Systematic Study Guide for Solid Mechanics
This guide follows the logical framework of "Basic Concepts - Core Theory - Specialized Analysis - Application Expansion," systematically decomposing the core knowledge modules of solid mechanics, and connecting various knowledge points through coherent article titles, clearly outlining the cognitive journey from basic assumptions to practical applications, thereby assisting learners in establishing a comprehensive knowledge system in solid mechanics and mastering the core methods of solid deformation and strength analysis.
Basic Concepts
Solid Mechanics: The Study Objects and Basic Assumptions (Continuity, Uniformity, Isotropy)
- The Scope of Solid Mechanics and Core Research Tasks
- Solid Mechanics and the Relevance of Engineering Practice
- Material Forms and Mechanical Properties of Solid Mechanics
- The core essence of the continuity assumption and its prerequisites for application
- The Simplification Value of Continuity Assumption in Solid Mechanics Analysis
- Definition of the Uniformity Assumption and Spatial Consistency of Material Properties
- The meaning of the isotropic assumption and the anisotropy of material mechanical properties
- Initial Understanding and Limitations of Assumptions for Anisotropic Materials
- Three Basic Assumptions in the Foundation of Solid Mechanics Theoretical Framework
Stress State Analysis (Normal Stress, Shear Stress, Principal Stress, Stress Tensor)
- Definition of Stress and the Mechanism of Stress Generation in Solids
- Criteria for Distinguishing Normal Stress from Shear Stress and Direction Determination
- Stress Description and Calculation in Uniaxial Stress State
- Definition of Plane Stress State and Common Engineering Scenarios
- Plane stress state stress analysis methods (analytical method, graphical method)
- Rules for Drawing the Stress Circle and Applications (Calculate Principal Stresses and Shear Stress)
- Principal stress definition and the criteria for determining principal planes
- Requirements for the Complex Stress Description in Three-Dimensional Stress States
- The Background and Mathematical Expression of the Stress Tensor
- The basic properties of the stress tensor and its invariant meaning
Strain State Analysis (Linear Strain, Shear Strain, Principal Strain, Strain Tensor)
- Definition of Strain and Quantitative Analysis of Solid Deformation
- Strain physics meaning and calculation expressions
- Shear strain's definition and quantitative description of angular deformation
- Sign Convention for Linear Strain and Shear Strain
- Deformation Analysis in Uniaxial Strain State
- Definition of Plane Strain State and Engineering Application Scenarios
- Plane Strain Strain Analysis Method
- Definition of Principal Strain and Determination of the Direction of Principal Strain
- The Logic and Mathematical Expression of Constructing the Strain Tensor
- Correspondence Between Strain and Stress Tensors
Material Relationship (Hooke's Law, Elastic Modulus, Poisson's Ratio)
- Definition of Constitutive Relations and the Significance of the Stress-Strain Relationship
- Uniaxial Tension/Compression: Mathematical Expression of Hooke's Law
- Physical Significance of Elastic Modulus and Intrinsic Properties of Materials
- Definition of Poisson's ratio and lateral deformation characteristics
- Definition of Shear Modulus and the Shear Stress-Strain Relationship
- Conversion Relationship Between Elastic Modulus, Shear Modulus, and Poisson's Ratio
- Generalized Hooke's Law in Plane Stress State
- Derivation of the Generalized Hooke's Law in a Three-Dimensional Stress State
- Conditions of Application and Elastic Limit of Hooke's Law
Core Theory
Basic Deformations (Tension/Compression, Shear, Bending, Torsion)
- Classification Criteria and Basic Deformation Forms Overview
- Axial Tension/Compression Force Characteristics and Deformation Characteristics
- Axial Tension and Compression Stress Calculation and Strength Conditions
- Axial Tension/Compression Deformation Calculation and Stiffness Conditions
- Characteristics of Shear Deformation and Practical Calculation Methods
- Shear Strength Conditions and Compression Strength Conditions
- Force Characteristics of Plane Bending and Stress Analysis of Beams
- Methods for Drawing Shear Force and Moment Diagrams in Beams
- Beam's bending stress calculation and strength conditions
- Calculation and Distribution Pattern of Bending Shear Stress in Beams
- Beam Bending Deformation Calculation Methods (Integration Method, Superposition Method)
- Torsion Stress Characteristics and Deformation Characteristics of Circular Shafts
- Calculation of Shear Stress in Circular Shafts and Strength Conditions
- Deformation Calculation and Stiffness Conditions for Circular Shafts Under Torsion
Strength Theory (First to Fourth Strength Theory)
- The definition of strength theory and the requirement for strength assessment in complex stress states
- Classification Criteria and Basic Assumptions of Strength Theory
- Core Concept of the First Theory of Strength (Maximum Principal Stress Theory)
- First Strength Theory and Applicable Materials in Engineering Scenarios
- The Essence of the Second Strength Theory (Maximum Strain Theory).
