Elasticity

Front Cover
Springer Science & Business Media, Nov 21, 2009 - Technology & Engineering - 534 pages
The subject of Elasticity can be approached from several points of view, - pending on whether the practitioner is principally interested in the mat- matical structure of the subject or in its use in engineering applications and, in the latter case, whether essentially numerical or analytical methods are envisaged as the solution method. My ?rst introduction to the subject was in response to a need for information about a speci?c problem in Tribology. As a practising Engineer with a background only in elementary Mechanics of - terials, I approached that problem initially using the concepts of concentrated forces and superposition. Today, with a rather more extensive knowledge of analytical techniques in Elasticity, I still ?nd it helpful to go back to these roots in the elementary theory and think through a problem physically as well as mathematically, whenever some new and unexpected feature presents di?culties in research. This way of thinking will be found to permeate this book. My engineering background will also reveal itself in a tendency to work examples through to ?nal expressions for stresses and displacements, rather than leave the derivation at a point where the remaining manipulations would be mathematically routine. The ?rst edition of this book, published in 1992, was based on a one semester graduate course on Linear Elasticity that I have taught at the U- versity of Michigan since 1983.
 

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Contents

Part I
2
1 INTRODUCTION
3
2 EQUILIBRIUM AND COMPATIBILITY
25
Part II
34
3 PLANE STRAIN AND PLANE STRESS
37
4 STRESS FUNCTION FORMULATION
45
5 PROBLEMS IN RECTANGULARCOORDINATES
54
6 END EFFECTS
77
18 PRELIMINARY MATHEMATICALRESULTS
273
19 APPLICATION TO ELASTICITYPROBLEMS
293
Part V
318
20 DISPLACEMENT FUNCTION SOLUTIONS
319
21 THE BOUSSINESQ POTENTIALS
333
22 THERMOELASTIC DISPLACEMENTPOTENTIALS
347
23SINGULAR SOLUTIONS
362
24 SPHERICAL HARMONICS
377

7 BODY FORCES
91
8 PROBLEMS IN POLAR COORDINATES
109
9 CALCULATION OF DISPLACEMENTS
123
10 CURVED BEAM PROBLEMS
135
11 WEDGE PROBLEMS
149
12 PLANE CONTACT PROBLEMS1
171
13 FORCES DISLOCATIONS AND CRACKS
199
14 THERMOELASTICITY
219
15 ANTIPLANE SHEAR
226
Part III
238
16 TORSION OF A PRISMATIC BAR
241
17 SHEAR OF A PRISMATIC BAR1
259
Part IV
270
25 CYLINDERS AND CIRCULAR PLATES
391
26 PROBLEMS IN SPHERICALCOORDINATES
405
27 AXISYMMETRIC TORSION
419
28 THE PRISMATIC BAR
429
29FRICTIONLESS CONTACT
449
30 THE BOUNDARYVALUE PROBLEM
459
31 THE PENNYSHAPED CRACK
479
32 THE INTERFACE CRACK
487
33 VARIATIONAL METHODS
499
34 THE RECIPROCAL THEOREM
517
A USING MAPLE AND MATHEMATICA
529
INDEX
531
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