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