Theory of Elasticity

(Department)  Biomedical Engineering         (Division)     
 
 (Level and Major) 
 

Course Title                Theory of Elasticity
 
Number of Credits       3             Prerequisite


Course Topics:
  • Mathematical Preliminaries, Kronecker Delta and Alternating Symbol
  • Coordinate Transformations & Cartesian Tensors
  • Vector, Matrix, and Tensor Algebra, Calculus of Cartesian Tensors
  • Orthogonal Curvilinear Coordinates
  • Deformation: Displacements and Strains
  • Geometric Construction of Small Deformation Theory
  • Strain Transformation, Principal Strains, Spherical and Deviatoric Strains
  • Strain Compatibility
  • Curvilinear Cylindrical and Spherical Coordinates
  • Stress and Equilibrium
  • Body and Surface Forces
  • Traction Vector and Stress Tensor
  • Stress Transformation, Principal Stresses, Spherical and Deviatoric Stresses
  • Equilibrium Equations,
  • Relations in Curvilinear Cylindrical and Spherical Coordinates
  • Material Behavior—Linear Elastic Solids, Material Characterization
  • Linear Elastic Materials—Hooke’s Law, Physical Meaning of Elastic Moduli
  • Thermoelastic Constitutive Relations,
  • Formulation and Solution Strategies,
  • Review of Field Equations,
  • Boundary Conditions and Fundamental Problem Classifications,
  • Stress & Displacement Formulations
  • Principle of Superposition,
  • Saint-Venant’s Principle,
  • General Solution Strategies,
  • Strain Energy and Related Principles,
  • Uniqueness of the Elasticity Boundary-Value Problem,
  • Bounds on the Elastic Constants,
  • Related Integral Theorems,
  • Principle of Virtual Work,
  • Principles of Minimum Potential and Complementary Energy,
  • Rayleigh-Ritz Method,
  • Two-Dimensional Formulation,
  • Plane Strain & Plane Stress,
  • Generalized Plane Stress,
  • Antiplane Strain,
  • Airy Stress Function,
  • Polar Coordinate Formulation,
  • Two-Dimensional Problem Solution,
  • Cartesian Coordinate Solutions Using Polynomials,
  • Cartesian Coordinate Solutions Using Fourier Methods,
  • General Solutions in Polar Coordinates,
  • Polar Coordinate Solutions,
  • Extension, Torsion, and Flexure of Elastic Cylinders, General Formulation,
  • Torsion Formulation & Torsion Solutions Derived from Boundary Equation,
  • Torsion Solutions Using Fourier Methods,
  • Torsion of Cylinders With Hollow Sections,
  • Flexure Formulation & Flexure Problems Without Twist,
  • Some Aspects of Objectivity, Change of Observer, and Objective Tensor Fields
  • Objective Rates
  • Invariance of Elastic Material Response
  • Isotropic Hyperelastic Materials,  
  • Incompressible & Compressible Hyperelastic Materials,
  • Some Forms of Strain-energy Functions,
  • Elasticity Tensors,
  • Transversely Isotropic Materials
  • Hyperelastic Composite Materials with Two Families of Fibers
 
Reading Resources:
 
Evaluation:

30% Final Exam
60%  Midterm Exam
10% Homework
 
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