Lec #  Topics  lecture notes 

Part 1: Review of the Equations of Linear Elasticity 

1 
Introduction 
Introduction (PDF) 
23 
Kinetics Stress at a Point Stress Tensor and the Cauchy Formula Transformation of Stress Components Principal Stresses and Principal Planes Equations of Motion Symmetry of the Stress Tensor 
Stress and Momentum Balance (PDF) Mathematical Aside: Vectors, Indicial Notation and Summation Convention (PDF) 
4 
Kinematics Strain at a Point Transformation of Stress Components Compatibility Conditions 
Kinematics of Deformation (PDF) 
5 
Thermodynamic Principles The First Law of Thermodynamics: Energy Equation The Second Law of Thermodynamics 
Thermodynamics Principles (PDF) 
6 
Constitutive Equations Generalized Hooke’s Law Strain Energy Density Function Elastic Symmetry Thermoelastic Constitutive Equations 
Constitutive Equations (PDF) 
7 
Boundary Value Problems of Elasticity Summary of Equations Classification of Boundary Value Problems Existence and Uniqueness of Solutions 
Boundary Value Problems of Linear Elasticity (PDF) 
Part 2: Energy and Variational Principles 

89 
Preliminary Concepts Introduction Work and Energy Strain and Complementary Strain Energy Virtual Work 
Concepts of Work and Energy (PDF) Strain Energy and Potential Energy of a Beam (PDF) Principles of Virtual Displacements (PDF) Principles of Virtual Forces (PDF) 
1011 
Concepts of Calculus of Variations Concept of a Functional 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 
Calculus of Variations (PDF) 
1214 
Virtual Work and Energy Principles Principle of Virtual Displacements Unit Dummy Displacement Method Principle of Total Potential Energy Principle of Virtual Forces and Complementary Potential Unit Dummy Load Method 

15 
Energy Theorems of Structural Mechanics Castigliano’s First Theorem Castigliano’s Second Theorem Betti’s and Maxwell’s Reciprocity Theorems 
Principle of Minimum Potential Energy and Castigliano’s First Theorem (PDF) 
16 
Some Preliminaries 

1718 
The Ritz Method Description of the Method Matrix Form of the Ritz Equations One Dimensional Examples 
Approximate Methods (PDF) The Ritz Method Cont. (PDF) 
19 
Weighted Residual Methods A Brief Description of Galerkin, Leastsquares and Collocation Methods 

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 
The Finite Element Method (PDF) The Finite Element Method II (PDF) The Finite Element Method III (PDF) The Finite Element Method IV: Imposition of Boundary Conditions (PDF) Finite Element Model of a Beam (PDF) 
23 
Convergence of Analysis Results Definition of Convergence Properties of the Finite Element Solution Rate of Convergence Calculation of Stresses and the Assessment of Error 
The Finite Element Method V: For ThreeDimensional Elasticity Problems (PDF) 
24 
Isoparametric Derivation of Bar Element Stiffness Matrix 
Formulation of Isoparametric Elements (PDF) 
2527 
Formulation of Continuum Elements Quadrilateral Elements Triangular Elements Convergence Considerations Element Matrices in Global Coordinate System 

2829 
Formulation of Structural Elements Beam Elements and Axisymmetric Shell Elements Plate and Shell Elements 

30 
Numerical Integration 
Numerical Integration (PDF) 
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 
Failure, Fracture, and Fatigue (PDF  2.4 MB) 
3437 
Fracture Mechanics Description of Phenomena and Importance 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 

3842 
Fatigue and Longevity Terminology, SN Diagrams, Goodman Diagrams 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 Approached to Design for Longevity Material Selection Example 
Lecture Notes
Course Info
Instructor
Departments
As Taught In
Spring
2005
Level
Learning Resource Types
assignment
Problem Sets
grading
Exams with Solutions
notes
Lecture Notes