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《Foundations of Solid Mechanics》PPT课件 东南大学 Gongye Zhang

Foundations of Solid Mechanics_东南大学
 
课件内容: 
Introduction 
In this chapter  briefly history of solid mechanics and a few important concepts and the application are introduced. 
1.1 Welcome Speech 
1.2 A Brief Historical Development 
1.3 Some Concepts 
1.4 Course Contents 
Quiz for Chapter 1 
Mathematical preliminaries 
In this chapter  some mathematical fundamentals are essential to the understanding of tensor analysis. 
2.1 Physical quantities and indicial notation 
2.2 Summation convention and two special arrays 
2.3 Tensor Algebra 
2.4 Tensor Calculus 
2.5 Sample problems 
Quiz for Chapter 2 
Analysis of stress 
In this chapter  the motivation and definition of the analysis of stress are shown. 
3.1 Review of elementary MOM 
3.2 Motivation & Definition 
3.3 Principal stresses 
3.4 Example: Principal stress 
Quiz for Chapter 3 
Stress and strain relations 
In this chapter  the basic concepts of stress-strain relations and their 2D and 3D cases are discussed. 
4.1 Basic concepts 
4.2 Constitutive relations (2D) 
4.3 Constitutive relations (3D) 
Quiz for Chapter 4 
Strain energy 
In this chapter  octahedral shear stress and deviatoric stress are introduced  and several strain energy forms are provided. 
5.1 Concepts and Formulas 
5.2 Octahedral shear stress 
5.3 Deviatoric stress 
5.4 Strain energy in special forms 
Quiz for Chapter 5 
Linear elasticity of isotropic materials 
In this chapter  concepts of linear elasticity of isotropic materials in 2D case are discussed. 
6.1 Concepts 
6.2 Constitutive equations in 2-D elasticity 
6.3 Strains and compatibility equations in 2-D elasticity 
6.4 Equilibrium and boundary conditions 
6.5 Example (a plate with a circular hole) 
Quiz for Chapter 6 
Stress function method in 2-D elasticity 
In this chapter  Airy’s stress function in 2D case is introduced and applied. 
7.1 Introduction to Airy’s stress function 
7.2 Defining equation for Airy’s stress function 
7.3 Example: Inverse method 
7.4 Example: Semi-inverse approach 
Quiz for Chapter 7 
Two-Dimensional Problems in Polar Coordinates 
In this chapter  Airy’s stress function in 2D polar coordinates is introduced and applied. 
8.1 Airy’s stress function in polar coordinates 
8.2 Example: Thick-walled cylindrical pressure vessels 
8.3 Example: A large plate with a small hole 
Quiz for Chapter 8 
Failure theories 
In this chapter  failure theories are introduced and summrized. 
9.1 Typical failure modes 
9.2 Brittle and ductile failure 
9.3 Introduction to linear elastic fracture mechanics 
9.4 Example: nondestructive test of pressurized pipes 
9.5 Introduction to Fatigue 
Quiz for Chapter 9 
Unsymmetric bending and curved beams 
In this chapter  stresses in beams under unsymmetric bending and curved beams are discussed. 
10.1 Symmetric Bending vs. Unsymmetric Bending 
10.2 Stress in beams under unsymmetric bending 
10.3 Shear stress due to transverse load 
10.4 Shear center 
10.5 Concepts of curved beams 
10.6 Tangential stress in curved beams 
Quiz for Chapter 10 
Torsion of prismatic members 
In this chapter  St. Venant torsion theory and Prandtl Stress Function method are introduced and applied for torsion of prismatic members. 
11.1 Reviews of MOM circular sections 
11.2 St. Venant torsion theory 
11.3 Prandtl Stress Function method 
11.4 Formulas for specific sections 
Quiz for Chapter 11 
Energy method and advanced topics 
In this chapter  some basic concepts for energy method and some advanced topics are introduced. 
12.1 Basic concepts for energy methods 
12.2 Principle of virtual work and minimum total potential energy 
12.3 Variational methods 
12.4 A New Non-classical Model for Reddy-Levinson Beams 
12.5 A Non-Classical Kirchhoff Plate Model 
12.6 A Simplified Micromorphic Theory and its application 
Quiz for Chapter 12 

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