Armenakas A.E. Advanced mechanics of materials and applied elasticity
Навигация

Выставка новых поступлений  |  Поступления иностранных книг в библиотеки СО РАН : 2003 | 2006 |2008
 
Книжные оглавления
Armenakas A.E. Advanced mechanics of materials and applied elasticity / Armenakas A.E. - Boca Raton: Taylor & Francis, 2006. - 975 p. - ISBN 0-8493-9899-1.
 
ОглавлениеСноска

Chapter 1 Cartesian Tensors ..................................................... 1

1.1  Vectors .................................................................... 1
1.2  Dyads ..................................................................... 11
1.3  Definition and Rules of Operation of Tensors of the Second Rank ........... 12
1.4  Transformation of the Cartesian Components of a Tensor of the Second
     Rank upon Rotation of the System of Axes to Which They Are Referred ....... 20
1.5  Definition of a Tensor of the Second Rank on the Basis of the Law of
     Transformation of Its Components .......................................... 21
1.6  Symmetric Tensors of the Second Rank ...................................... 22
1.7  Invariants of the Cartesian Components of a Symmetric Tensor of the
     Second Rank ............................................................... 22
1.8  Stationary Values of a Function Subject to a Constraining Relation ........ 23
1.9  Stationary Values of the Diagonal Components of a Symmetric Tensor of
     the Second Rank ........................................................... 26
1.10 Quasi Plane Form of Symmetric Tensors of the Second Rank .................. 31
1.11 Stationary Values of the Diagonal and the Non-Diagonal Components of
     the Quasi Plane, Symmetric Tensors of the Second Rank ..................... 33
1.12 Mohr's Circle for Quasi Plane, Symmetric Tensors of the Second Rank ....... 37
1.13 Maximum Values of the Non-Diagonal Components of a Symmetric Tensor of
     the Second Rank ........................................................... 43
1.14 Problems .................................................................. 44

Chapter 2 Strain and Stress Tensors ............................................ 53

2.1  The Continuum Model ....................................................... 53
2.2  External Loads ............................................................ 53
2.3  The Displacement Vector of a Particle of a Body ........................... 55
2.4  Components of Strain of a Particle of a Body .............................. 56
2.5  Implications of the Assumption of Small Deformation ....................... 62
2.6  Proof of the Tensorial Property of the Components of Strain ............... 64
2.7  Traction and Components of Stress Acting on a Plane of a Particle of
     a Body .................................................................... 66
2.8  Proof of the Tensorial Property of the Components of Stress ............... 68
2.9  Properties of the Strain and Stress Tensors ............................... 71
2.10 Components of Displacement for a General Rigid Body Motion of
     a Particle ................................................................ 80
2.11 The Compatibility Equations ............................................... 82
2.12 Measurement of Strain ..................................................... 84
2.13 The Requirements for Equilibrium of the Particles of a Body ............... 88
2.14 Cylindrical Coordinates ................................................... 91
2.15 Strain-Displacement Relations in Cylindrical Coordinates .................. 93
2.16 The Equations of Compatibility in Cylindrical Coordinates ................. 94
2.17 The Equations of Equilibrium in Cylindrical Coordinates ................... 95
2.18 Problems .................................................................. 96

Chapter 3 Stress-Strain Relations ............................................. 107

3.1  Introduction ............................................................. 107
3.2  The Uniaxial Tension or Compression Test Performed in an Environment
     of Constant Temperature .................................................. 108
3.3  Strain Energy Density and Complementary Energy Density for Elastic
     Materials Subjected to Uniaxial Tension or Compression in an
     Environment of Constant Temperature ...................................... 115
3.4  The Torsion Test ......................................................... 119
3.5  Effect of Pressure, Rate of Loading and Temperature on the Response of
     Materials Subjected to Uniaxial States of Stress ......................... 121
3.6  Models of Idealized Time-Independent Stress-Strain Relations for
     Uniaxial States of Stress ................................................ 124
3.7  Stress-Strain Relations for Elastic Materials Subjected to
     Three-Dimensional States of Stress ....................................... 126
3.8  Stress-Strain Relations of Linearly Elastic Materials Subjected to
     Three-Dimensional States of Stress ....................................... 128
3.9  Stress-Strain Relations for Orthotropic, Linearly Elastic Materials ...... 130
3.10 Stress-Strain Relations for Isotropic, Linearly Elastic Materials
     Subjected to Three-Dimensional States of Stress .......................... 133
3.11 Strain Energy Density and Complementary Energy Density of a Particle of
     a Body Subjected to External Forces in an Environment of Constant
     Temperature .............................................................. 135
3.12 Thermodynamic Considerations of Deformation Processes Involving Bodies
     Made from Elastic Materials .............................................. 142
3.13 Linear Response of Bodies Made from Linearly Elastic Materials ........... 146
3.14 Time-Dependent Stress-Strain Relations  .................................. 147
3.15 The Creep and the Relaxation Tests ....................................... 148
3.16 Problems ................................................................. 150

