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- INTRODUCTION AND REVIEW OF BASIC CONCEPTS, VIRTUAL WORK PRINCIPLES AND APPLICATIONS, DIRECT STIFNESS METHOD
- NONLINEAR ANALYSIS, GEOMETRIC NONLINEAR ANALYSIS, MATERIAL NONLINEAR ANALYSIS, SOLUTION OF LINEAR ALGEBRAIC EQUATIONS
- SOLUTION OF NONLINEAR EQUILIBRIUM EQUATIONS, SPECIAL ANALYSIS POCEDURES, Static and kinematic indeterminacy of structures
- Stiffness method of analysis of beams, 2D & 3D trusses and frames, Solution of simultaneous equations, Bandwidth calculation and banded solution, Analysis of beams, frames and trusses using computer programs,determinants properties,linear independent sets,quadratic forms,singular value decomposition
- 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, Strain at a Point, Transformation of Stress Components, Compatibility Conditions, Thermodynamic Principles, The First Law of Thermodynamics: Energy Equation, The Second Law of Thermodynamics, onstitutive Equations.
- Generalized Hooke's Law, Strain Energy Density Function, Elastic Symmetry, Thermoelastic Constitutive Equations, Boundary Value Problems of Elasticity, Summary of Equations, Classification of Boundary Value Problems, Existence and Uniqueness of Solutions, Preliminary Concepts, Introduction, Work and Energy, Strain and Complementary Strain Energy, Virtual Work, 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, 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, Energy, Unit Dummy Load Method, Energy Theorems of Structural Mechanics, Castigliano's First Theorem, Castigliano's Second Theorem.
- Betti's and Maxwell's Reciprocity Theorems, Ritz Method, Description of the Method, Matrix Form of the Ritz Equations, One Dimensional Examples, Weighted Residual Methods, 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, Convergence of Analysis Results, Definition of Convergence, Properties of the Finite Element Solution.
- Rate of Convergence, Calculation of Stresses and the Assessment of Error, Isoparametric Derivation of Bar Element Stiffness Matrix, ormulation of Continuum Elements, Quadrilateral Elements, Triangular Elements, Convergence Considerations, Element Matrices in Global Coordinate System, Formulation of Structural Elements, Beam Elements and Axisymmetric Shell Elements, Plate and Shell Elements, Numerical Integration, Direct Solution of Linear System of Equations, Types of Structural Failure, Yield Stress and Ultimate Stress, Maximum Normal Stress TheoryTresca 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, 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, Fatigue and Longevity, Terminology, SN Diagrams, Goodman Diagrams, Effects of R Value, Stress Concentrations, Ground-Air-Ground Cycle, Miner's Rule, Micromechanical Effects, Paris' Law, Fatigue Life Prediction, R Effects and Forman's Law, Sequencing Effects, Approached to Design for Longevity.