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
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