Partial differential equations in mechanics: 2 The biharmonic equation, Poisson's equation
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2000
|
| Schriftenreihe: | Engineering online library
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 698 S. graph. Darst. |
| ISBN: | 3540672842 |
Internformat
MARC
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| 100 | 1 | |a Selvadurai, Antony P. S. |d 1942- |e Verfasser |0 (DE-588)122052633 |4 aut | |
| 245 | 1 | 0 | |a Partial differential equations in mechanics |n 2 |p The biharmonic equation, Poisson's equation |c A. P. S. Selvadurai |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a XVIII, 698 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1804128092465135616 |
|---|---|
| adam_text | Contents
8. The biharmonic equation 1
8.1 The concept of a continuum 3
8.2 Displacements and strains in continua 5
8.2.1 Physical interpretations of the strain matrix 12
8.2.2 Physical interpretation of the rotation matrix 16
8.2.3 Indicial notation representations
of strain and rotation 18
8.2.4 Transformation of the strain matrix 19
8.2.5 Principal strains and strain invariants 24
8.2.6 Compatibility of strains 26
8.3 Stresses in a continuum 36
8.3.1 The stress dyadic and the stress matrix 37
8.3.2 Tractions on an arbitrary plane 39
8.3.3 Equations of equilibrium 41
8.3.4 Symmetry of the stress matrix 43
8.3.5 Sign convention for stresses 45
8.3.6 Transformation of the stress matrix 47
8.3.7 Principal stresses and stress invariants 49
8.4 Constitutive equations for linear elastic solids 57
8.4.1 Generalized Hooke s Law 57
8.4.2 The strain energy density 58
8.4.3 Symmetry of the elasticity matrix 60
8.4.4 Isotropic elastic material 62
8.4.5 Thermodynamic constraints on the elastic constants. 66
8.4.6 Boundary conditions 68
8.4.7 Time derivatives 71
8.5 Uniqueness theorem in the classical theory of elasticity 72
8.6 Plane problems in classical elasticity 81
8.7 The Airy stress function 92
8.8 Methods of solution of the biharmonic equation 104
8.8.1 Series solution in Cartesian coordinates 105
8.8.2 Variables separable solution
rectangular Cartesian coordinates 118
8.8.3 Integral transform solution
of the biharmonic equation governing plane problems 130
8.8.4 Line load problems for an infinite plane 138
8.8.5 Application of complex variable methods 145
8.9 Polar coordinate formulation
of the plane problem in elasticity 151
8.9.1 Definition of stresses in plane polar coordinates 152
8.9.2 Definition of strains in plane polar coordinates 154
8.9.3 Elastic stress strain relations in polar coordinates . . . 158
8.9.4 Transformation from Cartesian equations 159
8.9.5 The Airy stress function in plane polar coordinates . 161
8.9.6 Boundary conditions in plane polar coordinates 162
8.9.7 Development of the Airy stress function
in polar coordinates 164
8.9.8 An application of complex variable techniques 176
8.10 Biharmonic function formulation
of three dimensional problems in elasticity 181
8.10.1 The strain potential 182
8.10.2 The Galerkin vector 184
8.10.3 General properties of biharmonic functions 186
8.10.4 Love s strain function 193
8.10.5 Axisymmetric problem formulation 197
8.10.6 Polynomial solutions of the biharmonic equation;
the interior solution 199
8.10.7 Love s strain function approach: spherical polar
coordinate formulation for unbounded domains 209
8.10.8 Kelvin s problem 213
8.10.9 A centre of dilatation 222
8.10.10 Boussinesq s problem 225
8.10.11 The spherical cavity problem 233
8.10.12 Application of integral transforms 238
8.10.13 Mixed boundary value problems 258
8.11 Flexure of thin elastic plates 267
8.11.1 Deformation of the plate region 269
8.11.2 Flexural stresses and stress resultants 279
8.11.3 Plate stress strain relations 282
8.11.4 Equation of equilibrium for the plate 286
8.11.5 Strain energy of a plate 289
8.11.6 The principle of virtual work 291
8.11.7 Boundary conditions for plate problems 293
8.11.8 The classical theory of thin plates 297
8.11.9 Flexure of thin circular plates 305
8.11.10 Complex variable method for circular plates 325
8.11.11 Green s function for a thin plate 330
8.11.12 Flexure of rectangular plates 332
8.11.13 Certain general solutions of the biharmonic equation 339
