Theory of Elasticity (eBook)

Aldo Maceri (Autor)

eBook Download: PDF

2010 | 2010
X, 716 Seiten
Springer Berlin (Verlag)
978-3-642-11392-5 (ISBN)

Infos

This book provides the analytical tools for calculating stresses and deformations in a strained elastic body. It gives engineers, in a simple form, a clear indication of the necessary fundamental knowledge of the theory of elasticity.

Inhalt

Preface 5
Contents 7
1 The Three-Dimensional Problem 11
1.1 Analysis of Strain 11
1.1.1 Components of Displacement 11
1.1.2 Infinitesimal Deformation 12
1.1.3 Elongation and Shearing Strain 14
1.1.4 Small Deformations 15
1.1.5 Components of Strain 19
1.1.6 Principal Direction of Strain 24
1.1.7 Invariants of Strain 31
1.1.8 Plane State of Strain 33
1.1.9 Equations of Compatibility 34
1.1.10 Measurement of Strain 35
1.2 Analysis of Stress 37
1.2.1 Stress Vector 37
1.2.2 Normal Stress -- Shearing Stress 39
1.2.3 Components of Stress 40
1.2.4 Symmetry of t – Differential Equations of Equilibrium – Cauchy’s Boundary Conditions 41
1.2.5 Symmetry of Stress Vector 48
1.2.6 Relations Between Normal or Shearing Stress and Components of Stress 49
1.2.7 Principal Direction of Stress 50
1.2.8 Invariants of Stress 52
1.2.9 Mohr's Circle 53
1.2.10 Mohr's Principal Circles 67
1.2.11 Determination of the Maximum Normal Stress or Shearing Stress by the Mohr 's Principal Circles 71
1.2.12 Plane State of Stress 73
1.2.13 Uniaxial State of Stress 75
1.2.14 Measurement of Stress 76
1.3 Principle of Virtual Works 76
1.3.1 Principle of Virtual Works 76
1.4 Relations Between Stress and Strain 80
1.4.1 Tensile Breaking Test 80
1.4.2 Homogeneous and Isotropic Materials – Navier’s Relations 85
1.4.3 Bounds for the Elastic Modulus 88
1.5 The Elastic Equilibrium Problem 90
1.5.1 Classical Formulations 90
1.5.2 Variational Formulations 100
1.6 Strain Energy 105
1.6.1 Elements of Thermodynamics 105
1.6.2 Thermodynamics of the Problem of the Elastic Equilibrium 111
1.6.3 Strain Work 113
1.6.4 The Elastic Potential 117
1.6.5 Work Theorems 120
1.7 Strength Criterions 125
1.7.1 Structural Safety 125
1.7.2 The Maximum Shearing Stress Criterion 126
1.7.3 The Octahedral Shearing Stress Criterion 127
1.7.4 The Energetic Criterion 128
1.7.5 The Intrinsic Curve Criterion 134
2 The Problem of Saint Venant 136
2.1 Geometry of Areas 136
2.1.1 Centroid 136
2.1.2 Inertia Centroidal Ellipse 140
2.1.3 Antipolarity 150
2.1.4 Inertia Centroidal Kernel 168
2.2 The Problem of Saint Venant 173
2.2.1 Introduction 173
2.2.2 State of Stress 178
2.3 Bending 182
2.3.1 Right Bending of Axis x 182
2.3.2 Right Bending of Axis y 196
2.3.3 Deviated Bending 199
2.4 Axial Load 204
2.4.1 Centroidal Axial Load 204
2.4.2 Non Centroidal Axial Load 210
2.4.3 Material Non Resistant to Traction 224
2.5 Torsion 228
2.5.1 The Exact Solution 228
2.5.2 The Circular Cross Section 235
2.5.3 The Stress Concentration 241
2.5.4 Closed Thin Walled Cross Section 249
2.5.5 Open Thin Walled Cross Section 259
2.5.6 Non Uniform Torsion 273
