The nonlinear theory of elastic shells:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Univ. Pr.
1998
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 542 S. |
| ISBN: | 0521472369 |
Staff View
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| 245 | 1 | 0 | |a The nonlinear theory of elastic shells |c A. Libai ; J. G. Simmonds |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge |b Univ. Pr. |c 1998 | |
| 300 | |a XVI, 542 S. | ||
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Record in the Search Index
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| adam_text | THE NONLINEAR THEORY OF ELASTIC SHELLS SECOND EDITION A. LIBAI TECHNION,
ISRAEL INSTITUTE OF TECHNOLOGY J. G. SIMMONDS UNIVERSITY OF VIRGINIA *
CAMBRIDGE ** UNIVERSITY PRESS CONTENTS PREFACE XIII PREFACE TO THE FIRST
EDITION XV CHAPTER I: INTRODUCTION 1 A. WHAT IS A SHELL? 1 B. ELASTIC
SHELLS AND NONLINEAR BEHAVIOR 1 C. APPROACHES TO SHELL THEORY 2 D. THE
APPROACH OF THIS BOOK TO SHELL THEORY 3 E. OUTLINE OF THE BOOK 4
REFERENCES 6 CHAPTER II: THE GENERIC EQUATIONS OF THREE- DIMENSIONAL
CONTINUUM MECHANICS 11 A. THE INTEGRAL EQUATIONS OF MOTION 11 B. STRESS
VECTORS 13 C. HEAT 14 D. THE CLAUSIUS-DUHEM (-TRUESDELL-TOUPIN)
INEQUALITY 15 E. THE FIRST PIOLA-KIRCHHOFF STRESS TENSOR 15 *F. GROSS
EQUATIONS OF MOTION 16 REFERENCES 20 CHAPTER III: LONGITUDINAL MOTION OF
STRAIGHT RODS WITH BISYMMETRIC CROSS SECTIONS (BIRODS) 21 A. GEOMETRY OF
THE UNDEFORMED ROD 21 B. INTEGRAL EQUATION OF MOTION 21 C. DIFFERENTIAL
EQUATION OF MOTION 25 *D. JUMP CONDITION AND PROPAGATION OF
SINGULARITIES 25 E. THE WEAK FORM OF THE EQUATION OF MOTION 28 F. THE
MECHANICAL WORK IDENTITY 30 G. MECHANICAL BOUNDARY CONDITIONS 31 H. THE
PRINCIPLE OF VIRTUAL WORK 33 1. THE PRINCIPLE OF VIRTUAL WORK AND
BOUNDARY CONDITIONS IN STATICS 36 I. THE MECHANICAL THEORY OF BIRODS 36
J. THE MECHANICAL THEORY OF ELASTIC BIRODS 36 1. RESTRICTIONS ON THE
STRAIN-ENERGY DENSITY 37 2. THE EQUATION OF MOTION IN DISPLACEMENT AND
INTRINSIC FORMS 37 K. VARIATIONAL PRINCIPLES 38 AN ASTERISK (*)
INDICATES A SECTION THAT MAY BE OMITTED WITHOUT LOSS OF CONTINUITY VI
CONTENTS 1. HAMILTON S PRINCIPLE 40 2. VARIATIONAL PRINCIPLES FOR
ELASTOSTATICS 41 L. THERMAL EQUATIONS 45 M. THE FIRST LAW OF
THERMODYNAMICS 46 N. THERMOELASTIC BIRODS 46 1. LINEARIZED CONSTITUTIVE
EQUATIONS FOR N, H, AND I 48 REFERENCES 48 CHAPTER IV: CYLINDRICAL
MOTION OF INFINITE CYCLINDRICAL SHELLS (BEAMSHELLS) 51 A. GEOMETRY OF
THE UNDEFORMED SHELL AND PLANAR MOTION 51 B. INTEGRAL EQUATIONS OF
CYLINDRICAL MOTION 53 1. NATURAL INITIAL AND BOUNDARY CONDITIONS 56 C.
INITIAL AND SPIN BASES 57 *D. JUMP CONDITIONS AND PROPAGATION OF
SINGULARITIES 58 E. DIFFERENTIAL EQUATIONS OF CYLINDRICAL MOTION 59 F.