8.11.14 Navier and Levy solutions for rectangular plates .... 345
8.11.15 Application of integral transform techniques 366
8.11.16 Complex variable methods for the solution
of plate problems 374
8.11.17 Uniqueness of solution governing deflections
of a plate 386
8.11.18 Uniqueness of solution for plates
with clamped boundaries 390
8.12 Slow viscous flow 393
8.12.1 Kinematics of fluid flow 394
8.12.2 Equation of motion 397
8.12.3 Constitutive equations for a viscous fluid 397
8.12.4 Thermodynamic constraints
on the viscosity coefficients 399
8.12.5 Navier Stokes equation 403
8.12.6 Biharmonic formulations of problems
in slow viscous flow 404
8.12.7 Planar problems in slow viscous flow 407
8.12.8 Axisymmetric problems in slow viscous flow 409
8.12.9 Boundary conditions 411
8.12.10 Stokes paradox and related problems 419
8.12.11 Slow viscous flow past a sphere 424
8.12.12 Application of integral transform techniques 430
8.12.13 Diffusive motions in viscous fluids 440
8.13 The compatibility conditions 454
8.14 A proof of Stokes paradox 459
8.15 A uniqueness theorem for viscous flows 462
8.16 PROBLEM SET 8 465
9. Poisson s equation 503
9.1 Flow through porous media with internal sources 504
9.2 Heat conduction in the presence of heat sources 507
9.3 Transverse deflections
of a stretched transversely loaded membrane 508
9.4 Boundary conditions 508
9.4.1 Boundary conditions for flow in porous media 509
9.4.2 Boundary conditions for heat conduction 510
9.4.3 Boundary conditions for loaded membranes 511
9.5 Generalized results 513
9.6 Green s function for Poisson s equation 526
9.6.1 Integral transform techniques 531
9.6.2 Series solution techniques 535
9.6.3 Method of eigenfunctions 540
9.6.4 Symmetry of the Green s function 551
9.6.5 The method of images 553
9.7 A monotonicity result for Poisson s equation 557
9.8 Viscous flow in conduits 559
9.9 Torsion of prismatic elastic solids 565
9.9.1 General formulation of the torsion problem 568
9.9.2 Torsion of prismatic elements
with multiply connected cross sections 577
9.9.3 Solutions for torsion problems
derived from equations of boundaries 581
9.9.4 Variables separable solutions for the torsion problem 587
9.9.5 A complex variable formulation
of the torsion problem 600
9.10 An alternative derivation of the elastic torsion problem 608
9.11 The gravitational potential 614
9.11.1 Spatial distribution of matter 620
9.12 PROBLEM SET 9 634
Bibliography 649
Index 679
|
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| id | DE-604.BV013320245 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:45Z |
| institution | BVB |
| isbn | 3540672842 |
| language | English |
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| physical | XVIII, 698 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
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| series2 | Engineering online library |
| spelling | Selvadurai, Antony P. S. 1942- Verfasser (DE-588)122052633 aut Partial differential equations in mechanics 2 The biharmonic equation, Poisson's equation A. P. S. Selvadurai Berlin [u.a.] Springer 2000 XVIII, 698 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering online library (DE-604)BV013218493 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009083074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Selvadurai, Antony P. S. 1942- Partial differential equations in mechanics |
| title | Partial differential equations in mechanics |
| title_auth | Partial differential equations in mechanics |
| title_exact_search | Partial differential equations in mechanics |
| title_full | Partial differential equations in mechanics 2 The biharmonic equation, Poisson's equation A. P. S. Selvadurai |
| title_fullStr | Partial differential equations in mechanics 2 The biharmonic equation, Poisson's equation A. P. S. Selvadurai |
| title_full_unstemmed | Partial differential equations in mechanics 2 The biharmonic equation, Poisson's equation A. P. S. Selvadurai |
| title_short | Partial differential equations in mechanics |
| title_sort | partial differential equations in mechanics the biharmonic equation poisson s equation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009083074&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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