Chapter 4 Yield and Failure Criteria .......................................... 155

4.1  Yield Criteria for Materials Subjected to Triaxial States of Stress in
     an Environment of Constant Temperature ................................... 155
4.2  The Von Mises Yield Criterion ............................................ 159
4.3  The Tresca Yield Criterion ............................................... 162
4.4  Comparison of the Von Mises and the Tresca Yield Criteria ................ 162
4.5  Failure of Structures — Factor of Safety for Design ...................... 167
4.6  The Maximum Normal Component of Stress Criterion for Fracture of Bodies
     Made from a Brittle, Isotropic, Linearly Elastic Material ................ 173
4.7  The Mohr's Fracture Criterion for Brittle Materials Subjected to States
     of Plane Stress .......................................................... 175
4.8  Problems ................................................................. 179

Chapter 5 Formulation and Solution of Boundary Value
Problems Using the Linear Theory of Elasticity ................................ 185

5.1  Introduction ............................................................. 185
5.2  Boundary Value Problems for Computing the Displacement and Stress Fields
     of Solid Bodies on the Basis of the Assumption of Small Defor ............ 186
5.3  The Principle of Saint Venant ............................................ 193
5.4  Methods for Finding Exact Solutions for Boundary Value Problems in the
     Linear Theory of Elasticity .............................................. 196
5.5  Solution of Boundary Value Problems for Computing the Displacement and
     Stress Fields of Prismatic Bodies Made from Homogeneous, Isotropic,
     Linearly Elastic Materials ............................................... 196
5.6  Problems ................................................................. 216

Chapter 6 Prismatic Bodies Subjected to Torsional Moments
at Their Ends ................................................................. 221

6.1  Description of the Boundary Value Problem for Computing the Displacement
     and Stress Fields in Prismatic Bodies Subjected to Torsional Moments at
     Their Ends ............................................................... 221
6.2  Relations among the Coordinates of a Point Located on a Curved Boundary
     of a Plane Surface ....................................................... 223
6.3  Formulation of the Torsion Problem for Prismatic of Arbitary Cross
     Section on the Basis of the Linear Theory of Elasticity .................. 224
6.4  Interpretation of the Results of the Torsion Problem ..................... 233
6.5  Computation of the Stress and Displacement Fields of Bodies of Solid
     Elliptical and Circular Cross Section Subjected to Equal and Opposite
     Torsional Moments at Their Ends .......................................... 236
6.6  Multiply Connected Prismatic Bodies Subjected to Equal and Opposite
     Torsional Moments at Their Ends .......................................... 241
6.7  Available Results ........................................................ 249
6.8  Direction and Magnitude of the Shearing Stress Acting on the Cross
     Sections of a Prismatic Body of Arbitrary Cross Section Subjected to
     Torsional Moments at Its Ends ............................................ 249
6.9  The Membrane Analogy to the Torsion Problem .............................. 251
6.10 Stress Distribution in Prismatic Bodies of Thin Rectangular Cross
     Section Subjected to Equal and Opposite Torsional Moments at Their
     Ends ..................................................................... 258
6.11 Torsion of Prismatic Bodies of Composite Simply Connected Cross
     Sections ................................................................. 261
6.12 Numerical Solutions of Torsion Problems Using Finite Differences ......... 263
6.13 Problems ................................................................. 268

Chapter 7 Plane Strain and Plane Stress Problems in Elasticity ................ 271

7.1  Plane Strain ............................................................. 271
7.2  Formulation of the Boundary Value Problem for Computing the Stress
     and the Displacement Fields in a Prismatic Body in a State of Plane
     Strain Using the Airy Stress Function .................................... 273
7.3  Prismatic Bodies of Multiply Connected Cross Sections in a State of
     Plane Strain ............................................................. 278
7.4  The Plane Strain Equations in Cylindrical Coordinates .................... 280
7.5  Plane Stress ............................................................. 287
7.6  Simply Connected Thin Prismatic Bodies (Plates) in a State of Plane
     Stress Subjected on Their Lateral Surface to Symmetric in x1 
     Components of Traction Tn2 and Tn3 ........................................ 290
7.7  Two-Dimensional or Generalized Plane Stress .............................. 295
7.8  Prismatic Members in a State of Axisymmetric Plane Strain or Plane
     Stress ................................................................... 306
7.9  Problems ................................................................. 322

