Lec #  Topics  key dates 

Part 1: Review of the Equations of Linear Elasticity  
1  Introduction  
23 
Kinetics Stress Tensor and the Cauchy Formula Transformation of Stress Components Principal Stresses and Principal Planes Equations of Motion Symmetry of the Stress Tensor 

4 
Kinematics Strain at a Point Transformation of Stress Components Compatibility Conditions 

5 
Thermodynamic Principles The Second Law of Thermodynamics 

6 
Constitutive Equations Strain Energy Density Function Elastic Symmetry Thermoelastic Constitutive Equations 

7 
Boundary Value Problems of Elasticity Classification of Boundary Value Problems Existence and Uniqueness of Solutions 
Assignment 1 due 
Part 2: Energy and Variational Principles  
89 
Preliminary Concepts Work and Energy Strain and Complementary Strain Energy Virtual Work 

1011 
Concepts of Calculus of Variations The Variational Operator The First Variation of a Functional Extremum of a Functional The Euler Equations Natural and Essential Boundary Conditions A More General Functional Minimization with Linear Equality Constraints 
Assignment 2 due in lecture 11 
1214 
Virtual Work and Energy Principles Unit Dummy Displacement Method Principle of Total Potential Energy Principle of Virtual Forces and Complementary Potential Unit Dummy Load Method 
Assignment 3 due in lecture 14 
15 
Energy Theorems of Structural Mechanics Castigliano’s Second Theorem Betti’s and Maxwell’s Reciprocity Theorems 

16  Some Preliminaries  
1718 
The Ritz Method Description of the Method Matrix Form of the Ritz Equations One Dimensional Examples 
Assignment 4 due in lecture 17 
19 
Weighted Residual Methods A Brief Description of Galerkin, Leastsquares and Collocation Methods 
Assignment 5 due 
2022 
Formulation of the Displacement Based Finite Element Method General Derivation of Finite Element Equilibrium Equations Imposition of Displacement Boundary Conditions Generalized Coordinate Models for Specific Problems Lumping of Structure Properties and Loads 

23 
Convergence of Analysis Results Properties of the Finite Element Solution Rate of Convergence Calculation of Stresses and the Assessment of Error 

24  Isoparametric Derivation of Bar Element Stiffness Matrix  
2527 
Formulation of Continuum Elements Quadrilateral Elements Triangular Elements Convergence Considerations Element Matrices in Global Coordinate System 
Assignment 6 due in lecture 25 
2829 
Formulation of Structural Elements Plate and Shell Elements 
Assignment 7 due in lecture 28 
30  Numerical Integration  
31  Direct Solution of Linear System of Equations  
3233 
Types of Structural Failure Yield Stress and Ultimate Stress Maximum Normal Stress Theory Tresca Condition, Hydraulic Stress, von Mises Criterion, Distortion Energy Interpretation Graphical Representation of Failure Regions Extension to Orthotropic Materials, Hill Criterion, Hoffman Criterion Nature of Failure Criteria, Functional Forms General Failure Analysis Procedure Application to Pressure Tank 
Assignment 8 due in lecture 33 
3437 
Fracture Mechanics Energy Approach to Crack Growth, Energy Consumed by Crack Growth, Griffith’s Experiment and Formula Definition of Stress Intensity Factor Stresses at Crack Tip, Mode I, II and III Cracks Solutions of Linear Elastic Fracture Mechanics, Geometry Effects Combined Loading; Material Selection Example 
Assignment 9 due in lecture 36 Term Project due in lecture 36 
3842 
Fatigue and Longevity Effects of R Value, Stress Concentrations GroundAirGround Cycle, Miner’s Rule Micromechanical Effects Paris’ Law Fatigue Life Prediction R Effects and Forman’s Law, Sequencing Effects Approach to Design for Longevity Material Selection Example 
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Spring
2005
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