Verfügbarkeit: Applied mechanics of solids

Applied mechanics of solids:

Gespeichert in:

Bibliographische Detailangaben
1. Verfasser:	Bower, Allan F. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Boca Raton, Fla. [u.a.] CRC Press 2010
Schlagworte:	Mechanics, Applied Solids Elasticity Strength of materials Kontinuumsmechanik Festkörpermechanik
Online-Zugang:	lizenzfrei Inhaltsverzeichnis
Beschreibung:	XXV, 794 S. Ill., graph. Darst.
ISBN:	9781439802472

Internformat

MARC


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Datensatz im Suchindex

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adam_text	APPLIED MECHANICS OF SOLIDS ALLAN F. BOWER O CRC PRESS C;1LJ TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK CRC PRESS IS AN IMPRINT OF THE TAYLOR & FRANCIS GROUP, AN INFORMA BUSINESS CONTENTS PREFACE, XXIII AUTHOR, XXV CHAPTER 1 OVERVIEW OF SOLID MECHANICS 1.1 DEFINING A PROBLEM IN SOLID MECHANICS 1.1.1 DECIDING WHAT TO CALCULATE 1.1.2 DEFINING THE GEOMETRY OF THE SOLID 1.1.3 DEFINING LOADING 1.1.4 DECIDING WHAT PHYSIES TO INCLUDE IN THE MODEL 1.1.5 DEFINING MATERIAL BEHAVIOR 1.1.6 A REPRESENTATIVE INITIAL VALUE PROBLEM IN SOLID MECHANIES 1.1.7 CHOOSING A METHOD OF ANALYSIS CHAPTER 2 GOVERNING EQUATIONS 2.1 MATHEMATICAL DESCRIPTION OF SHAPE CHANGES IN SOLIDS 2.1.1 DISPLACEMENT AND VELOCITY FIELDS 2.1.2 DISPLACEMENT GRADIENT AND DEFORMATION GRADIENT TENSORS 2.1.3 DEFORMATION GRADIENT RESULTING FROM TWO SUCCESSIVE DEFORMATIONS 2.1.4 THE JACOBIAN OFTHE DEFORMATION GRADIENT 2.1.5 LAGRANGE STRAIN TENSOR 2.1.6 EULERIAN STRAIN TENSOR 2.1.7 INFINITESIMAL STRAIN TENSOR 2.1.8 ENGINEERING SHEAR STRAINS 2.1.9 DECOMPOSITION OFINFINITESIMAL STRAIN INTO VOLUMETRIE AND DEVIATORIE PARTS 2.1.10 INFINITESIMAL ROTATION TENSOR 2.1.11 PRINCIPAL VALUES AND DIRECTIONS OF THE INFINITESIMAL STRAIN TENSOR 2.1.12 CAUCHY-GREEN DEFORMATION TENSORS 2 3 4 5 6 7 10 11 13 13 13 14 18 19 20 22 22 24 24 25 26 27 V VI * CONTENTS 2.2 2.3 2.4 2.1.13 ROTATION TENSOR AND LEFT AND RIGHT STRETCH TENSORS 2.1.14 PRINCIPAL STRETCHES 2.1.15 GENERALIZED STRAIN MEASURES 2.1.16 THE VELOCITY GRADIENT 2.1.17 STRETCH RATE AND SPIN TENSORS 2.1.18 INFINITESIMAL STRAIN RATE AND ROTATION RATE 2.1.19 OTHER DEFORMATION RATE MEASURES 2.1.20 STRAIN EQUATIONS OF COMPATIBILITY FOR INFINITESIMAL STRAINS MATHEMATICAL DESCRIPTION OF INTERNAL FORCES IN SOLIDS 2.2.1 SURFACE TRACTION AND INTERNAL BODY FORCE 2.2.2 TRACTION ACTING ON PLANES WITHIN ASOLID 2.2.3 CAUCHY (TRUE) STRESS TENSOR 2.2.4 OTHER STRESS MEASURES: KIRCHHOFF, NOMINAL, AND MATERIAL STRESS TENSORS 2.2.5 STRESS MEASURES FOR INFINITESIMAL DEFORMATIONS 2.2.6 PRINCIPAL STRESSES AND DIRECTIONS 2.2.7 HYDROSTATIC, DEVIATORIC, AND VON MISES EFFECTIVE STRESS 2.2.8 STRESSES NEAR AN EXTERNAL SURFACE OR EDGE: BOUNDARY CONDITIONS ON STRESSES EQUATIONS OF MOTION AND EQUILIBRIUM FOR DEFORMABLE SOLIDS 2.3.1 LINEAR MOMENTUM BALANCE IN TERMS OFCAUCHY STRESS 2.3.2 ANGULAR MOMENTUM BALANCE IN TERMS OF CAUCHY STRESS 2.3.3 EQUATIONS OF MOTION IN TERMS OF OTHER STRESS MEASURES WORK DONE BY STRESSES: PRINCLPLE OF VIRTUAL WORK 2.4.1 WORK DONE BY CAUCHY STRESSES 2.4.2 RATE OF MECHANICAL WORK IN TERMS OF OTHER STRESS MEASURES 2.4.3 RATE OF MECHANICAL WORK FOR INFINITESIMAL DEFORMATIONS 2.4.4 THE PRINCIPLE OFVIRTUAL WORK 2.4.5 THE VIRTUAL WORK EQUATION IN TERMS OF OTHER STRESS MEASURES 2.4.6 THE VIRTUAL WORK EQUATION FOR INFINITESIMAL DEFORMATIONS 27 29 30 31 32 33 33 34 38 38 40 43 44 47 47 48 49 49 49 51 53 54 54 56 57 58 61 62 CHAPTER 3 CONSTITUTIVE MODELS: RELATIONS BETWEEN STRESS ARID STRAIN 65 3.1 GENERAL REQUIREMENTS FOR CONSTITUTIVE EQUATIONS 66 3.1.1 THERMODYNAMIC RESTRICTIONS 66 3.1.2 OBJECTIVITY 66 3.1.3 DRUCKER STABILITY 67 CONTENTS - VII 3.2 LINEAR ELASTIC MATERIAL BEHAVIOR 69 3.2.1 