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Unit #1
- Notes (PDF)
- Concept Questions
- 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)
Unit #3
- Reading Assignments
- Textbook, Section 3.3: Kinematics of Deformation
- Notes (PDF)
- Concept Questions
- Mathematica Notebooks
- Comparison of Linear and Nonlinear Strain (NB)
Unit #4
- Reading Assignments
- No Reading Assignment for this Unit
- Notes (PDF)
- Concept Questions
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
- 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
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