Chapter 8 Theories of Mechanics of Materials .................................. 327

8.1  Introduction ............................................................. 327
8.2  Fundamental Assumptions of the Theories of Mechanics of Materials for
     Line Members ............................................................. 329
8.3  Internal Actions Acting on a Cross Section of Line Members ............... 337
8.4  Framed Structures ........................................................ 338
8.5  Types of Framed Structures ............................................... 340
8.6  Internal Action Release Mechanisms ....................................... 342
8.7  Statically Determinate and Indeterminate Framed Structures ............... 343
8.8  Computation of the Internal Actions of the Members of Statically
     Determinate Framed Structures ............................................ 346
8.9  Action Equations of Equilibrium for Line Members ......................... 355
8.10 Shear and Moment Diagrams for Beams by the Summation Method .............. 358
8.11 Stress-Strain Relations for a Particle of a Line Member Made from an
     Isotropic Linearly Elastic Material ...................................... 362
8.12 The Boundary Value Problems in the Theories of Mechanics of Materials
     for Line Members ......................................................... 365
8.13 The Boundary Value Problem for Computing the Axial Component of
     Translation and the Internal Force in a Member Made from an Isotropic,
     Linearly Elastic Material Subjected to Axial Centroidal Forces and to
     a Uniform Change in Temperature .......................................... 368
8.14 The Boundary Value Problem for Computing the Angle of Twist and the
     Internal Torsional Moment in Members of Circular Cross Section Made
     from an Isotropic, Linearly Elastic Material Subjected to Torsional
     Moments .................................................................. 378
8.15 Problems ................................................................. 384

Chapter 9 Theories of Mechanics of Materials for Straight Beams Made from
Isotropic, Linearly Elastic Materials ......................................... 391

9.1  Formulation of the Boundary Value Problems for Computing the Components
     of Displacement and the Internal Actions in Prismatic Straight Beams
     Made from Isotropic, Linearly Elastic Materials .......................... 391
9.2  The Classical Theory of Beams ............................................ 405
9.3  Solution of the Boundary Value Problem for  Computing the Transverse
     Components of Translation and the Internal Actions in Prismatic Beams
     Made from Isotropic, Linearly Elastic Materials Using Functions of
     Discontinuity ............................................................ 414
9.4  The Timoshenko Theory of Beams ........................................... 421
9.5  Computation of the Shearing Components of Stress in Prismatic Beams
     Subjected to Bending without Twisting .................................... 430
9.6  Build-Up Beams ........................................................... 444
9.7  Location of the Shear Center of Thin-Walled Open Sections ................ 448
9.8  Members Whose Cross Sections Are Subjected to a Combination of Internal
     Actions .................................................................. 454
9.9  Composite Beams .......................................................... 460
9.10 Prismatic Beams on Elastic Foundation .................................... 473
9.11 Effect of Restraining the Warping of One Cross Section of a Prismatic
     Member Subjected to Torsional Moments at Its Ends ........................ 477
9.12 Problems ................................................................. 486

Chapter 10 Non-Prismatic Members — Stress Concentrations ...................... 499

10.1  Computation of the Components of Displacement and Stress of
      Non-Prismatic Members ................................................... 499
10.2  Stresses in Symmetrically Tapered Beams ................................. 500
10.3  Stress Concentrations ................................................... 505
10.4  Problems ................................................................ 509

Chapter 11 Planar Curved Beams ................................................ 511

11.1  Introduction ............................................................ 511
11.2  Derivation of the Equations of Equilibrium for a Segment of
      Infinitesimal Length of a Planar Curved Beam ............................ 511
11.3  Computation of the Circumferential Component of Stress Acting on the
      Cross Sections of Planar Curved Beams Subjected to Bending without
      Twisting ................................................................ 514
11.4  Computation of the Radial and Shearing Components of Stress in Curved
      Beams ................................................................... 528
11.5  Problems ................................................................ 534

Chapter 12 Thin-Walled, Tubular Members ....................................... 537