ISOTROPIE, LINEAR ELASTIE MATERIAL BEHAVIOR 69 3.2.2 STRESS-STRAIN RELATIONS FOR ISOTROPIE, LINEAR ELASTIE MATERIALS: YOUNG SMODULUS, POISSON S RATIO, AND THE THERMAL EXPANSION COEFFICIENT 70 3.2.3 REDUCED STRESS-STRAIN EQUATIONS FOR PLANE DEFORMATION OF ISOTROPIE SOLIDS 72 3.2.4 REPRESENTATIVE VALUES FOR DENSITY AND ELASTIE CONSTANTS OF ISOTROPIE SOLIDS 73 3.2.5 OTHER ELASTIC CONSTANTS: BULK, SHEAR, AND LAME MODULUS 74 3.2.6 PHYSIEAL INTERPRETATION OF ELASTIE CONSTANTS FOR ISOTROPIE SOLIDS 75 3.2.7 STRAIN ENERGY DENSITY FOR ISOTROPIE SOLIDS 75 3.2.8 STRESS-STRAIN RELATION FOR A GENERAL ANISOTROPIE LINEAR ELASTIE MATERIAL: ELASTIE STIFFNESS AND COMPLIANCE TENSORS 76 3.2.9 PHYSIEAL INTERPRETATION OF THE ANISOTROPIE ELASTIE CONSTANTS 78 3.2.10 STRAIN ENERGY DENSITY FOR ANISOTROPIE, LINEAR ELASTIE SOLIDS 79 3.2.11 BASIS CHANGE FORMULAS FOR ANISOTROPIE ELASTIE CONSTANTS 79 3.2.12 THE EFFECT OF MATERIAL SYMMETRY ON STRESS-STRAIN RELATIONS FOR ANISOTROPIE MATERIALS 81 3.2.13 STRESS-STRAIN RELATIONS FOR LINEAR ELASTIE ORTHOTROPIE MATERIALS 82 3.2.14 STRESS-STRAIN RELATIONS FOR LINEAR ELASTIE TRANSVERSELY ISOTROPIE MATERIAL 83 3.2.15 REPRESENTATIVE VALUES FOR ELASTIC CONSTANTS OFTRANSVERSELY ISOTROPIE HEXAGONAL CLOSE-PACKED CRYSTALS 85 3.2.16 LINEAR ELASTIE STRESS-STRAIN RELATIONS FOR CUBIE MATERIALS 85 3.2.17 REPRESENTATIVE VALUES FOR ELASTIC PROPERTIES OF CUBIE CRYSTALS AND COMPOUNDS 87 3.3 HYPOELASTICLTY: ELASTIC MATERIALS WITH A NONLINEAR STRESS-STRAIN RELATION UNDER SMALL DEFORMATION 87 3.4 GENERALIZED HOOKE S LAW: ELASTIC MATERIALS SUBJECTED TO SMALL STRETCHES BUT LARGE ROTATIONS 91 3.5 HYPERELASTICLTY: TIME-INDEPENDENT BEHAVIOR OF RUBBERS AND FOAMS SUBJECTED TO LARGE STRAINS 93 3.5.1 DEFORMATION MEASURES USED IN FINITE ELASTICITY 95 3.5.2 STRESS MEASURES USED IN FINITE ELASTICITY 96 3.5.3 CALCULATING STRESS-STRAIN RELATIONS FROM THE STRAIN ENERGY DENSITY 97 3.5.4 A NOTE ON PERFECTLY INCOMPRESSIBLE MATERIALS 99 VIII CONTENTS 3.5.5 SPECIFIC FORMS OF THE STRAIN ENERGY DENSITY 100 3.5.6 CALIBRATING NONLINEAR ELASTICITY MODELS 102 3.5.7 REPRESENTATIVE VALUES OF MATERIAL PROPERTIES FOR RUBBERS 103 3.6 LINEAR VISCOELASTIC MATERIALS: TIME-DEPENDENT BEHAVIOR OF POLYMERS AT SMALL STRAINS 103 3.6.1 FEATURES OF THE SMALL STRAIN RATE-DEPENDENT RESPONSE OF POLYMERS 104 3.6.2 GENERAL CONSTITUTIVE EQUATIONS FOR LINEAR VISCOELASTIC SOLIDS 109 3.6.3 SPRING-DAMPER APPROXIMATIONS TO THE RELAXATION MODULUS 110 3.6.4 PRONY SERIES REPRESENTATION FOR THE RELAXATION MODULUS 112 3.6.5 CALIBRATING THE CONSTITUTIVE LAWS FOR LINEAR VISCOELASTIC SOLIDS 112 3.6.6 REPRESENTATIVE VALUES FOR VISCOELASTIC PROPERTIES OFPOLYMERS 113 3.7 SMALL STRAIN, RATE-II LDEPENDENT PLASTICLTY: METALS LOADED BEYOND YIELD 113 3.7.1 FEATURES OF THE INELASTIC RESPONSE OF METALS 115 3.7.2 DECOMPOSITION OF STRAIN INTO ELASTIC AND PLASTIC PARTS 118 3.7.3 YIELD CRITERIA 118 3.7.4 GRAPHICAL REPRESENTATION OF THE YIELD SURFACE 119 3.7.5 STRAIN HARDENING LAWS 120 3.7.6 PLASTIC FLOW LAW 122 3.7.7 ELASTIC UNLOADING CONDITION 126 3.7.8 COMPLETE INCREMENTAL STRESS-STRAIN RELATIONS FOR A RATE-INDEPENDENT ELASTIC- PLASTIC SOLID 126 3.7.9 TYPICAL VALUES FOR YIELD STRESS OF POLYCRYSTALLINE METALS 129 3.7.10 PERSPECTIVES ON PLASTIC CONSTITUTIVE EQUATIONS: PRINCIPLE OF MAXIMUM PLASTIC RESISTANCE 129 3.7.11 PERSPECTIVES ON PLASTIC CONSTITUTIVE EQUATIONS: DRUCKER S POSTULATE 131 3.7.12 MICROSCOPIC PERSPECTIVES ON PLASTIC FLOW IN METALS 132 3.8 SMALL STRAIN VISCOPLASTICLTY: CREEP AND HIGH STRAIN RATE DEFORMATION OF CRYSTALLINE SOLIDS 135 3.8.1 FEATURES OF CREEP BEHAVIOR 135 3.8.2 FEATURES OF HIGH STRAIN RATE BEHAVIOR 137 3.8.3 SMALL STRAIN, VISCOPLASTIC CONSTITUTIVE EQUATIONS 137 3.8.4 REPRESENTATIVE VALUES OFPARAMETERS FOR VISCOPLASTIC MODELS OF CREEPING SOLIDS 142 3.8.5 