本书旨在系统阐述固体力学的核心理论与方法，突破传统教材边界，注重理论与工程实践的深度融合。内容涵盖张量基础、三维应力与应变分析、失效理论、二维弹性理论、棱柱体扭转、能量方法、高阶弹性理论及可变形半导体等专题，辅以丰富的实例解析。书中特别强调数学工具与力学概念的协同运用，帮助读者掌握解决复杂工程问题的能力，适用于力学、土木工程、航空航天、机械工程、材料科学、生物工程等多学科领域。 本书面向高年级本科生与研究生，要求读者具备高等数学、线性代数、静力学及材料力学等方面的知识基础。通过循序渐进的章节，学生不仅能夯实理论基础，还能培养创新思维，将抽象原理转化为实际解决方案。编写过程中，我们整合了多年授课讲义，并广泛参考领域内经典著作与前沿研究，力求内容严谨且与时俱进。希望《固体力学基础》能成为读者探索固体力学世界的桥梁，激发新一代工程师与科学家推动学科发展的热情，为应对全球工程挑战贡献智慧。

Contents
Chapter 1 Introduction
1.1 A brief historical development
1.2 Some concepts
1.3 Book contents
Chapter 2 Mathematical Preliminaries
2.1 Physical quantities and index notation
2.2 Summation convention and two special arrays
2.3 Tensor algebra
2.4 Tensor calculus
Chapter 3 Analysis of Stress
3.1 Review of elementary MoM
3.2 Motivation & definition
3.3 Traction vector and cauchy relation
3.4 Stress transformation
3.5 Principal stresses
Chapter 4 Constitutive Relations
4.1 Basic concepts
4.2 Engineering materials
4.3 Constitutive relations for isotropic material (2-D)
4.4 Constitutive relations for isotropic material (3-D)
4.5 Constitutive relations for anisotropic materials
4.6 Constitutive relations for thermoelasticity
Chapter 5 Strain Energy
5.1 Concepts and formulas
5.2 Strain energy density for isotropic materials in some basic modes
5.3 Strain energy for isotropic materials in common structures
5.4 Octahedral shear stress
5.5 Deviatoric stress
5.6 Complementary strain energy
Chapter 6 Linear Elasticity of Isotropic Materials
6.1 Concepts
6.2 Constitutive equations in 2-D elasticity
6.3 Strains and compatibility equations in 2-D elasticity
6.4 Equilibrium equations
6.5 Boundary conditions
Chapter 7 Stress Function Method in 2-D Elasticity
7.1 Introduction to Airy stress function
7.2 Defining equation for Airy stress function
7.3 Solution techniques: inverse method
7.4 Solution techniques: semi-inverse approach
7.5 Solution techniques: Fourier methods
Chapter 8 Two-Dimensional Problems in Polar Coordinates
8.1 Polar coordinate formulation
8.2 Airy stress function in polar coordinates
8.3 General solutions in polar coordinates
Chapter 9 Failure Theories
9.1 Typical failure modes
9.2 Brittle and ductile failure
9.3 Introduction to linear elastic fracture mechanics
9.4 Introduction to fatigue
Chapter 10 Unsymmetric Bending and Curved Beams
10.1 Unsymmetric bending
10.2 Shear center
10.3 Curved beams
Chapter 11 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 Prandtl's membrane analogy
Chapter 12 Energy Methods
12.1 Basic concepts for energy methods
12.2 Principles of virtual work and minimum total potential energy
12.3 Variational methods
Chapter 13 Advanced Topic I: Higher-Order Elasticity
13.1 Couple stress theory
13.2 A reformulated strain gradient elasticity theory
13.3 Simplified micromorphic theory
Chapter 14 Advanced Topic II: Magneto-Electro-Elastic Structure Theories
14.1 Theoretical framework
14.2 New MEE beam model incorporating foundation effect
14.3 New MEE microplate model
14.4 New FG-MEE composite beam model
Chapter 15 Advanced Topic III: Deformable Semiconductors
15.1 Field equations for piezoelectric semiconductor
15.2 Field equations for flexoelectric semiconductor