THE WEAK FORM OF THE EQUATIONS OF MOTION 60 G. THE MECHANICAL WORK
IDENTITY 60 H. MECHANICAL BOUNDARY CONDITIONS 61 1. GENERAL BOUNDARY
CONDITIONS FOR NONHOLONOMIC CONSTRAINTS 61 2. CLASSICAL BOUNDARY
CONDITIONS 63 3. TYPICAL BOUNDARY CONDITIONS 64 *APPENDIX: THE PRINCIPLE
OF MECHANICAL BOUNDARY CONDITIONS (BY DAWN FISHER) 67 I. THE PRINCIPLE
OF VIRTUAL WORK 67 J. POTENTIAL (CONSERVATIVE) LOADS 69 1. DEAD LOADING
(AND A TORSIONAL SPRING) 69 2. CENTRIFUGAL LOADING 69 3. PRESSURE
LOADING (CONSTANT OR HYDROSTATIC) 70 *4. GENERAL DISCUSSION AND EXAMPLES
71 K. STRAINS 76 L. ALTERNATIVE STRAINS AND STRESSES 77 M. THE
MECHANICAL THEORY OF BEAMSHELLS 80 N. ELASTIC BEAMSHELLS AND
STRAIN-ENERGY DENSITIES 81 1. QUADRATIC STRAIN-ENERGY DENSITIES 82 *2.
GENERAL STRAIN-ENERGY DENSITIES 85 *3. STRAIN-ENERGY DENSITY BY DESCENT
FROM THREE DIMENSIONS 89 O. ELASTOSTATICS 94 1. INEXTENSIONAL BEAMSHELLS
96 2. PRESSURE LOADED BEAMSHELLS 100 P. ELASTODYNAMICS 105 1.
DISPLACEMENT-SHEAR STRAIN FORM 106 2. STRESS RESULTANT-ROTATION FORM 109
3. A SYSTEM OF FIRST-ORDER EQUATIONS 109 4. CLASSICAL FLEXURAL MOTION
110 5. CARTESIAN FRAMES 111 Q. VARIATIONAL PRINCIPLES FOR BEAMSHELLS 114
CONTENTS VII 1. HAMILTON S PRINCIPLE 114 2. VARIATIONAL PRINCIPLES FOR
ELASTOSTATICS 115 R. THE MECHANICAL THEORY OF STABILITY 122 1. BUCKLING
EQUATIONS 127 2. SHALLOW BEAMSHELLS 133 S. SOME REMARKS ON FAILURE
CRITERIA AND STRESS CALCULATIONS 136 1. SOME LARGE-STRAIN REFINEMENTS
138 2. DETERMINATION OF THE DEFORMED CONFIGURATION 139 T. THERMODYNAMICS
140 U. THE THERMODYNAMIC THEORY OF STABILITY OF EQUILIBRIUM 147
REFERENCES 149 CHAPTER V: TORSIONLESS, AXISYMMETRIC MOTION OF SHELLS OF
REVOLUTION (AXISHELLS) 159 A. GEOMETRY OF THE UNDEFORMED SHELL 160 B.
INTEGRAL EQUATIONS OF MOTION 161 * DIFFERENTIAL EQUATIONS OF MOTION 166
D. DIFFERENTIAL AND INTEGRAL EQUATIONS OF TORSIONLESS, AXISYMMETRIC
MOTION 166 E. INITIAL AND SPIN BASES 168 *F. JUMP CONDITIONS AND
PROPAGATION OF SINGULARITIES 168 G. THE WEAK FORM OF THE EQUATIONS OF
MOTION 169 H. THE MECHANICAL WORK INDENTITY 169 I. MECHANICAL BOUNDARY
CONDITIONS 170 J. THE PRINCIPLE OF VIRTUAL WORK 172 K. LOAD POTENTIALS
173 1. SELF-WEIGHT (GRAVITY LOADING) 173 2. CENTRIFUGAL LOADING 174 3.
ARBITRARY NORMAL PRESSURE 174 L. STRAINS 175 M. COMPATIBILITY CONDITIONS
177 N. THE MECHANICAL THEORY OF AXISHELLS 178 O. ELASTIC AXISHELLS AND
STRAIN-ENERGY DENSITIES 179 1. QUADRATIC STRAIN-ENERGY DENSITIES 180 *2.
GENERAL STRAIN-ENERGY DENSITIES 182 *3. ELASTIC ISOTROPY 184 *4.