REPRESENTATIVE VALUES OF PARAMETERS FOR VISCOPLASTIC MODELS OF HIGH STRAIN RATE DEFORMATION 142 CONTENTS - IX 3.9 LARGE STRAIN, RATE-DEPENDENT PLASTICITY 143 3.9.1 KINEMATICS OFFINITE STRAIN PLASTICITY 143 3.9.2 STRESS MEASURES FOR FINITE DEFORMATION PLASTICITY 145 3.9.3 ELASTIC STRESS-STRAIN RELATION FOR FINITE STRAIN PLASTICITY 146 3.9.4 PLASTIC CONSTITUTIVE LAW FOR FINITE STRAIN VISCOPLASTICITY 147 3.10 LARGE STRAIN VISCOELASTICITY 148 3.10.1 KINEMATICS FOR FINITE STRAIN VISCOELASTICITY 148 3.10.2 STRESS MEASURES FOR FINITE STRAIN VISCOELASTICITY 150 3.10.3 RELATION AMONG STRESS, DEFORMATION MEASURES, AND STRAIN ENERGY DENSITY 150 3.10.4 STRAIN RELAXATION 151 3.10.5 REPRESENTATIVE VALUES FOR MATERIAL PARAMETERS IN A FINITE STRAIN VISCOELASTIC MODEL 152 3.11 CRITICAL STATE MODELS FOR SOLLS 152 3.11.1 FEATURES OF THE BEHAVIOR OF SOILS 152 3.11.2 CONSTITUTIVE EQUATIONS FOR CAM-CLAY 153 3.11.3 APPLICATION OF THE CRITICAL STATE EQUATIONS TO SIMPLE 2D LOADING 160 3.11.4 TYPICAL VALUES OF MATERIAL PROPERTIES FOR SOILS 161 3.12 CONSTITUTIVE MODELS FOR METAL SINGLE CRYSTALS 161 3.12.1 REVIEW OFSOME IMPORTANT CONCEPTS FROM CRYSTALLOGRAPHY 162 3.12.2 FEATURES OF PLASTIC FLOW IN SINGLE CRYSTALS 166 3.12.3 KINEMATIC DESCRIPTIONS USED IN CONSTITUTIVE MODELS OF SINGLE CRYSTALS 171 3.12.4 STRESS MEASURES USED IN CRYSTAL PLASTICITY 173 3.12.5 ELASTIC STRESS-STRAIN RELATION USED IN CRYSTAL PLASTICITY 174 3.12.6 PLASTIC STRESS-STRAIN RELATION USED IN CRYSTAL PLASTICITY 174 3.12.7 REPRESENTATIVE VALUES FOR PLASTIC PROPERTIES OFSINGLE CRYSTALS 176 3.13 CONSTITUTIVE MODELS FOR CONTACTING SURFACES AND II LTERFACES IN SOLIDS 176 3.13.1 COHESIVE ZONE MODELS OFINTERFACES 176 3.13.2 MODELS OF CONTACT AND FRICTION BETWEEN SURFACES 182 CHARTER 4* SOLUTIONS TO SIMPLE BOUNDARY AND INITIAL VALUE PROBLEMS 193 4.1 AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC LINEAR ELASTIC PROBLEMS 193 4.1.1 SUMMARY OF GOVERNING EQUATIONS OF LINEAR ELASTICITY IN CARTESIAN COMPONENTS 193 X * CONTENTS 4.1.2 SIMPLIFIED EQUATIONS FOR SPHERIEALLY SYMMETRIE LINEAR ELASTICITY PROBLEMS 194 4.1.3 GENERAL SOLUTION TO THE SPHERIEALLY SYMMETRIE LINEAR ELASTICITY PROBLEM 197 4.2 4.3 4.4 4.1.4 PRESSURIZED HOLLOW SPHERE 4.1.5 GRAVITATING SPHERE 4.1.6 SPHERE WITH STEADY-STATE HEAT FLOW 4.1.7 SIMPLIFIED EQUATIONS FOR AXIALLY SYMMETRIE LINEAR ELASTICITY PROBLEMS 4.1.8 GENERAL SOLUTION TO THE AXISYMMETRIE BOUNDARY VALUE PROBLEM 4.1.9 LONG (GENERALIZED PLANE STRAIN) CYLINDER SUBJECTED TO INTERNAL AND EXTERNAL PRESSURE 4.1.10 SPINNING CIREULAR PLATE 4.1.11 STRESSES INDUEED BYAN INTERFERENEE FIT BETWEEN TWO CYLINDERS AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC ELASTIC-PLASTIC PROBLEMS 4.2.1 SUMMARY OF GOVERNING EQUATIONS 4.2.2 SIMPLIFIED EQUATIONS FOR SPHERIEALLY SYMMETRIE PROBLEMS 4.2.3 ELASTIE PERFEETLY PLASTIE HOLLOW SPHERE SUBJEETED TO MONOTONIEALLY INEREASING INTERNAL PRESSURE 4.2.4 ELASTIE PERFEETLY PLASTIE HOLLOW SPHERE SUBJEETED TO CYCLIE INTERNAL PRESSURE 4.2.5 SIMPLIFIED EQUATIONS FOR PLANE STRAIN AXIALLY SYMMETRIE ELASTIC- PERFEETLY PLASTIE SOLIDS 4.2.6 LONG (PLANE STRAIN) CYLINDER SUBJEETED TO INTERNAL PRESSURE SPHERICALLY SYMMETRIC SOLUTION TO QUASI-STATIC LARGE STRAIN ELASTICITY PROBLEMS 4.3.1 SUMMARY OF GOVERNING EQUATIONS OF FINITE ELASTIEITY IN CARTESIAN COMPONENTS 4.3.2 SIMPLIFIED EQUATIONS FOR INEOMPRESSIBLE SPHERIEALLY SYMMETRIE SOLIDS 4.3.3 PRESSURIZED HOLLOW SPHERE MADE FROM AN INEOMPRESSIBLE RUBBER SIMPLE DYNAMIC SOLUTIONS FOR LINEAR ELASTIC MATERIALS 4.4.1 SURFAEE SUBJEETED TO TIME-VARYING NORMAL PRESSURE 4.4.2 SURFAEE SUBJEETED TO TIME-VARYING SHEAR TRACTION 4.4.3 ONE-DIMENSIONAL BAR SUBJEETED TO END LOADING 4.4.4 PLANE WAVES IN AN INFINITE SOLID 4.4.5 SUMMARY OFWAVE SPEEDS IN ISOTROPIE ELASTIC SOLIDS 197 199 200 