In view of these considerations this book covers the following main topics: 1. The classical theory of linear elasticity 2. The mathemati-cal theory of the composite elastic structures. Here the mathematical method proposed by the authors is presented. 3. The numerical method for solving elastic structural problems--the finite element method. The authors try to treat these three topics within the framework f a unified theory.

 The book covers three main topics: the classical theory of linear elasticity, the mathematical theory of composite elastic structures, as an application of the theory of elliptic equations on composite manifolds developed by the first author, and the finite element method for solving elastic structural problems.The authors treat these topics within the framework of a unified theory. The book carries on a theoretical discussion on the mathematical basis of the principle of minimum potential theory. The emphasis is on the accuracy and completeness of the mathematical formulation of elastic structural problems. The book will be useful to applied mathematicians,engineers and graduate students. It may also serve as a course in elasticity for undergraduate students in applied sciences.

Chapter 1 Simple Modes of Elastic Deformation

1 Simple Stretching and Compression of Springs

 1.1 Deformation mode

 1.2 Variational principles and equilibrium equation

2 Stretching and Compression of Uniform Rods

 2.1 Deformation modes

 2.2 Variational principles and equilibrium equations

 2.3 Peiecewise uniform rods 

 2.4 Systems of rods in plane tension

3 Stretching and Compression of Nonuniform Rods

 3.1 Deformation modes

 3.2 Variational principles

 3.3 Boundary value problems

 3.4 Equilibrium equations

 3.5 Strainless states

4 Stretching and Compression in Various Directions

 4.1 Hooke's law and strain energy

 4.2 Changes of volume

5 Shear Deformations

 5.1 Shearing stresses

 5.2 Shear strains

 5.3 Hooke's law and the strain energy of shear deformations

6 Torsion of Circular Rods

 6.1 Deformation modes

 6.2 Variational principles and equilibrium equations

 6.3 Torsion of circular tubes

7 Bending of Beams

 7.1 Deformation modes

 7.2 Variational principles and equilibrium equations

 7.3 Boundary conditions and interface conditions

 7.4 Strainless states

Chapter 2 Static Elasticity

1 Displacements and Strains

 1.1 Strains

 1.2 Rotations

 1.3 Stralnless states and infinitesimal rigid displacements ..

2 Transformation of Principal Axes and Principal Strains

 2.1 Rotation of coordinate axes

 2.2 Strain tensors in the transformed and original systems of coordinates

 2.3 Principal axes and principal strains

3 Stresses

 3.1 Components of stress

 3.2 Equilibrium equations

 3.3 Principal stresses

4 Hooke's Law and Strain Energy

 4.1 Hooke's law

 4.2 Strain energy

5 Variational Principles and Elastic Equilibrium

 5.1 Variational principles

 5.2 Equilibrium equations

 5.3 Boundary conditions and interface conditions

 5.4 Strainless states

 5.5 On variational principles and finite element methods

6 Geometrical Compatibility

 6.1 Integrability conditions of vector fields and topological properties of domain

 6.2 Equations of geometric compatibility and conditions for intergrability

7 Thermal Effects

 7.1 Hooke's law and strain energy

 7.2 Variational principles and equilibrium equations

Chapter 3 Typical Problems of Elastic Equilibrium

1 Plane Elastic Problems

 1.1 Plane strain problems

 1.2 Plane stress problems

 1.3 Comparisons

 1.4 One dimensional problems

2 Plane Geometrical Compatibility and Stress Function

 2.1 Plane geometric compatibility

 2.2 Stress function

 2.3 Boundary conditions

 2.4 Multiply-connected domains

3 Torsion of Cylinders

 3.1 Deformation modes

 3.2 Torsion function

 3.3 Stress function

 3.4 Torsion formulas of several specified cross sections

4 Bending of Thin Plates

 4.1 Deformation modes

 4.2 Variational principles

 4.3 Equilibrium equations

 4.4 Boundary conditions and interface conditions

 4.5 Strainless states

 4.6 Thermal effects

5 Bending of Spatial Beams

 5.1 Deformation modes

 5.2 Variational principles

 5.3 Equilibrium equations

 5.4 Boundary conditions and interface conditions

 5.5 Strainless states

 5.6 Thermal effects

Chapter 4 Composite Elastic Structures

1 Introduction

2 Plane Composite Structures

 2.1 Geometric description

 2.2 Fundamental members

 2.3 The rigid connection

 2.4 Boundary conditions

 2.5 The pinned connection

 2.6 Variational principles

 2.7 Equilibrium equations

 2.8 Stralnless states

3 Space Composite Structures

 3.1 Geometric description

 3.2 Fundamental members

 3.3 The rigid connection

 3.4 Boundary conditions

 3.5 The pinned connection

 3.6 Variational principles

 3.7 Equilibrium equations

 3.8 Stralnless states

 3.9 Treatment of the offset distance

Chapter 5 Finite Element Methods

1 Introduction

2 Stretching and Torsion of Rods

 2.1 Variational problems

 2.2 Subdivision and interpolation

 2.3 Analysis of elements (linear elements

 2.4 Assembly

 2.5 Treatment of essential conditions

 2.6 Applications of the quadratic element

3 Bending of Beam.

 3.1 Variational problems

 3.2 The cubic hermite element

 4 Poisson Equation

 4.1 Variational problems

 4.2 Subdivision and interpolation

 4.3 Analysis of elements (linear elements and quadratic elements

 4.4 Assembly and the others

 5 Problems of Plane Elasticity

 5.1 Variational problems

 5.2 Bilinear rectangular elements

 5.3 Essential boundary conditions

 6 Bending Thin Plates

 6.1 Variational principles

 6.2 Incomplete bicubic rectangular elements ( addini-clough-melosh elements

 6.3 Incomplete cubic triangular elements (zienkiewicz elements

 6.4 Complete quadratic triangular elements(morley elements

 6.5 On noncomforming elements

7 Composite Structures

 7.1 Plane composite structures

 7.2 Space composite structures

 7.3 Nonstandard connections and the treatment of the offset distance

References

Index