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Lecture Notes

Mathematica software is required to run the .nb files in this section.
Unit #1
  • Notes (PDF)

  • Concept Questions
    • Concept Question 1 (PDF)

  • Mathematica Notebooks
    • Beam 1 Degrees of Freedom (NB)
    • Beam 3 Degrees of Freedom (NB)
    • Spring System (NB)
Unit #2
  • Notes (PDF)

  • Concept Questions
    • Concept Question 2 (PDF)
    • Concept Question 3 (PDF)
    • Concept Question 4 (PDF)
    • Concept Question 5 (PDF)
  • Math Aside (PDF)
Unit #3
  • Reading Assignments
    • Textbook, Section 3.3: Kinematics of Deformation
  • Notes (PDF)

  • Concept Questions
    • Concept Question 6 (PDF)

  • Mathematica Notebooks
    • Comparison of Linear and Nonlinear Strain (NB)
Unit #4
  • Reading Assignments
    • No Reading Assignment for this Unit
  • Notes (PDF)

  • Concept Questions
    • Concept Question 7 (PDF)
Unit #5
  • Reading Assignments
    • Textbook, Section 3.4: Constitutive Equations
  • Notes (PDF)

  • Concept Questions
    • Concept Question 8 (PDF)
    • Concept Question 9 (PDF)
Unit #6
  • Reading Assignments
    • No Reading Assignments for this Unit

  • Notes (PDF)
Unit #7
  • Reading Assignments
    • Textbook, Section 4.1: Work and Energy
    • Textbook, Section 4.2: Strain Energy and Complementary Strain Energy

  • Notes (PDF)

  • Concept Questions
    • Concept Question 10 (PDF)
    • Concept Question 11 (PDF)

  • Examples
    • Application to Beam Theory (PDF)
Unit #8
  • Reading Assignments
    • Textbook, Section 4.3 and 5.1: Principle of Virtual Displacements
  • Notes (PDF)

  • Concept Questions
    • Concept Question 12 (PDF)
    • Concept Question 13 (PDF)
Unit #9
  • Reading Assignments
    • Textbook: Calculus of Variations: Section 4.4.1 to 4.4.7, Section 4.3 and 5.1
Unit #10
  • Reading Assignments
    • Textbook: Principle of Total Potential Energy, Section 5.2

  • Notes (PDF)

  • Concept Questions
    • Concept Question 14 (PDF)
    • Concept Question 15 (PDF)

  • Mathematica Notebooks
    • Example of Application of Castigliano's 1st Theorem (NB - 1.2 MB
Unit #11
  • Reading Assignments
    • Textbook: Principle of Virtual Forces and Maximum Complementary Potential Energy, Reciprocity Theorems, Section 5.3, 5.4 and 5.5
  • Mathematica Notebooks
Unit #12
  • Reading Assignments
    • Textbook: Direct Variational Methods, Section 7.1
    • Section 7.2 (Optional)
    • Section 7.3 Ritz Method

  • Notes (PDF)
  • Notes (cont'd) (PDF)

  • Concept Questions
    • Concept Question 16 (PDF)
    • Concept Question 17 (PDF)

  • Mathematica Notebooks
    • Application of Ritz Method to Beam Theory (NB)
    • Application of Ritz Method to a Bar with Variable Cross Section (NB - 1.1 MB)
Unit #13
  • Reading Assignments
    • Textbook: The Finite Element Method, Chapter 9
    • Section 9.1
    • Section 9.2

  • Notes (Part I) (PDF - 1.2 MB)
  • Notes (Part II) (PDF - 1.4 MB)
  • Notes (Part III) (PDF - 1.1 MB)
  • Notes (Part IV) (PDF)

  • Concept Questions
    • Concept Question 18 (PDF)
    • Concept Question 19 (PDF)
    • Concept Question 20 (PDF)

  • Mathematica Notebooks
    • Making Progress Towards the Finite Element Method (NB)
    • Formulation of Finite Element Matrices for 1D Problems (NB)
Unit #14
  • Reading Assignments
    • Section 9.3

  • Notes (PDF)

  • Concept Questions
    • Concept Question 21 (PDF)

  • Mathematica Notebooks
    • Formulation of Euler Beam Finite Element (NB)
Unit #15
  • Notes (PDF - 1.1 MB)
  • Notes (Part II) (PDF)

  • Concept Questions
    • Concept Question 22 (PDF)
    • Concept Question 23 (PDF)

  • Mathematica Notebooks
    • Formulation of Linear Square Elasticity Element (NB)
    • Formulation of Quadratic Square Elasticity Element (NB - 1.3 MB)
    • Formulation of Isoparametric 4-Node Elasticity Element (NB)
Unit #16
  • Notes (PDF)
  • Concept Questions

    • Concept Question 24 (PDF)
    • Concept Question 25 (PDF)

  • Mathematica Notebooks
    • Motivation for Numerical Integration (NB)
    • Gauss Quadrature Integration Rules (NB)
Unit #17