202 205 206 208 209 211 212 213 215 219 223 226 229 229 230 232 236 236 239 239 240 241 CONTENTS - XI 4.4.6 4.4.7 4.4.8 REFLECTION OFWAVES TRAVELING NORMAL TO A FREE SURFACE REFLECTION AND TRANSMISSION OFWAVES NORMAL TO AN INTERFACE SIMPLE EXAMPLE INVOLVING PLANE WAVE PROPAGATION: PLATE IMPACT EXPERIMENT 242 243 245 270 274 277 278 280 272 257 259 260 262 264 265 266 266 255 256 267 268 CYLINDRICAL HOLE IN AN INFINITE SOLID UNDER REMOTE LOADING CRACK IN AN INFINITE ELASTIC SOLID UNDER REMOTE LOADING FIELDS NEAR THE TIP OF A CRACK ON BIMATERIAL INTERFACE 5.3.5 5.3.6 5.3.7 5.2.1 AIRY SOLUTION IN RECTANGULAR COORDINATES 5.2.2 DEMONSTRATION THAT THE AIRY SOLUTION SATISFIES THE GOVERNING EQUATIONS 5.2.3 AIRY SOLUTION IN CYLINDRICAL-POLAR COORDINATES 5.2.4 AIRY FUNCTION SOLUTION TO THE END-LOADED CANTILEVER 5.2.5 2D LINE LOAD ACTING PERPENDICULAR TO THE SURFACE OF AN INFINITE SOLID 5.2.6 2D LINE LOAD ACTING PARALLEL TO THE SURFACE OF AN INFINITE SOLID 5.2.7 ARBITRARY PRESSURE ACTING ON A FLAT SURFACE 5.2.8 UNIFORM NORMAL PRESSURE ACTING ON A STRIP 5.2.9 STRESSES NEAR THE TIP OF A CRACK COMPLEX VARIABLE SOLUTION TO PLANE STRAIN STATIC LINEAR ELASTIC PROBLEMS 5.3.1 COMPLEX VARIABLE SOLUTIONS TO ELASTICITY PROBLEMS 5.3.2 DEMONSTRATION THAT THE COMPLEX VARIABLE SOLUTION SATISFIES THE GOVERNING EQUATIONS 5.3.3 COMPLEX VARIABLE SOLUTION FOR A LINE FORCE IN AN INFINITE SOLID (PLANE STRAIN DEFORMATION) 5.3.4 COMPLEX VARIABLE SOLUTION FOR AN EDGE DISLOCATION IN AN INFINITE SOLID 5.2 5.3 CHAPTER 5 SOLUTIONS FUER LINEAR ELASTIC SOLIDS 249 5.1 GENERAL PRIT ICIPLES 250 5.1.1 SUMMARY OFTHE GOVERNING EQUATIONS OFLINEAR ELASTICITY 250 5.1.2 ALTERNATIVE FORM OFTHE GOVERNING EQUATIONS: NAVIER EQUATION 251 5.1.3 SUPERPOSITION AND LINEARITY OF SOLUTIONS 251 5.1.4 UNIQUENESS AND EXISTENCE OFSOLUTIONS TO THE LINEAR ELASTICITY EQUATIONS 252 5.1.5 SAINT-VENANT SPRINCIPLE 252 AIRY FUNCTION SOLUTION TO PLANE STRESS AT ID STRAIN STATIC LINEAR ELASTIC PROBLEMS XII CONTENTS 5.3.8 FRICTIONLESS RIGID FLAT INDENTER IN CONTACT WITH A HALF-SPACE 283 5.3.9 FRICTIONLESS PARABOLIC (CYLINDRIEAL) INDENTER IN CONTACT WITH A HALF-SPACE 284 5.3.10 LINE CONTACT BETWEEN TWO NONCONFORMAL FRIETIONLESS ELASTIE SOLIDS 286 5.3.11 SLIDING CONTACT BETWEEN TWO ROUGH ELASTIC CYLINDERS 287 5.3.12 DISLOCATION NEAR THE SURFACE OF A HALF-SPACE 289 5.4 SOLUTIONS TO 3D STATIC PROBLEMS IN LINEAR ELASTICITY 290 5.4.1 PAPKOVIEH NEUBER POTENTIAL REPRESENTATIONS FOR 3D SOLUTIONS FOR ISOTROPIE SOLIDS 290 5.4.2 DEMONSTRATION THAT THE PAPKOVICH NEUBER SOLUTION SATISFIES THE GOVERNING EQUATIONS 291 5.4.3 POINT FORCE IN AN INFINITE SOLID 292 5.4.4 POINT FORCE NORMAL TO THE SURFACE OF AN INFINITE HALF-SPACE 293 5.4.5 POINT FORCE TANGENT TO THE SURFACE OF AN INFINITE HALF-SPACE 293 5.4.6 THE ESHELBY INCLUSION PROBLEM 294 5.4.7 ELASTICALLY MISMATCHED ELLIPSOIDAL INCLUSION IN AN INFINITE SOLID SUBJECTED TO REMOTE STRESS 299 5.4.8 SPHERIEAL CAVITY IN AN INFINITE SOLID SUBJECTED TO REMOTE STRESS 300 5.4.9 FLAT-ENDED CYLINDRICAL INDENTER IN CONTACT WITH AN ELASTIE HALF-SPACE 302 5.4.10 FRIETIONLESS CONTACT BETWEEN TWO ELASTIC SPHERES 304 5.4.11 CONTACT AREA, PRESSURE, STIFFNESS, AND ELASTIE LIMIT FOR GENERAL NONCONFORMAL CONTACTS 306 5.4.12 LOAD DISPLACEMENT-CONTACT AREA RELATIONS FOR ARBITRARILY SHAPED AXISYMMETRIE CONTACTS 308 5.5 SOLUTIONS TO GENERALIZED PLANE PROBLEMS FOR ANISOTROPIC LINEAR ELASTIC SOLIDS 310 5.5.1 GOVERNING EQUATIONS OF ELASTICITY FOR ANISOTROPIE SOLIDS 310 5.5.2 STROH REPRESENTATION FOR FIELDS IN ANISOTROPIE SOLIDS 312 5.5.3 DEMONSTRATION THAT THE STROH REPRESENTATION SATISFIES THE GOVERNING EQUATIONS 314 5.5.4 STROH EIGENVALUES AND ANISOTROPY MATRICES FOR CUBIE MATERIALS 316 5.5.5 DEGENERATE MATERIALS 317 5.5.6 FUNDAMENTAL ELASTICITY MATRIX 317 5.5.7 