinates and its relationship with Isoparametric coordinates
    3. Area Coordinates for Higher Order Triangular Element
    4. Constant Strain Triangle in Area Coordinates
    5. Linear Strain Triangle in Area Coordinates
  7. Lecture 07: Errors and Convergence in FEM
    1. Modeling Error
    2. Discretization Error
    3. Truncation Error or Roundoff Error
    4. Manipulation Error
    5. Numerical Error
    6. User Generated Error
    7. Software Bugs
    8. Ill- Conditioning
    9. Condition Number
    10. Error Estimation by Residual
    11. Convergence of FE Solution
    12. Monotonic Convergence
    13. Requirement for Monotonic Convergence with Monotonically Increasing and Solution Converging to Upper an Bound
    14. Completeness
    15. Compatibility
    16. Types and Rate of Convergence
    17. R Refinement or R Convergence
    18. P Refinement or P Convergence
    19. h/p Refinement or R/P Convergence
    20. Stress Recovery and Smoothing
    21. Nodal Averaging
    22. Stress Smoothing by Patch Recovery
    23. Stress Smoothing by Patch Smoothing
    24. Energy Based Error Norms
    25. ZZ Error Estimate
    26. Global Strain Energy Norm

Other Materials:

  1. Course Outline
  2. Assignment and Solution
  3. Exam Papers