| 1 |
Introduction, Some Mathematical Preliminaries |
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| 2 |
Review of Equations of Solid Mechanics |
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| 3 |
Introduction of Variational Calculus, Euler’s Method of Finite Differences |
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| 4 |
The Leibnitz Rule, Fundamental Lemma of Calculus of Variations, The Epsilon-Method (or the Alpha-Method) |
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| 5 |
The Epsilon-Method (or the Alpha-Method) (Continue), Functionals Involoving Higher-Order Derivatives |
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| 6 |
Functionals with Several Dependent Variables |
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| 7 |
The Delta-Operator, Functional Involving More Than One Independent Variable |
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| 8 |
Functionals with Variable (Movable) Boundary, Variable (Movable) Boundary Lying on a Curve |
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| 9 |
Functional with Variable (Movable) Boundaries, First Integrals of Euler’s Equations |
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| 10 |
Functionals with Equality Constraints |
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| 11 |
Introduction to Different Types of Constraints |
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| 12 |
Functionals with Equality Constraints (Continue) |
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| 13 |
Work and Energy |
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| 14 |
Strain Energy and Complementary Strain Energy, Virtual Work |
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| 15 |
Introduction of Energy Principles of Structural Mechanics, The Principle of Virtual Displacements |
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| 16 |
Unit-Dummy-Displacement Method |
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| 17 |
Principle of Minimum Total Potential Energy |
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| 18 |
Catigliano’s Theorem I |
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| 19 |
Principles of Virtual Forces and Complementary Potential Energy |
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| 20 |
MIDTERM EXAMINATION |
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| 21 |
Principles of Complementary Potential Energy, Catigliano’s Theorem II |
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| 22 |
Betti’s and Maxwell’s Reciprocity Theorems |
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| 23 |
Introduction of Dynamic Systems: Hamilton’s Principle |
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| 24 |
Hamilton’s Principle for Particles and Rigid Bodies |
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| 25 |
Hamilton’s Principle for a Continuum |
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| 26 |
Hamilton’s Principle for a Continuum (Continue) |
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| 27 |
Solution of Some Dynamic Problems |
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| 28 |
Introduction of Direct Variational Methods |
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| 29 |
Some Mathematical Concepts |
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| 30 |
The Ritz Method, General Boundary-Value Problems, Introduction to Weighted-Residual Methods |
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