ORTHOGONAL PROPERTIES OF STROH MATRICES A AND B 318 5.5.8 BARNETT-LOTHE TENSORS AND THE IMPEDANCE TENSOR 319 CONTENTS - XIII 5.6 5.7 5.8 5.9 5.5.9 USEFUL PROPERTIES OF MATRIEES IN ANISOTROPIE ELASTICITY 5.5.10 BASIS CHANGE FORMULAS FOR MATRIEES USED IN ANISOTROPIE ELASTICITY 5.5.11 BARNETT-LOTHE INTEGRALS 5.5.12 STROH REPRESENTATION FOR ASTATE OF UNIFORM STRESS 5.5.13 LINE LOAD AND DISLOEATION IN AN INFINITE ANISOTROPIE SOLID 5.5.14 LINE LOAD AND DISLOEATION BELOW THE SURFAEE OF AN ANISOTROPIE HALF-SPAEE SOLUTIONS TO DYNAMIC PROBLEMS FOR ISOTROPIC LINEAR ELASTIC SOLIDS 5.6.1 LOVE POTENTIALS FOR DYNAMIE SOLUTIONS FOR ISOTROPIE SOLIDS 5.6.2 PRESSURE SUDDENLY APPLIED TO THE SURFAEE OF A SPHERIEAL CAVITY IN AN INFINITE SOLID 5.6.3 RAYLEIGH WAVES 5.6.4 LOVE WAVES 5.6.5 ELASTIE WAVES IN WAVEGUIDES ENERGY METHODS FOR SOLVII LG STATIC LINEAR ELASTICITY PROBLEMS 5.7.1 DEFINITION OF THE POTENTIAL ENERGY OF A LINEAR ELASTIE SOLID UNDER STATIE LOADING 5.7.2 PRINEIPLE OF STATIONARY AND MINIMUM POTENTIAL ENERGY 5.7.3 UNIAXIAL COMPRESSION OF A CYLINDER SOLVED BY ENERGY METHODS 5.7.4 VARIATIONAL DERIVATION OF THE BEAM EQUATIONS 5.7.5 ENERGY METHODS FOR CALCULATING STIFFNESS RECLPROCAL THEOREM AND APPLICATIONS 5.8.1 STATEMENT AND PROOF OFTHE REEIPROEAL THEOREM 5.8.2 SIMPLE EXAMPLE USING THE RECIPROEAL THEOREM 5.8.3 FORMULAS RELATING INTERNAL AND BOUNDARY VALUES OF FIELD QUANTITIES 5.8.4 CLASSIEAL SOLUTIONS FOR DISPLAEEMENT AND STRESS INDUEED BY A 3D DISLOEATION LOOP IN AN INFINITE SOLID ENERGETICS OF DISLOCATIONS IN ELASTIC SOLIDS 320 321 323 325 327 329 330 330 331 333 335 337 339 339 341 344 346 350 352 352 353 355 356 359 5.9.1 5.9.2 5.9.3 5.9.4 5.9.5 CLASSIEAL SOLUTION FOR POTENTIAL ENERGY OF AN ISOLATED DISLOEATION LOOP IN AN INFINITE SOLID NONSINGULAR DISLOEATION THEORY ENERGY OF A DISLOEATION LOOP IN A STRESSED, FINITE ELASTIE SOLID ENERGY OF TWO INTERAETING DISLOEATION LOOPS DRIVING FOREE FOR DISLOEATION MOTION: PEAEH-KOEHLER FORMULA 359 362 365 369 370 XIV * CONTENTS 5.10 RAYLEIGH-RITZ METHOD FOR ESTIMATING NATURAL FREQUENCY OF AN ELASTIC SOLID 375 5.10.1 MODE SHAPES AND NATURAL FREQUENCIES; ORTHOGONALITY OF MODE SHAPES AND RAYLEIGH S PRINCIPLE 375 5.10.2 ESTIMATE OFNATURAL FREQUENCY OFVIBRATION FOR A BEAM USING RAYLEIGH-RITZ METHOD 379 CHARTER 6* SOLUTIONS FUER PLASTIC SOLIDS 381 6.1 SLLP-L1NE FIELD THEORY 381 6.1.1 INTERPRETING A SLIP-LINE FIELD 382 6.1.2 DERIVATION OF THE SLIP-LINE FIELD METHOD 386 6.1.3 EXAMPLES OF SLIP-LINE FIELD SOLUTIONS TO BOUNDARY VALUE PROBLEMS 392 BOUNDING THEOREMS IN PLASTICITY AND THEIR APPLICATIONS 6.2 6.2.1 6.2.2 6.2.3 6.2.4 6.2.5 6.2.6 6.2.7 6.2.8 6.2.9 6.2.10 DEFINITION OF THE PLASTIC DISSIPATION PRINCIPLE OF MINIMUM PLASTIC DISSIPATION UPPER BOUND PLASTIC COLLAPSE THEOREM EXAMPLES OF APPLICATIONS OF THE UPPER BOUND THEOREM LOWER BOUND PLASTIC COLLAPSE THEOREM EXAMPLES OF APPLICATIONS OF THE LOWER BOUND PLASTIC COLLAPSE THEOREM LOWER BOUND SHAKEDOWN THEOREM EXAMPLES OF APPLICATIONS OF THE LOWER BOUND SHAKEDOWN THEOREM UPPER BOUND SHAKEDOWN THEOREM EXAMPLES OF APPLICATIONS OF THE UPPER BOUND SHAKEDOWN THEOREM 398 399 401 404 405 410 411 412 415 417 419 CHARTER 7* FINITE ELEMENT ANALYSIS: AN INTRODUCTION 421 7.1 A GUIDE TO USING FINITE ELEMENT SOFTWARE 423 7.1.1 FINITE ELEMENT MESH FOR A 2D OR 3D COMPONENT 425 7.1.2 NODES AND ELEMENTS IN A MESH 428 7.1.3 SPECIAL ELEMENTS: BEAMS, PLATES, SHELLS, AND TRUSS ELEMENTS 432 7.1.4 MATERIAL BEHAVIOR 434 7.1.5 BOUNDARY CONDITIONS 435 7.1.6 CONSTRAINTS 438 CONTENTS - XV 7.1.7 CONTACTING SURFACES AND INTERFACES 439 7.1.8 INITIAL CONDITIONS AND EXTERNAL FIELDS 441 7.1.9 SOLUTION PROCEDURES AND TIME INCREMENTS 441 7.1.10 OUTPUT 445 7.1.11 UNITS IN FINITE ELEMENT COMPUTATIONS 446 7.1.12 USING DIMENSIONAL ANALYSIS TO SIMPLIFY FEA 447 