- Conditions of Applicability and Limitations of the Second Strength Theory
- The Core Idea of the Third Strength Theory (Maximum Shear Stress Theory)
- Equivalent Stress Expression of the Third Strength Theory and Its Application
- Connotation of the Fourth Strength Theory (Shape Change Strain Energy Theory)
- The Expression of Equivalent Stress in the Fourth Strength Theory and Its Applicable Scenarios
- Principles of Selection for Different Strength Theories and Their Comparison with Engineering Applications
Focused analysis
Energy Method (Strain Energy, Unit Load Method, Virtual Work Principle)
- Core Concept and Application Value of the Energy Method in Solid Mechanics
- Definition of Strain Energy and Strain Energy Calculation for Axial Tension and Compression Members
- Beam's bending strain energy calculation method
- Strain Energy Calculation in Circular Shaft Torsion
- Principle of Superposition in Composite Deformation
- Basic Formulation and Physical Significance of the Virtual Work Principle
- Virtual Displacement Principle in the Application of Static Equilibrium
- Derivation Approach and Basic Principles of the Unit Load Method
- Steps and Examples for Calculating Linear Displacement Using the Unit Load Method
- Unit Load Method for Calculating Angular Displacement
- Energy Method in the Analysis of Statically Indeterminate Structures
Column Stability (Critical Pressure, Euler's Formula)
- Definition of Stability and Engineering Hazards of Instability
- The fundamental difference between stability and strength in compression members.
- Definition of Critical Pressure and Criteria for Determining Press Rod Stability
- Derivation Conditions and Applicability of Euler's Formula
- Slenderness coefficient of a column under different support conditions
- Euler Critical Stress Calculation and Application Limits
- Critical Stress Definition and Total Critical Stress Diagram
- Stability Conditions and Safety Factor for Compressive Members
- Measures and Methods to Improve Column Stability
Fundamentals of Elasticity (Equilibrium Equations, Geometric Equations, Boundary Conditions)
- The scope of elasticity mechanics and its relation to classical mechanics
- Fundamental Assumptions and Research Simplification in Elastic Mechanics
- Derivation of Balance Equations (Relationship between Stress and Volume Force)
- Simplified Equilibrium Equations for Planar Problems
- Derivation of Geometric Equations (Strain-Displacement Relationship)
- Simplification of Geometric Equations in Plane Problems
- Physical equations (constitutive equations) in elastic mechanics
- Classification of Boundary Conditions (Stress Boundary Conditions, Displacement Boundary Conditions)
- Mathematical Expression and Application of Stress Boundary Conditions
- Mathematical Representation and Application of Displacement Boundary Conditions
- The Approach to Solving Planar Problems in Elasticity Mechanics
Introduction to Plasticity Mechanics (Yield Criterion, Plastic Flow Law)
- The Scope of Plasticity Theory and the Difference from Elasticity Theory
- Features of Plastic Deformation and Yield Phenomenon
- Definition and Role of Yield Criterion (Determine Material Yield)
- Tresca's Criterion (Maximum Shear Stress Yield Criterion)
- Mises Yield Criterion (Strain Energy Criterion)
- A Comparison of Two Yield Criteria and Their Suitable Materials
- The Core Idea of the Plastic Flow Law (Strain Rate Increment and Stress Relationship)
- Stress-Strain Relationship of Ideal Plasticity Materials
- Fundamental Assumptions and Simplified Models in Plasticity Mechanics
- Initial Understanding of Engineering Applications in Plasticity Mechanics
Fundamentals of Fracture Mechanics (Crack Propagation, Fracture Toughness)
- The Research Objectives and Engineering Background of Fracture Mechanics
- Types of material failure (brittle fracture, ductile fracture)
- Common Types of Cracks and Their Geometric Characteristics
- Definition and physical significance of the stress intensity factor
- Definition of Fracture Toughness and Material Intrinsic Properties
- Establishment of Fracture Criterion (Stress Intensity Factor Criterion)
- Types of Crack Propagation and Extension Mechanisms
- Factors Influencing Fracture Toughness of Materials
- Fracture Mechanics in the Application of Engineering Structural Safety Assessment
Application Expansion
Composite Material Mechanics
- Definition and Composition Characteristics of Composite Material
- Classification of Composite Materials (Fiber-Reinforced, Particle-Reinforced, etc.)
- Superior Performance of Composite Materials and Engineering Application Benefits
- Basic Assumptions and Simplification of Composite Material Research
- Unidirectional Composite Materials' Macroscopic Constitutive Relationship
- Calculation of Elastic Modulus of Unidirectional Composite Materials
- Composite laminated panel basic concepts
- Basic Stress-Strain Analysis of Laminated Plates
- Research Characteristics and Challenges of Composite Material Mechanics
Foundation of Vibration and Waves (Free Vibration of Solids and Forced Vibration)
- The scope of research on solid vibrations and its engineering significance
- Free Vibration Equations of a Single-Degree-of-Freedom System
- Determination of the Intrinsic Frequency of a Single-Degree-of-Freedom System in Free Vibration
- Forced Vibration Equation of a Single-Degree-of-Freedom System
- Forced Vibration Steady-State Response and Resonance
- The effect of damping on solid vibrations
- Basic Concepts of Vibration
- Propagation of Elastic Waves in Solids
- Types of Elastic Waves (P-waves, S-waves) and Propagation Speed
- Solid Vibration and Wave Phenomena in Engineering Applications (Non-Destructive Testing etc.)