非线性变形体动力学

Chapter 1 Introduction

1.1.Deforfflable.body dynamics

1.1.1.Cable dynamics

1.1.2.Beams and rods

1.1.3.Plates and shells

1.1.4.Soft webs

1.2.Book layout

References

Chapter 2 Tensor Analysis

2.1.Vectors and tensors

2.1.1.Vector algebra

2.1.2.Base vectors and metric tensors

2.1.3.Local base vector transformation

2.1.4.Tensor algebra

2.2.Second.order tensors

2.2.1.Second.order tensor algebra

2.2.2.Basic properties

2.2.3.Tensor decompositions

2.2.4.Tensor functions

2.3.Tensor calculus

2.3.1.Differentiation

2.3.2.Invariant differential operators and integral theorems

2.3.3.Riemann-Christoffel curvature tensors

2.4.Two.point tensor fields

2.4.1.Two-point tensors

2.4.2.Independent coordinates

2.4.3.Correlated coordinates

2.4.4.Shifter tensor fields

References

Chapter 3 Deformation，Kinematics and Dynamics

3.1.Deformation geometry

3.1.1.Curvilinear coordinates

3.1.2.Deformation gradient and tensors

3.1.3.Green-Cauchy strain tensors and engineering strain

3.1.4.Principal strains and directions

3.2.Kinematics

3.2.1.Material derivatives

3.2.2.Strain rates

3.3.Dynamics

3.3.1.Forces and stresses

3.3.2.Transport theorem

3.3.3.Cauchy stress and couple-stress tensors

3.4.Energy conservation

References

Chapter 4 Constitutive Laws and Damage Theory

4.1.Constitutive equations

4.2.Material damage and effective stress

4.3.Equivalence principles

4.4.An anisotropic damage theory

4.5.Applications

4.5.1.Uniaxial tensional models

4.5.2.Pure torsion

4.5.3.Elastic perfectly-plastic materials

References Chapter 5 Nonlinear Cables

5.1.A nonlinear theory of cables

5.2.Traveling and rotating cables

5.3.Equilibrium of traveling elastic cables

5.3.1.Existence conditions

5.3.2.Displacements

5.3.3.Applications

5.4.Nonlinear dynamics of cables

5.4.1.Equations of motion

5.4.2.Motions of inextensible cables

5.4.3.Motions ofdef01Tnable cables

References

Chapter 6 Nonlinear Plates and Waves

6.1.A nonlinear theory of plates

6.1.1.Deformation of a 3-D body

6.1.2.Strains in thin plates

6.1.3.Equations of motion

6.1.4.Reduction to established theories

6.2.Waves in traveling plates

6.2.1.An approximate theory

6.2.2.Perturbation analysis

6.2.3.Static waves

6.2.4.Nonlinear waves

6.2.5 Chaotic waves

6.3.Waves in rotating disks

6.3.1.Equations of motions

6.3.2.Nonlinear waves

6.3.3.Resonant and stationary waves

6.4.Conclusions

References

Chapter 7 Nonlinear Webs.Membranes and Shells

7.1.Nonlinear webs

7.1.1.Cable-network webs

7.1.2.Cable-fabric webs

7.1.3.Continuum webs

7.2.Nonlinear membranes

7.2.1.A membrane theory based on the Cartesian coordinates-

7.2.2.A membrane theory based on the curvilinear coordinates

7.3.Nonlinear shells

7.3.1.A shell theory based on the Cartesian Coordinates

7.3.2.A shell theory based on the curvilinear coordinates

References

Chapter 8 Nonlinear Beams and Rods

8.1.Differential geometry of curves

8.2.A nonlinear theory of straight beams

8.3.Nonlinear curved beams

8.3.1.A nonlinear theory based on the Cartesian C00rdinates

8.3.2.A nonlinear theory based on the curvilinear coordinates

8.4.A nonlinear theory of straight rods

8.5.Nonlinear curved rods

8.5.1.A curved rod theory based on the Cartesian coordinates

8.5.2.A curved rod theory based on the curvilinear coordinates

References

Subject Index

Nonlinear Deformable-body Dynamics mainly consists in a mathematical treatise of approximate theories for thin deformable bodies，including cables，beams，rods，webs，membranes，plates，and shells．The intent of the book is to stimulate more researches in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications．For instance，the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues，and the nonlinear theory of deformable bodies，based on the Kirchhoff assumptions，is a special case discussed．This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics，mathematics，engineering and biophysics．

Nonlinear Physical Science focuses on the recent advances of fundamental theories and principles，analytical and symbolic approaches，as well as computational techniques in nonlinear physical science and nonlinear mathematics with engineering applications．