7.1.13 SIMPLIFYING FEA BY SCALING THE GOVERNING EQUATIONS 449 7.1.14 DIMENSIONAL ANALYSIS: CLOSING REMARKS 451 7.2 A SIMPLE FINITE ELEMENT PROGRAM 451 7.2.1 FINITE ELEMENT MESH AND ELEMENT CONNECTIVITY 452 7.2.2 GLOBAL DISPLACEMENT VECTOR 453 7.2.3 ELEMENT INTERPOLATION FUNCTIONS 453 7.2.4 ELEMENT STRAINS, STRESSES, AND STRAIN ENERGY DENSITY 454 7.2.5 ELEMENT STIFFNESS MATRIX 455 7.2.6 GLOBAL STIFFNESS MATRIX 456 7.2.7 BOUNDARY LOADING 459 7.2.8 GLOBAL RESIDUAL FORCE VECTOR 461 7.2.9 MINIMIZING THE POTENTIAL ENERGY 461 7.2.10 ELIMINATING PRESCRIBED DISPLACEMENTS 462 7.2.11 SOLUTION 463 7.2.12 POSTPROCESSING 463 7.2.13 EXAMPLE FEA CODE 464 CHAPTER 8* FINITE ELEMENT ANALYSIS: THEORY AND IMPLEMENTATION 467 8.1 GENERALIZED FEM FOR STATIC LINEAR ELASTICITY 468 8.1.1 REVIEW OF THE PRINCIPLE OFVIRTUAL WORK 468 8.1.2 INTEGRAL (WEAK) FORM OFTHE GOVERNING EQUATIONS OFLINEAR ELASTICITY 469 8.1.3 INTERPOLATING THE DISPLACEMENT FIELD AND THE VIRTUAL VELOCITY FIELD 470 8.1.4 FINITE ELEMENT EQUATIONS 472 8.1.5 SIMPLE ID IMPLEMENTATION OF THE FEM 472 8.1.6 SUMMARY OFTHE ID FINITE ELEMENT PROCEDURE 476 8.1.7 EXAMPLE FEM CODE AND SOLUTION 477 8.1.8 EXTENDING THE ID FEM TO 2D AND 3D 480 8.1.9 INTERPOLATION FUNCTIONS FOR 2D ELEMENTS 481 8.1.10 INTERPOLATION FUNCTIONS FOR 3D ELEMENTS 481 XVI * CONTENTS 8.1.11 VOLUME INTEGRALS FOR STIFFNESS AND FORCE IN TERMS OFNORMALIZED COORDINATES 482 8.1.12 NUMERICAL INTEGRATION SCHEMES FOR 2D AND 3D ELEMENTS 485 8.1.13 SUMMARY OFFORMULAS FOR ELEMENT STIFFNESS AND FORCE MATRICES 486 8.1.14 SAMPIE 2D/3D LINEAR ELASTOSTATIC FEM CODE 486 8.2 THE FEM FOR DYNAMIC LINEAR ELASTICITY 490 8.2.1 REVIEW OF THE GOVERNING EQUATIONS OF DYNAMIC LINEAR ELASTICITY 490 8.2.2 EXPRESSING THE GOVERNING EQUATIONS USING THE PRINCIPLE OFVIRTUAL WORK 491 8.2.3 FINITE ELEMENT EQUATIONS OF MOTION FOR LINEAR ELASTIC SOLIDS 491 8.2.4 NEWMARK TIME INTEGRATION FOR ELASTODYNAMICS 493 8.2.5 1D IMPLEMENTATION OF A NEWMARK SCHEME 495 8.2.6 EXAMPLE 1D DYNAMIC FEM CODE AND SOLUTION 497 8.2.7 LUMPED MASS MATRICES 499 8.2.8 EXAMPLE 2D AND 3D DYNAMIC LINEAR ELASTIC CODE AND SOLUTION 501 8.2.9 MODAL METHOD OFTIME INTEGRATION 501 8.2.10 NATURAL FREQUENCIES AND MODE SHAPES 502 8.2.11 EXAMPLE 1D CODE WITH MODAL DYNAMICS 503 8.2.12 EXAMPLE 2D AND 3D FEM CODE TO COMPUTE MODE SHAPES AND NATURAL FREQUENCIES 505 8.3 FEM FOR NONLINEAR (HYPOELASTIC) MATERIALS 505 8.3.1 SUMMARY OF GOVERNING EQUATIONS 505 8.3.2 GOVERNING EQUATIONS IN TERMS OF THE VIRTUAL WORK PRINCIPLE 507 8.3.3 FINITE ELEMENT EQUATIONS 507 8.3.4 SOLVING THE FINITE ELEMENT EQUATIONS USING NEWTON-RAPHSON ITERATION 509 8.3.5 TANGENT MODULI FOR THE HYPOELASTIC SOLID 510 8.3.6 SUMMARY OF THE NEWTON-RAPHSON PROCEDURE FOR HYPOELASTIC SOLIDS 511 8.3.7 WHAT TO DO IF THE NEWTON-RAPHSON ITERATIONS DO NOT CONVERGE 511 8.3.8 VARIATIONS ON NEWTON-RAPHSON ITERATION 512 8.3.9 EXAMPLE HYPOELASTIC FEM CODE 512 8.4 FEM FOR LARGE DEFORMATIONS: HYPERELASTIC MATERIALS 514 8.4.1 SUMMARY OF GOVERNING EQUATIONS 514 8.4.2 GOVERNING EQUATIONS IN TERMS OF THE PRINCIPLE OF VIRTUAL WORK 515 8.4.3 FINITE ELEMENT EQUATIONS 515 CONTENTS - XVII 8.4.4 SOLUTION USING CONSISTENT NEWTON-RAPHSON ITERATION 517 8.4.5 TANGENT STIFFNESS FOR THE NEO-HOOKEAN MATERIAL 519 8.4.6 EVALUATING THE BOUNDARY TRACTION INTEGRALS 520 8.4.7 EXAMPLE HYPERELASTIE FINITE ELEMENT CODE 521 8.5 THE FEM FOR VISCOPLASTICITY 522 8.5.1 SUMMARY OF GOVERNING EQUATIONS 522 8.5.2 GOVERNING EQUATIONS IN TERMS OF THE VIRTUAL WORK PRINCIPLE 523 8.5.3 FINITE ELEMENT EQUATIONS 524 8.5.4 INTEGRATING THE PLASTIE STRESS-STRAIN LAW 525 8.5.5 MATERIAL TANGENT 527 8.5.6 SOLUTION USING CONSISTENT NEWTON-RAPHSON ITERATION 528 8.5.7 EXAMPLE SMALL STRAIN PLASTIE FEM CODE 529 8.6 ADVANCED ELEMET IT FORMULATIONS: INCOMPATIBLE MODES, REDUCED