PART Ⅲ SOLID MECHANICS
13 The general equations of linear elasticity
13.1 Back to the stress—strain law of linear elasticity： the elasticity coefficients of a material
13.2 Boundary value problems in linear elasticity： the linearization principle
13.3 Other equations
13.4 The limit of elasticity criteria
14 Classical problems of elastostatics
14.1 Longitudinal traction——compression of a cylindrical bar
14.2 Uniform compression of an arbitrary body
14.3 Equilibrium of a spherical container subjected to external and internal pressures
14.4 Deformation of a vertical cylindrical body under the action of its weight
14.5 Simple bending of a cylindrical beam
14.6 Torsion of cylindrical shafts
14.7 The Saint—Venant principle
15 Energy theorems， duality， and variational formulations
15.1 Elastic energy of a material
15.2 Duality—generalization
15.3 The energy theorems
15.4 Variational formulations
15.5 Virtual power theorem and variational formulations
16 Introduction to nonlinear constitutive laws and to homogenization
16.1 Nonlinear constitutive laws （nonlinear elasticity）
16.2 Nonlinear elasticity with a threshold（Henky's elastoplastic model）
16.3 Nonconvex energy functions
16.4 Composite materials： the problem of homogenization
17 Nonlinear elasticity and an application to biomechanics
17.1 The equations of nonlinear elasticity
17.2 Boundary conditions—boundary value problems
17.3 Hyperelastic materials
17.4 Hyperelastic materials in biomechanics

PART Ⅳ INTRODUCTION TO WAVE PHENOMENA
18 Linear wave equations in mechanics
18.1 Returning to the equations of linear acoustics and of linear elasticity
18.2 Solution of the one—dimensional wave equation
18.3 Normal modes
18.4 Solution of the wave equation
18.5 Superposition of waves， beats， and packets of waves
19 The soliton equation： the Korteweg—de Vries equation
19.1 Water—wave equations
19.2 Simplified form of the water—wave equations
19.3 The Korteweg—de Vries equation
19.4 The soliton solutions of the KdV equation
20 The nonlinear Schrodinger equation
20.1 Maxwell equations for polarized media
20.2 Equations of the electric field： the linear case
20.3 General case
20.4 The nonlinear Schrodinger equation
20.5 Soliton solutions of the NLS equation
Appendix.The partial differential equations of mechanics
Hints for the exercises
References
Index

 2/2   首页 上一页 1 2

自然科学 数学 应用数学

在线阅读