APPROXIMATIONS TO THE STRAIN-ENERGY DENSITY 186 *5. STRAIN-ENERGY
DENSITY BY DESCENT FROM THREE DIMENSIONS 187 P. ALTERNATIVE STRAINS AND
STRESSES 192 Q. ELASTOSTATICS 196 1. GENERAL FIELD EQUATIONS USING THE
MODIFIED STRAIN-ENERGY DENSITY Y = * - GQ 19 7 2. GENERAL FIELD
EQUATIONS USING A MIXED-ENERGY DENSITY 4* 199 R. THE SIMPLIFIED REISSNER
EQUATIONS FOR SMALL STATIC STRAINS 200 1. MEMBRANE THEORY 204 2.
MODERATE ROTATION THEORY 205 3. NONLINEAR SHALLOW SHELL THEORY 205 VIUE
CONTENTS S. SPECIAL CASES OF THE SIMPLIFIED REISSNER EQUATIONS 206 1.
CYLINDRICAL SHELLS AND MEMBRANES 206 2. CIRCULAR PLATES AND MEMBRANES
215 3. CONICAL SHELLS 221 4. SPHERICAL SHELLS AND MEMBRANES 229 5.
TOROIDAL SHELLS AND MEMBRANES OF GENERAL CROSS SECTION 250 T. NONLINEAR,
LARGE-STRAIN MEMBRANE THEORY (INCLUDING WRINKLING) 259 1. WHAT IS A
MEMBRANE? 259 2. CONSTITUTIVE RELATIONS 262 3. FIELD EQUATIONS AND
BOUNDARY CONDITIONS 265 4. SOME SPECIAL LARGE-STRAIN PROBLEMS 268 5.
ASYMPTOTIC APPROXIMATIONS 275 6. WRINKLED MEMBRANES 276 U.
ELASTODYNAMICS 280 1. DISPLACEMENT-SHEAR STRAIN FORM 280 2.
ROTATION-STRESS RESULTANT FORM 282 3. A SYSTEM OF FIRST-ORDER EQUATIONS
283 4. INTRINSIC FORM 284 5. SOME SPECIAL TOPICS 287 6. TWISTED
AXISHELLS 288 V. VARIATIONAL PRINCIPLES FOR AXISHELLS 290 1. HAMILTON S
PRINCIPLE 290 2. VARIATIONAL PRINCIPLES FOR ELASTOSTATICS 291 3. REMARKS
296 4. EXAMPLES 298 W. THE MECHANICAL THEORY OF STABILITY OF AXISHELLS
301 1. BUCKLING EQUATIONS 303 2. EFFECTS OF OTHER LOADS 308 3.
SIMPLIFICATION OF THE BUCKLING EQUATIONS 309 4. BUCKLING OF AXISYMMETRIC
PLATES 313 5. THE POSTBUCKLING OF SHELLS OF REVOLUTION: A SHORT SURVEY
317 X. THERMODYNAMICS 322 REFERENCES 328 CHAPTER VI: SHELLS SUFFERING
ONE-DIMENSIONAL STRAINS (UNISHELLS) 343 A. IN-PLANE BENDING OF
PRESSURIZED CURVED TUBES 344 1. INTRODUCTION 344 2. GEOMETRY 345 3.
EXTERNAL LOADS 345 4. SEMI-INVERSE APPROACH 345 5. KINEMATICS OF
DEFORMATION 346 6. EQUILIBRIUM EQUATIONS 348 7. CONSTITUTIVE RELATIONS
349 8. BOUNDARY AND END CONDITIONS 349 9. REDUCTIONS AND APPROXIMATIONS
352 10. THE COLLAPSE OF TUBES IN BENDING 354 CONTENTS IX *. VARIATIONAL
PRINCIPLES FOR CURVED TUBES 357 1. GENERAL REMARKS 357 2. PRINCIPLES OF
VIRTUAL WORK AND STATIONARY TOTAL POTENTIAL 358 3. EXTENDED VARIATIONAL
PRINCIPLES 360 * HELICOIDAL SHELLS 363 1. DEFORMATION OF AN ARBITRARY
SHELL 363 2. DEPENDENCE OF THE METRIC AND CURVATURE COMPONENTS ON THE
SAME, SINGLE SURFACE COORDINATE IMPLIES A GENERAL HELICOID 364 3. THE
GEOMETRY OF A GENERAL HELICOID 365 D. FORCE AND MOMENT EQUILIBRIUM 365
E. VIRTUAL WORK AND STRAINS 368 F. THE ROTATION VECTOR FOR
ONE-DIMENSIONAL STRAINS 370 G. STRAIN COMPATIBILITY 372 H. COMPONENT
FORM OF THE FIELD EQUATIONS 372 1. COMPATIBILITY CONDITIONS 372 2. FORCE
EQUILIBRIUM 375 3. MOMENT EQUILIBRIUM 375 4. CONSTITUTIVE RELATIONS 376
I. SPECIAL CASES 378 1. AXISHELLS 378 2. PURE BENDING OF PRESSURIZED
CURVED TUBES 378 3. TORSION, INFLATION, AND EXTENSION OF AN INFINITE
TUBE 378 4. EXTENSION AND TWIST OF A RIGHT HELICOIDAL SHELL 380 5.