INTEGRATION, AND HYBRID ELEMET ITS 530 8.6.1 SHEAR LOCKING AND INCOMPATIBLE MODE ELEMENTS 531 8.6.2 VOLUMETRIE LOCKING AND REDUCED INTEGRATION ELEMENTS 533 8.6.3 HYBRID ELEMENTS FOR MODELING NEAR-INCOMPRESSIBLE MATERIALS 541 8.7 LIST OF EXAMPLE FEA PROGRAMS AND INPUT FILES 544 CHAPTER 9* MODELING MATERIAL FAILURE 547 9.1 SUMMARY OF MECHANISMS OF FRACTURE AND FATIGUE UNDER STATIC AND CYCLIC LOADING 548 9.2 9.1.1 FAILURE UNDER MONOTONIE LOADING 9.1.2 FAILURE UNDER CYDIE LOADING STRESS- AND STRAIN-BASED FRACTURE AND FATIGUE CRITERIA 9.2.1 STRESS-BASED FAILURE CRITERIA FOR BRITTLE SOLIDS AND COMPOSITES 9.2.2 PROBABILISTIC DESIGN METHODS FOR BRITTLE FRACTURE (WEIBULL STATISTICS) 9.2.3 STATIC FATIGUE CRITERION FOR BRITTLE MATERIALS 9.2.4 CONSTITUTIVE LAWS FOR CRUSHING FAILURE OFBRITTLE MATERIALS 9.2.5 DUCTILE FRACTURE CRITERIA 9.2.6 DUCTILE FAILURE BY STRAIN LOCALIZATION 9.2.7 CRITERIA FOR FAILURE BY HIGH CYDE FATIGUE UNDER CONSTANT AMPLITUDE CYDIC LOADING 9.2.8 CRITERIA FOR FAILURE BY LOW CYDE FATIGUE 9.2.9 CRITERIA FOR FAILURE UNDER VARIABLE AMPLITUDE CYDIC LOADING 548 550 553 553 556 557 558 559 562 564 565 566 XVIII * CONTENTS 9.3 MODELING FALLURE BY CRACK GROWTH: LINEAR ELASTIC FRACTURE MECHANICS 567 9.3.1 CRACK TIP FIELDS IN AN ISOTROPIE, LINEAR ELASTIE SOLID 567 9.3.2 ASSUMPTIONS AND APPLICATION OFPHENOMENOLOGIEAL LINEAR ELASTIE FRACTURE MECHANICS 569 9.3.3 CALCULATING STRESS INTENSITY FACTORS 572 9.3.4 CALCULATING STRESS INTENSITY FACTORS USING FEA 578 9.3.5 MEASURING FRACTURE TOUGHNESS 580 9.3.6 TYPIEAL VALUES FOR FRACTURE TOUGHNESS 581 9.3.7 STABLE TEARING: KR CURVES AND CRACK STABILITY 581 9.3.8 MIXED-MODE FRACTURE CRITERIA 584 9.3.9 STATIC FATIGUE CRACK GROWTH 584 9.3.10 CYDIC FATIGUE CRACK GROWTH 586 9.3.11 FINDING CRACKS IN STRUCTURES 587 9.4 ENERGY METHODS IN FRACTURE MECHANICS 588 9.4.1 DEFINITION OF CRACK TIP ENERGY RELEASE RATE FOR CRACKS IN LINEAR ELASTIC SOLIDS 588 9.4.2 ENERGY RELEASE RATE AS A FRACTURE CRITERION 589 9.4.3 RELATION BETWEEN ENERGY RELEASE RATE AND STRESS INTENSITY FACTOR 589 9.4.4 RELATION BETWEEN ENERGY RELEASE RATE AND COMPLIANCE 591 9.4.5 CALCULATING STRESS INTENSITY FACTORS USING COMPLIANCE 592 9.4.6 INTEGRAL EXPRESSIONS FOR ENERGY FLUX TO A CRACK TIP 593 9.4.7 RICE S!INTEGRAL 596 9.4.8 CALCULATING ENERGY RELEASE RATES USING THE J INTEGRAL 598 9.5 PLASTIC FRACTURE MECHANICS 599 9.5.1 DUGDALE-BARENBLATT COHESIVE ZONE MODEL OFYIELD AT A CRACK TIP 599 9.5.2 HUTCHINSON-RICE-ROSENGREN CRACK TIP FIELDS FOR STATIONARY CRACK IN APOWER LAW HARDENING SOLID 601 9.5.3 PLASTIC FRACTURE MECHANIES BASED ON J 605 9.6 LINEAR ELASTIC FRACTURE MECHANICS OF INTERFACES 607 9.6.1 9.6.2 9.6.3 9.6.4 CRACK TIP FIELDS FOR A CRACK ON AN INTERFACE PHENOMENOLOGICAL THEORY OF INTERFACE FRACTURE STRESS INTENSITY FACTORS FOR SOME INTERFACE CRACKS CRACK PATH SELECTION 607 610 612 613 617 CONTENTS - XIX CHAPTER 10* SOLUTIONS FUER RADS, BEAMS, MEMBRANES, PLATES, AND SHELLS 615 10.1 PRELIMINARIES: DYADIC NOTATION FOR VECTORS AND TENSORS 616 10.2 MOTION AND DEFORMATION OF SLENDER RODS 617 10.2.1 VARIABLES CHARACTERIZING THE GEOMETRY OF A ROD SCROSS SEETION 10.2.2 COORDINATE SYSTEMS AND VARIABLES CHARAETERIZING THE DEFORMATION OF A ROD 10.2.3 ADDITIONAL DEFORMATION MEASURES AND USEFUL KINEMATIE RELATIONS 618 620 10.2.4 APPROXIMATING THE DISPLACEMENT, VELOCITY, AND ACCELERATION IN A ROD 624 10.2.5 APPROXIMATING THE DEFORMATION GRADIENT 625 10.2.6 OTHER STRAIN MEASURES 626 10.2.7 KINEMATIES OF RODS LHAT ARE BENT AND TWISTED IN THE UNSTRESSED STATE 628 10.2.8 REPRESENTATION OF FOREES AND MOMENTS IN SLENDER RODS 630 10.2.9 EQUATIONS OF MOTION AND BOUNDARY CONDITIONS 631 10.2.10 CONSTITUTIVE EQUATIONS RELATING FOREES TO DEFORMATION MEASURES ~FU~K~~ 6~ 10.2.11 STRAIN ENERGY OF AN ELASTIC ROD 639 10.3 