《ANALYSIS OF STRUCTURAL MEMBER SYSTEMS》求取 ⇩

Ⅰ—MATHEMATICAL PRELIMINARIES3

1Introduction to Matrix Algebra3

1-1 Definition of a Matrix3

1-2 Equality， Addition， and Subtraction of Matrices5

1-3 Matrix Multiplication5

1-4 Transpose of a Matrix8

1-5 Special Square Matrices10

1-6 Operations on Partitioned Matrices12

1-7 Definition and Properties of a Determinant16

1-8 Cofactor Expansion Formula19

1-9 Cramer’s Rule21

1-10 Adjoint and Inverse Matrices22

1-11 Elementary Operations on a Matrix24

1-12 Rank of a Matrix27

1-13 Solvability of Linear Algebraic Equations30

2Characteristic-Value Problems and Quadratic Forms46

2-1 Introduction46

2-2 Second-Order Characteristic-Value Problem48

2-3 Similarity and Orthogonal Transformations52

2-4 The nth-Order Symmetrical Characteristic-Value Problem55

2-5 Quadratic Forms57

3Relative Extrema for a Function66

3-1 Relative Extrema for a Function of One Variable66

3-2 Relative Extrema for a Function of n Independent Variables71

3-3 Lagrange Multipliers75

4Differential Geometry of a Member Element81

4-1 Parametric Representation of a Space Curve81

4-2 Arc Length82

4-3 Unit Tangent Vector85

4-4 Principal Normal and Binormal Vectors86

4-5 Curvature， Torsion， and the Frenet Equations88

4-6 Summary of the Geometrical Relations for a Space Curve91

4-7 Local Reference Frame for a Member Element92

4-8 Curvilinear Coordinates for a Member Element94

5Matrix Transformations for a Member Element100

5-1 Rotation Transformation100

5-2 Three-Dimensional Force Transformations103

5-3 Three-Dimensional Displacement Transformations109

Ⅱ—ANALYSIS OF AN IDEAL TRUSS115

6Governing Equations for an Ideal Truss115

6-1 General115

6-2 Elongation—Joint Displacement Relation for a Bar116

6-3 General Elongation—Joint Displacement Relation120

6-4 Force-Elongation Relation for a Bar125

6-5 General Bar Force—Joint Displacement Relation130

6-6 Joint Force-Equilibrium Equations130

6-7 Introduction of Displacement Restraints； Governing Equations132

6-8 Arbitrary Restraint Direction134

6-9 Initial Instability137

7Variational Principles for an Ideal Truss152

7-1 General152

7-2 Principle of Virtual Displacements153

7-3 Principle of Virtual Forces159

7-4 Strain Energy； Principle of Stationary Potential Energy162

7-5 Complementary Energy； Principle of Stationary Complementary Energy165

7-6 Stability Criteria169

8Displacement Method—Ideal Truss178

8-1 General178

8-2 Operation on the Partitioned Equations178

8-3 The Direct Stiffness Method180

8-4 Incremental Formulation； Classical Stability Criterion191

8-5 Linearized Stability Analysis200

9Force Method—Ideal Truss210

9-1 General210

9-2 Governing Equations—Algebraic Approach211

9-3 Governing Equations—Variational Approach216

9-4 Comparison of the Force and Mesh Methods217

Ⅲ—ANALYSIS OF A MEMBER ELEMENT229

10Governing Equations for a Deformable Solid229

10-1 General229

10-2 Summation Convention； Cartesian Tensors230

10-3 Analysis of Deformation； Cartesian Strains232

10-4 Analysis of Stress’240

10-5 Elastic Stress-Strain Relations248

10-6 Principle of Virtual Displacements； Principle of Stationary Potential Energy； Classical Stability Criteria253

10-7 Principle of Virtual Forces； Principle of Stationary Complementary Energy257

11St. Venant Theory of Torsion-Flexure of Prismatic Members271

11-1 introduction and Notation271

11-2 The Pure-Torsion Problem273

11-3 Approximate Solution of the Torsion Problem for Thin-Walled Open CrossSections281

11-4 Approximate Solution of the Torsion Problem for Thin-Walled Closed Cross Sections286

11-5 Torsion-Flexure with Unrestrained Warping293

11-6 Exact Flexural Shear Stress Distribution for a Rectangular Cross Section303

11-7 Engineering Theory of Flexural Shear Stress Distribution in Thin-Walled Cross Sections306

12Engineering Theory of Prismatic Members330

12-1 Introduction330

12-2 Force-Equilibrium Equations331

12-3 Force-Displacement Relations； Principle of Virtual Forces333

12-4 Summary of the Governing Equations339

12-5 Displacement Method of Solution—Prismatic Member340

12-6 Force Method of Solution349

13Restrained Torsion-Flexure of a Prismatic Member371

13-1 Introduction371

13-2 Displacement Expansions； Equilibrium Equations372

13-3 Force-Displacement Relations—Displacement Model375

13-4 Solution for Restrained Torsion—Displacement Model379

13-5 Force-Displacement Relations—Mixed Formulation383

13-6 Solution for Restrained Torsion—Mixed Formulation389

13-7 Application to Thin-Walled Open Cross Sections395

13-8 Application to Thin-Walled Closed Cross Sections405

13-9 Governing Equations--Geometrically Nonlinear Restrained Torsion414

14Planar Deformation of a Planar Member425

14-1 Introduction； Geometrical Relations425

14-2 Force-Equilibrium Equations427

14-3 Force-Displacement Relations； Principle of Virtual Forces429

14-4 Force-Displacement Relations—Displacement Expansion Approach； Principle of Virtual Displacements435

14-5 Cartesian Formulation445

14-6 Displacement Method of Solution—Circular Member449

14-7 Force Method of Solution458

14-8 Numerical Integration Procedures473

15Engineering Theory of an Arbitrary Member485

15-1 Introduction； Geometrical Relations485

15-2 Force-Equilibrium Equations488

15-3 Force-Displacement Relations—Negligible Warping Restraint； Principle of Virtual Forces490

15-4 Displacement Method—Circular Planar Member493

15-5 Force Method—Examples499

15-6 Restrained Warping Formulation507

15-7 Member Force-Displacement Relations—Complete End Restraint511

15-8 Generation of Member Matrices517

15-9 Member Matrices—Prismatic Member520

15-10 Member Matrices—Thin Planar Circular Member524

15-11 Flexibility Matrix—Circular Helix531

15-12 Member Force-Displacement Relations—Partial End Restraint535

Ⅳ—ANALYSIS OF A MEMBER SYSTEM545

16Direct Stiffness Method—Linear System545

16-1 Introduction545

16-2 Member Force-Displacement Relations546

16-3 System Equilibrium Equations547

16-4 Introduction of Joint Displacement Restraints548

17General Formulation—Linear System554

17-1 Introduction554

17-2 Member Equations555

17-3 System Force-Displacement Relations557

17-4 System Equilibrium Equations559

17-5 Introduction of Joint Displacement Restraints； Governing Equations560

17-6 Network Formulation562

17-7 Displacement Method565

17-8 Force Method567

17-9 Variational Principles570

17-10 Introduction of Member Deformation Constraints573

18 Analysis of Geometrically Nonlinear Systems585

18-1Introduction585

18-2 Member Equations—Planar Deformation585

18-3 Member Equations—Arbitrary Deformation591

18-4 Solution Techniques； Stability Analysis597

Index605