12.1  Introduction ............................................................ 537
12.2  Computation of the Shearing Stress Acting on the Cross Sections of
      Thin-Walled, Single-Cell, Tubular Members Subjected to Equal and
      Opposite Torsional Moments at Their Ends ................................ 538
12.3  Computation of the Angle of Twist per Unit Length of Thin-Walled,
      Single-Cell, Tubular Members Subjected to Equal and Opposite Torsional
      Moment at Their Ends .................................................... 540
12.4  Prismatic Thin-Walled, Single-Cell, Tubular Members with Thin Fins
      Subjected to Torsional Moments .......................................... 546
12.5  Thin-Walled, Multi-Cell, Tubular Members Subjected to Torsional
      Moments ................................................................. 551
12.6  Thin-Walled, Single-Cell, Tubular Beams Subjected to Bending without
      Twisting ................................................................ 555
12.7  Thin-Walled, Multi-Cell, Tubular Beams Subjected to Bending without
      Twisting ................................................................ 565
12.8  Single-Cell, Tubular Beams with Longitudinal Stringers subjected to
      Bending without Twisting ................................................ 572
12.9  Problems ................................................................ 576

Chapter 13 Integral Theorems of Structural Mechanics .......................... 581

13.1  A Statically Admissible Stress Field and an Admissible Displacement
      Field of a Body ......................................................... 581
13.2  Derivation of the Principle of Virtual Work for Deformable Bodies ....... 582
13.3  Statically Admissible Reactions and Internal Actions of Framed
      Structures .............................................................. 587
13.4  The Principle of Virtual Work for Framed Structures ..................... 588
13.5  The Unit Load Method .................................................... 597
13.6  The Principle of Virtual Work for Framed Structures, Including the
      Effect of Shear Deformation ............................................. 606
13.7  The Strong Form of One-Dimensional, Linear Boundary Value Problems ...... 610
13.8  Approximation of the Solution of One-Dimensional, Linear Boundary
      Value Problems Using Trial Functions .................................... 613
13.9  The Classical Weighted Residual Form for Second Order,
      One-Dimensional, Linear Boundary Value Problems ......................... 615
13.10 The Classical Weighted Residual Form for Fourth Order,
      One-Dimensional, Linear Boundary Value Problems ......................... 617
13.11 Discretization of Boundary Value Problems Using the Classical Weighted
      Residual Methods ........................................................ 619
13.12 The Modified Weighted Residual (Weak) Form of One-Dimensional, Linear
      Boundary Value Problems ................................................. 620
13.13 Total Strain Energy of Framed Structures ................................ 629
13.14 Castigliano's Second Theorem ............................................ 630
13.15 Betti-Maxwell Reciprocal Theorem ........................................ 637
13.16 Proof That the Center of Twist of a Cross Section Coincides with Its
      Shear Center ............................................................ 639
13.17 The Variational Form of the Boundary Value Problem for Computing the
      Components of Displacement of a Deformable Body — Theorem of
      Stationary Total Potential Energy ....................................... 640
13.18 Comments on the Modified Gallerkin Form and the Theorem of Stationary
      Total Potential Energy .................................................. 651
13.19 Problems ................................................................ 651

Chapter 14 Analysis of Statically Indeterminate Framed Structures ............. 657

14.1  The Basic Force or Flexibility Method ................................... 657
14.2  Computation of Components of Displacement of Points of Statically
      Indeterminate Structures ................................................ 664
14.3  Problems ................................................................ 666

Chapter 15 The Finite Element Method .......................................... 671

15.1  Introduction ............................................................ 671
15.2  The Finite Element Method for One-Dimensional, Second Order, Linear
      Boundary Value Problems as a Modified Galerkin Method ................... 671
15.3  Element Shape Functions ................................................. 677
15.4  Assembly of the Stiffness Matrix for the Domain of One-Dimensional,
      Second Order, Linear Boundary Value Problems from the Stiffness
      Matrices of Their Elements .............................................. 680
15.5  Construction of the Force Vector for the Domain of One-Dimensional,
      Second Order, Linear Boundary Value Problems ............................ 683
15.6  Direct Computation of the Contribution of an Element to the Stiffness
      Matrix and the Load Vector of the Domain of One-Dimensional, Second
      Order, Linear Boundary Value Problems ................................... 685
15.7  Approximate Solution of Linear Boundary Value Problems Using the
      Finite Element Method ................................................... 689
15.8  Application of the Finite Element Method to the Analysis of Framed
      Structures .............................................................. 699
15.9  Approximate Solution of Scalar Two-Dimensional, Second Order, Linear
      Boundary Value Problems Using the Finite Element Method ................. 736
15.10 Problems ................................................................ 758

Chapter 16 Plastic Analysis and Design of Structures .......................... 763