2.6 Shear 287
2.6.1 The Exact Solution 287
2.6.2 The Approximate Solution 303
2.6.3 The Circular Cross Section 313
2.6.4 Open Thin Walled Cross Section 317
2.6.5 Closed Thin Walled Cross Section 360
3 The Two-Dimensional Problems 367
3.1 Panels 367
3.1.1 The Problem of the Panel 367
3.1.2 Rectangular Panels 372
3.1.3 Circular Panels 378
3.1.4 Effect of a Hole 395
3.2 Plates 400
3.2.1 Small Deflections of Thin Plates 400
3.2.2 Thin Plates on Elastic Foundation 410
3.3 Shells 411
3.3.1 Membranes 411
3.3.2 Thin Shells 419
3.4 Plane Strain Problems 430
3.4.1 Plane Strain Problems 430
4 The One-Dimensional Problems 435
4.1 Ropes 435
4.1.1 The Funicular 435
4.1.2 The Ropes 438
4.2 Beams 441
4.2.1 The Deflected Beam 441
4.2.2 The Analogy of Mohr 457
4.2.3 Principle of Virtual Works 470
4.2.4 Strain Energy 471
4.2.5 Deflected Beams on Elastic Foundation 489
4.3 Arches 490
4.3.1 Arches with Small Curvature 490
4.3.2 Arches with Great Curvature 496
5 Thermoelasticity 500
5.1 Mechanics of Continuous Media 500
5.1.1 Introduction 500
5.1.2 Classical Thermodynamics 501
5.1.3 The Equations of Balance 508
5.1.4 Thermodynamics of the Irreversible Processes 510
5.2 Fluid Dynamics 513
5.2.1 The Mathematical Model 513
5.2.2 The Characteristic Numbers 517
5.2.3 Non Dissipative Flows 531
5.2.4 Dissipative Flows 544
5.3 Mechanics of Solids 559
5.3.1 The Dynamic Thermoelastic Problem 559
5.3.2 The Thermoelastic Dissipation 569
5.3.3 The Uncoupled Thermoelastic Problem 570
5.3.4 Thermoelasticity 573
5.3.5 The One-Dimensional Problem 580
6 Stability 599
6.1 Stability of the Elastic Equilibrium 599
6.1.1 The Buckling 599
6.1.2 The Ultimate Strength 601
6.2 Energy Method 602
6.2.1 Introduction 602
6.2.2 Some Elementary Application 604
6.3 Static Method 613
6.3.1 The Beam Axially Loaded 613
6.3.2 Approximate Analysis 613
6.3.3 Exact Analysis 624
6.3.4 Effect of the Imperfections 628
6.3.5 Limit Slenderness 630
6.3.6 Other Ways of Buckling 633
6.4 Second Type Instability 635
6.4.1 The Snapping 635
7 Anisotropy 641
7.1 The Three-Dimensional Anisotropic Problem 641
7.1.1 Introduction 641
7.1.2 Constituent Links 642
7.1.3 The Anisotropic Elastic Body 645
7.1.4 Energetic Aspects 647
7.1.5 The Anisotropic Saint Venant's Problem 648
7.2 The Macroscopic Anisotropy 655
7.2.1 Composite Materials 655
7.2.2 Structural Anisotropy 662
8 Nonlinear Elasticity 668
8.1 Nonlinear Problems 668
8.1.1 The Nonlinearity Causes 668
8.2 Finite Deformations 669
8.2.1 Three-Dimensional Problem 669
8.2.2 Large Deflections of Thin Plates 674
8.3 Unilateral Problems 678
8.3.1 Introduction 678
8.3.2 Contact Problems 679
8.3.3 Unilateral Constraints 689
Bibliography 710
Author Index 711
Subject Index 712

Produkt-Details

• Erscheint lt. Verlag: 23.7.2010
• Zusatzinfo: X, 716 p.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Cauchy • Fluid Dynamics • nonlinear elasticity • Saint Venant • stability • Thermoelasticity
• ISBN-10: 3-642-11392-3 / 3642113923
• ISBN-13: 978-3-642-11392-5 / 9783642113925