Theory of Elasticity
INTRODUCTION: Objectives, Historical
STRAIN AND STRESS TENSORS: The continuum model, External loads, The displacement vector, Components of strain, Assumption of small deformation, Proof of the tensorial property of strain, Traction and components of stress, Proof of the tensorial property of stress, Properties of the strain and stress tensors, Components of displacement for rigid body motion, The compatibility equations, The equilibrium equations, Cylindrical coordinates, Strain-displacement relations in cylindrical coordinates, Equilibrium equations in cylindrical coordinates, Compatibility equations in cylindrical coordinates.
STRESS-STRAIN RELATIONS: Uniaxial tension or compression under constant temperature, The torsion test, Effect of temperature, Stress-strain relations for elastic materials subjected to three-dimensional stress state, Stress-strain relations for linear elastic materials subjected to three-dimensional stress state, Stress-strain relations for orthotropic linear elastic materials, Stress-strain relations for isotropic linear elastic materials subjected to three-dimensional stress state.
FORMULATION AND SOLUTION OF BOUNDARY VALUE PROBLEMS: Introduction, Boundary value problems for computing the displacement and stress fields, The principle of Saint-Venant, Methods for finding exact solutions for boundary value problems, Prismatic body subjected to uniaxial tension, Prismatic body subjected to bending, Prismatic body subjected to torsion.
PLAIN STRAIN AND PLAIN STRESS PROBLEMS: Plane strain, Formulation of problems using the Airy stress function, Prismatic bodies in plain strain condition, The equations of plain strain condition in cylindrical coordinates, Plain stress, Plates in plain stress condition, Two-dimensional plain stress condition, Prismatic bodies in axisymmetric plain strain or plain stress conditions.
To give the students the basics of Theory of Elasticity which are required for the understanding of the elastic behavior of isotropic materials. The knowledge gained is used in many courses of the Mechanical & Aeronautical Engineer such as the Introduction to the Finite Element Method, Introduction to Mechanics of Composite Materials, Advanced Strength of Materials, Fracture Mechanics & Structural Integrity, Mechanics of Composite Materials, etc.
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