16.1  Strain-Curvature Relation of Prismatic Beams Subjected to Bending
      without Twisting ........................................................ 763
16.2  Initiation of Yielding Moment and Fully Plastic Moment of Beams Made
      from Isotropic, Linearly Elastic, Ideally Plastic Materials ............. 765
16.3  Distribution of the Shearing Component of Stress Acting on the Cross
      Sections of Beams Where M2Y<M2<M2P ........................................ 769
16.4  Location of the Elastoplastic Boundaries — Moment-Curvature Relation .... 772
16.5  Computation of the Deflection of Beams Made from Isotropic, Linearly
      Elastic, Ideally Plastic Materials ...................................... 778
16.6  Effect of Stress Concentrations on the Design of Line Members ........... 780
16.7  Elastic and Plastic Design for Strength of Statically Determinate
      Structures .............................................................. 782
16.8  Plastic Analysis and Design of Planar Statically, Indeterminate Beams
      and Frames .............................................................. 785
16.9  Direct Computations of the Collapse Load of Beams and Frames ............ 790
16.10 Derivation of the Equations of Equilibrium for a Structure Using the
      Principle of Virtual Work ............................................... 793
16.11 Theorems for Limit Analysis ............................................. 795
16.12 Systematic Procedure for Plastic Analysis of Structures ................. 797
16.13 Problems ................................................................ 802

Chapter 17 Mechanics of Materials Theory for Thin Plates ...................... 807

17.1  Introduction ............................................................ 807
17.2  Fundamental Assumptions of the Theories of Mechanics of Materials for
      Thin Plates ............................................................. 809
17.3  Internal Action Intensities Acting on an Element of a Plate ............. 812
17.4  Internal Action Intensities Acting on Planes Which Are Inclined to
      the x1 and x2 Axes ....................................................... 815
17.5  Equations of Equilibrium for a Plate .................................... 816
17.6  Boundary Conditions for Plates .......................................... 819
17.7  Analysis of Simply Supported Rectangular Plates Subjected to a General
      Distribution of Transverse Forces ....................................... 825
17.8  The Method of Levy for Computing the Deflection of Rectangular Plates
      Having a Simply Supported Pair of Parallel Edges ........................ 832
17.9  Bending of Circular Plates .............................................. 839
17.10 Use of the Weighted Residual Methods to Construct Approximate
      Expressions for the Deflection of Plates ................................ 845
17.11 The Theorem of Total Stationary Potential Energy for Plates ............. 856
17.12 Problems ................................................................ 858

Chapter 18 Instability of Elastic Structures .................................. 861

18.1  States of Unstable Equilibrium of Structures ............................ 861
18.2  The Non-Linear Theory of Elasticity and the Theory of Moderate
      Rotations ............................................................... 872
18.3  Criterion for the Stability or Instability of an Equilibrium
      Configuration of Structures ............................................. 875
18.4  Investigation of the Beginning of Buckling .............................. 875
18.5  Buckling of Structures Having One Degree of Freedom ..................... 876
18.6  Buckling of Structures Having Infinite Degrees of Freedom — The Direct
      Equilibrium Approach .................................................... 888
18.7  Buckling of Structures Having Infinite Degrees of Freedom — The
      Stationary Total Potential Energy Approach .............................. 895
18.8  Determination of the Critical Load at Buckling of Infinite Degree of
      Freedom Structures by Investigating the Beginning of Buckling ........... 897
18.9  Columns Subjected to Eccentric Axial Compressive Forces at Their Ends ... 900
18.10 Local Buckling of Columns ............................................... 904
18.11 Problems ................................................................ 904

Appendices .................................................................... 905

A Mechanical Properties of Materials .......................................... 907
B Stress-Strain Relations for Orthotropic and Isotropic Materials ............. 909
C Centroid, Moments and Products of Inertia of Plane Surfaces ................. 919
D Method of Finite Differences ................................................ 929
E Elements of Calculus of Variations .......................................... 943
F Derivation of the Expression for the Plane Stress Functions X(x1, x2, x3) .... 951
G Functions of Discontinuity .................................................. 957
H Properties of Rolled Shapes ................................................. 961

Index ......................................................................... 967


Вверх Armenakas A.E. Advanced mechanics of materials and applied elasticity / Armenakas A.E. - Boca Raton: Taylor & Francis, 2006. - 975 p. - ISBN 0-8493-9899-1.

Сигла: 015По алфавиту | По темам ||| Математика | Физика | Химия
[О библиотеке | Академгородок | Новости | Выставки | Ресурсы | Библиография | Партнеры | ИнфоЛоция | Поиск | English]
  Пожелания и письма: branch@gpntbsib.ru
© 1997-2021 Отделение ГПНТБ СО РАН (Новосибирск)
Статистика доступов: архив | текущая статистика
 

Документ изменен: Wed Feb 27 14:51:50 2019. Размер: 33,281 bytes.
Посещение N 4584 с 24.09.2007