INEXTENSIONAL DEFORMATION 383 REFERENCES 385 CHAPTER VII: GENERAL
NONLINEAR MEMBRANE THEORY (INCLUDING WRINKLING) 389 A. THE EQUATIONS OF
MOTION 389 B. NATURAL INITIAL AND FORCE BOUNDARY CONDITIONS 391 * SHOCKS
392 D. THE MEMBRANE STRESS RESULTANT TENSOR 393 E. DIFFERENTIAL
EQUATIONS OF MOTION 395 F. HYBRID AND COMPONENT FORMS OF THE EQUATIONS
OF MOTION 396 1. A USEFUL HYBRID NOTATION 396 2. ALTERNATIVE HYBRID
FORMS 397 3. COMPONENT FORMS 398 G. WEAK FORM OF THE EQUATIONS OF MOTION
400 *1. DIRECT DERIVATION OF THE WEAK FORM FROM THE INTEGRAL FORM 401 H.
THE MECHANICAL WORK IDENTITY AND THE LAGRANGIAN STRAIN TENSOR 401 I.
STRAIN COMPATIBILITY 403 J. BOUNDARY CONDITIONS AND THE PRINCIPLE OF
VIRTUAL WORK 406 1. CLASSICAL BOUNDARY CONDITIONS FOR STATIC MEMBRANE
PROBLEMS 410 K. LOAD POTENTIALS 411 1. PRESSURE A FUNCTION OF TOTAL
VOLUME ONLY 412 2. POSITION DEPENDENT PRESSURE 413 L. CONSTITUTIVE
RELATIONS FOR ELASTIC ISOTHERMAL MEMBRANES 414 X CONTENTS 1. QUADRATIC
STRAIN-ENERGY DENSITIES 416 2. COMPLEMENTARY-ENERGY DENSITIES 417 3.
INEXTENSIONAL TRUE MEMBRANES 418 4. LARGE [0(1)] STRAIN MEMBRANE
PROBLEMS 419 5. REDUCTION FROM THREE DIMENSIONS 419 M. ELASTOSTATICS 421
1. ANGULAR DISCONTINUITIES 422 2. THE NATURE OF THE MEMBRANE PROBLEM 423
3. SMALL-STRAIN, LARGE-ROTATION THEORY 425 4. SMALL-STRAIN, LINEARIZED
THEORY 425 N. CIRCULAR CYLINDRICAL MEMBRANES 427 1. EXAMPLE 429 O.
WRINKLING OF MEMBRANES 431 P. THE BENDING AND WRINKLING OF INFLATED
MEMBRANE TUBES 437 Q. PLANE WRINKLED MEMBRANES 439 R. ISOTROPIC STATES
OF STRESS AND SOAP FILMS 441 S. DYNAMICS OF MEMBRANES 443 APPENDIX:
MEMBRANE STATES 448 REFERENCES 448 CHAPTER VIII: GENERAL SHELLS 453 A.
GEOMETRY OF THE UNDEFORMED SHELL 453 B. INTEGRAL EQUATIONS OF MOTION 455
C. NATURAL INITIAL AND BOUNDARY CONDITIONS 457 D. SHOCKS 458 E. STRESS
RESULTANT AND STRESS COUPLE TENSORS 459 F. DIFFERENTIAL (LOCAL)
EQUATIONS OF MOTION 460 G. HYBRID FORM OF THE EQUATIONS OF MOTION 461 H.
