Theory Of Elasticity/Advanced Solid Mechanics

Published 10/2023
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz
Language: English | Size: 11.31 GB | Duration: 8h 35m

elasticity, solid mechanics, stress analysis

What you'll learn
Define and use the notation for forces and stresses in different directions and planes
Identify and calculate the principal stresses, principal planes, stress invariants, mean and deviator stress, strain energy and distortion strain energy
Solve two-dimensional problems in Cartesian co-ordinates using polynomials, St. Venant's principle, uniqueness of solution, and Airy's stress function
Solve two-dimensional problems in polar co-ordinates using the stress-strain components, equilibrium and compatibility equations, and Airy's stress function
Solve torsion problems for bars with different shapes and cross-sections using the stress function method, energy method, soap films, and membrane analogy

Requirements
Knowledge on strength of materials, solid mechanics and structural analysis is a pre-requisite

Description
This course introduces the basic concepts and methods of elasticity theory, which is the study of how materials deform and stress under external forces. The course objectives are to enable the students to:Understand the definitions and notations of forces, stresses, strains, and Hooke's law in two and three dimensions.Apply the transformation of stress and strain components under different coordinate systems.Identify the principal stresses and strains, stress and strain invariants, strain energy, and superposition principle.Solve two-dimensional problems in Cartesian and polar coordinates using Airy's stress function method.Analyze torsion of bars with different cross-sectional shapes using stress function, energy, and numerical methods.The course will also expose the students to some experimental techniques and analytical tools for solving elasticity problems, such as soap films and Prandtl's membrane analogy. The course will require the students to apply the concepts and methods learned in class to solve homework assignments and design projects. The course will also prepare the students for more advanced courses in solid mechanics, such as plasticity, fracture mechanics, and finite element analysis. The course is suitable for students who have completed courses in engineering mechanics, mathematics, and physics. The course will be taught through online video lectures.The topics covered in this course are:Introduction: Definition and notation for forces and stresses, components of stress and strain, Generalized Hooke's law, Stress-strain relations in three directions, Plane stress and plane strain, Equations of equilibrium and compatibility in two and three dimensions, Stress components on an oblique plane, Transformation of stress components under change of co-ordinate system.Principal stresses and principal planes: Stress invariants, Mean and Deviator stress, Strain energy per unit volume, Distortion strain energy per unit volume, Octahedral shear stress, Strain of a line element. Principal strains, Strain invariants, Volume strain, Principle of superposition, reciprocal theorem.Two dimensional problems in Cartesian co-ordinates: Solution by polynomials, St. Venant's Principle, Uniqueness of solution, Stress components in terms of Airy's stress function. Applications to Cantilever, simply supported and fixed beams with simple loading.Two dimensional problems in Polar co-ordinates: Stress-strain components, Equilibrium equations, Compatibility equations, Applications using Airy's strain functions in polar co-ordinates for stress distributions symmetric about an axis, Effect of hole on stress distribution in a plate in tension, Stress due to load at a point on a semi-infinite straight boundary, Stresses in a circular disc under diametrical loading.Torsion: Torsion of various shapes of bars, Stress function method of solution applied to circular and elliptical bars, Torsion of rectangular bars, Solution of Torsional problems by energy method, use of soap films in solving torsion problems, Prandtl's membrane analogy. Solution of torsion of rectangular bars by (i) Raleigh Ritz method and (ii) Finite difference method.

Overview
Section 1: Introduction

Lecture 1 Introduction, Notation of stresses and strains

Lecture 2 Generalized Hooke's Law

Lecture 3 Stress strain relationships, plane stress and plane strain

Lecture 4 Differential equations of equillibrium, equations of compatibility

Lecture 5 Compatibility equation interms of stress for a plane strain and plane s

Lecture 6 Stress components on an oblique plane

Lecture 7 Transformation of stresses

Section 2: Principal stresses and principal planes

Lecture 8 Principal stresses, stress invariants

Lecture 9 Principal shear stresses, mean and deviator stress, octahedral stresses

Lecture 10 Strain energy per unit volume, distortional strain energy

Lecture 11 Strain of a line element

Lecture 12 Principal strains, strain invariants

Section 3: Two dimensional problems in Cartesian co-ordinates

Lecture 13 Saint Venant's principle, Uniqueness theorem, Airy's stress functions

Lecture 14 Cartesian coordinate solutions using polynomials

Lecture 15 Bending of a cantilever loaded at its end

Lecture 16 Pure bending of a beam

Lecture 17 Bending of a simply supported beam by uniform load

Section 4: Two dimensional problems in Polar co-ordinates

Lecture 18 Introduction to Polar Coordinates

Lecture 19 Equilibrium equations in polar coordinates

Lecture 20 Strain-displacement relations in Polar Coordinates

Lecture 21 Airy's stress functions in polar coordinates

Lecture 22 Stress distribution symmetrical about an axis

Lecture 23 Effect of circular hole in stress distribution of a plate

Lecture 24 Stress due to point load on a semi-infinite straight boundary

Lecture 25 Stresses in a circular disc under diametrical loading

Section 5: Torsion

Lecture 26 General solution of a torsion problem

Lecture 27 Torsion of a bar having an elliptical cross-section

Lecture 28 Membrane Analogy

Lecture 29 Torsion of a rectangular bar

This course is intended for ME or MTech Structural Engineering students

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