WEAK FORM OF THE EQUATIONS OF MOTION 461 I. THE MECHANICAL WORK IDENTITY
463 J. STRAINS 464 1. LOCAL OR OBJECTIVE RATES 464 K. STRAIN
COMPATIBILITY CONDITIONS 466 L. FINITE ROTATION VECTORS 468 1. AN
ALTERNATIVE, COORDINATE-FREE REPRESENTATION OF |/ 469 M. ALGEBRAIC AND
DIFFERENTIAL MECHANICAL BOUNDARY CONDITIONS; VIRTUAL WORK 470 N. LOAD
POTENTIALS 472 O. THE MECHANICAL THEORY OF SHELLS 473 P. ELASTIC SHELLS
AND STRAIN-ENERGY DENSITIES 474 1. MIXED-ENERGY DENSITY 475 Q. THE
KIRCHHOFF HYPOTHESIS 476 1. FORM S (FOR SPIN BASIS) 476 2. AN
ALTERNATIVE APPROACH TO THE KIRCHHOFF HYPOTHESIS: FORM D (FOR DEFORMED
BASIS) 479 3. SOME TYPICAL STRAIN- AND MIXED-ENERGY DENSITIES 485 4.
LIMITING FORMS AS E = H/L *»0 489 CONTENTS XI 5. THE EFFECTS OF
TRANSVERSE SHEARING STRAINS ON W 490 6. THE APPROXIMATE TWO-DIMENSIONAL
STRAIN-ENERGY DENSITY 490 7. EXAMPLE: THE NEO-HOOKEAN STRAIN-ENERGY
DENSITY 492 8. NOTE ON THE EXTERNAL POWER OF THE EDGE LOADS UNDER THE
KIRCHHOFF HYPOTHESIS 493 R. COMPONENT FORM OF THE EQUATIONS OF MOTION
494 1. ALTERNATIVE DISPLACEMENT COMPONENTS 496 2. COMPONENT FORM UNDER
THE KIRCHHOFF HYPOTHESIS (D-FORM) 496 S. ELASTOSTATICS 498 1. SATISFYING
FORCE EQUILIBRIUM WITH A STRESS FUNCTION 498 2. SATISFYING MOMENT
EQUILIBRIUM WITH ANOTHER STRESS FUNCTION 498 3. FIELD EQUATIONS FOR
STRESS FUNCTION AND FINITE ROTATION VECTORS: GENERAL THEORY 499 4. FIELD
EQUATIONS FOR STRESS FUNCTION AND FINITE ROTATION VECTORS: THE KIRCHHOFF
HYPOTHESIS 499 5. INTRINSIC STATIC FIELD EQUATIONS 502 T.
SIMPLIFICATIONS OF THE SHELL EQUATIONS 502 1. DYNAMIC, QUASI-SHALLOW
SHELL THEORY 503 2. SHELL MEMBRANES 505 REFERENCES 507 APPENDICES 511 A.
GUIDE TO NOTATION 511 1. GENERAL SCHEME OF NOTATION 511 2. GLOBAL
NOTATIONS 511 B. SOME ISOTROPIC, THREE-DIMENSIONAL STRAIN-ENERGY
DENSITIES 513 REFERENCES 514 INDEX 517
|
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| id | DE-604.BV024487825 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:00:39Z |
| institution | BVB |
| isbn | 0521472369 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018463185 |
| oclc_num | 247162069 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | XVI, 542 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Univ. Pr. |
| record_format | marc |
| spelling | Libai, Avinoam Verfasser aut The nonlinear theory of elastic shells A. Libai ; J. G. Simmonds 2. ed. Cambridge Univ. Pr. 1998 XVI, 542 S. txt rdacontent n rdamedia nc rdacarrier Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd rswk-swf Elastische Schale (DE-588)4151689-8 gnd rswk-swf Nichtlineare Elastizitätstheorie (DE-588)4171750-8 s Elastische Schale (DE-588)4151689-8 s DE-604 Simmonds, James G. Sonstige oth GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018463185&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Libai, Avinoam The nonlinear theory of elastic shells Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd Elastische Schale (DE-588)4151689-8 gnd |
| subject_GND | (DE-588)4171750-8 (DE-588)4151689-8 |
| title | The nonlinear theory of elastic shells |
| title_auth | The nonlinear theory of elastic shells |
| title_exact_search | The nonlinear theory of elastic shells |
| title_full | The nonlinear theory of elastic shells A. Libai ; J. G. Simmonds |
| title_fullStr | The nonlinear theory of elastic shells A. Libai ; J. G. Simmonds |
| title_full_unstemmed | The nonlinear theory of elastic shells A. Libai ; J. G. Simmonds |
| title_short | The nonlinear theory of elastic shells |
| title_sort | the nonlinear theory of elastic shells |
| topic | Nichtlineare Elastizitätstheorie (DE-588)4171750-8 gnd Elastische Schale (DE-588)4151689-8 gnd |
| topic_facet | Nichtlineare Elastizitätstheorie Elastische Schale |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018463185&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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