SIMPLIFIED VERSIONS OF THE GENERAL THEORY OF DEFORMABLE RODS 641 10.3.1 STRETCHED FLEXIBLE STRING WITH SMALL TRANSVERSE DEFLEETIONS 641 10.3.2 STRAIGHT ELASTK BEAM WITH SMALL DEFLECTIONS AND NO AXIAL FORCE (EULER-BERNOULLI BEAM LHEORY) 642 10.3.3 STRAIGHT ELASTIC BEAM WITH SMALL TRANSVERSE DEFLECTIONS AND SIGNIFICANT AXIAL FORCE 643 10.4 EXACT SOLUTIONS TO SIMPLE PROBLEMS INVOLVING ELASTIC RODS 644 10.4.1 FREE VIBRATION OF A STRAIGHT BEAM WITHOUT AXIAL FORCE 645 10.4.2 BUCKLING OF A COLUMN SUBJECTED TO GRAVITATIONAL LOADING 648 10.4.3 POST-BUCKLED SHAPE OF AN INITIALLY STRAIGHT ROD SUBJECTED TO END LHRUST 650 10.4.4 ROD BENT AND TWISTED INTO A HELIX 653 10.4.5 HE/KAI SPRING 655 XX * CONTENTS 10.5 MOTION AND DEFORMATION OF THIN SHELLS: GENERAL THEORY 657 10.5.1 COORDINATE SYSTEMS AND VARIABLES CHARACTERIZING DEFORMATION OF SHELLS 657 10.5.2 10.5.3 10.5.4 10.5.5 10.5.6 10.5.7 10.5.8 10.5.9 VECTORS AND TENSOR COMPONENTS IN NONORTHOGONAL BASES: COVARIANT AND CONTRAVARIANT COMPONENTS ADDITIONAL DEFORMATION MEASURES AND KINEMATIC RELATIONS APPROXIMATING THE DISPLAEEMENT AND VELOEITY FIELD APPROXIMATING THE DEFORMATION GRADIENT OTHER DEFORMATION MEASURES REPRESENTATION OF FOREES AND MOMENTS IN SHELLS EQUATIONS OF MOTION AND BOUNDARY CONDITIONS CONSTITUTIVE EQUATIONS RELATING FOREES TO DEFORMATION MEASURES IN ELASTIC SHELLS 10.5.10 STRAIN ENERGY AND KINETIE ENERGY OF AN ELASTIE SHELL 10.6 SIMPLIFIED VERSIONS OF GENERAL SHELL THEORY: FLAT PLATES AND MEMBRAN ES 10.6.1 FLAT PLATES WITH SMALL OUT-OF-PLANE DEFLEETIONS AND NEGLIGIBLE IN-PLANE LOADING 10.6.2 FLAT PLATES WITH SMALL OUT-OF-PLANE DEFLECTIONS AND SIGNIFIEANT IN-PLANE LOADING 10.6.3 FLAT PLATES WITH SMALLLN-PLANE AND LARGE TRANSVERSE DEFLEETIONS (VON KARMAN THEORY) 10.6.4 STRETCHED, FLAT MEMBRANE WITH SMALL OUT-OF-PLANE DEFLECTIONS 10.6.5 MEMBRANE EQUATIONS IN CYLINDRICAL-POLAR COORDINATES 10.7 SOLUTIONS TO SIMPLE PROBLEMS INVOLVING MEMBRAN ES, PLATES, AND SHELLS 10.7.1 THIN CIREULAR PLATE BENT BY PRESSURE APPLIED TO ONE FACE 10.7.2 VIBRATION MODES AND NATURAL FREQUENCIES FOR A CIRCULAR MEMBRANE 659 660 664 665 666 667 670 678 680 681 681 684 686 688 689 692 692 694 10.7.3 ESTIMATE FOR THE FUNDAMENTAL FREQUENCY OFVIBRATION OF A SIMPLY SUPPORTED RECTANGULAR FLAT PLATE 696 10.7.4 BENDING INDUCED BY INELASTIC STRAIN IN A THIN FILM ON A SUBSTRATE 697 10.7.5 BENDING OF A CIRCULAR PLATE CAUSED BY A THROUGH-THIEKNESS TEMPERATURE GRADIENT 700 CONTENTS * XXI 10.7.6 10.7.7 10.7.8 BUCKLING OF A CYLINDRICAL SHELL SUBJECTED TO AXIAL LOADING TORSION OF AN OPEN-WALLED CIRCULAR CYLINDER MEMBRANE SHELL THEORY ANALYSIS OF A SPHERICAL DOME UNDER GRAVITATIONAL LOADING 703 705 708 APPENDIX A: REVIEW OFVECTORS AND MATRICES 711 APPENDIX B: INTRODUCTION TO TENSORS AND THEIR PROPERTIES 729 APPENDIX C: INDEX NOTATION FOR VECTOR AND TENSOR OPERATIONS 741 APPENDIX 0: VECTORS AND TENSOR OPERATIONS IN POLAR COORDINATES 749 APPENDIX E: MISCELLANEOUS DERIVATIONS 765 REFERENCES 771 INDEX 775
any_adam_object	1
author	Bower, Allan F.
author_facet	Bower, Allan F.
author_role	aut
author_sort	Bower, Allan F.
author_variant	a f b af afb
building	Verbundindex
bvnumber	BV035989943
classification_rvk	UF 1500
classification_tum	MTA 010f PHY 210f
ctrlnum	(OCoLC)636299460 (DE-599)OBVAC07531822
dewey-full	620.105
dewey-hundreds	600 - Technology (Applied sciences)
dewey-ones	620 - Engineering and allied operations
dewey-raw	620.105
dewey-search	620.105
dewey-sort	3620.105
dewey-tens	620 - Engineering and allied operations
discipline	Physik
format	Book
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id	DE-604.BV035989943
illustrated	Illustrated
indexdate	2024-07-09T22:09:08Z
institution	BVB
isbn	9781439802472
language	English
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-018882673
oclc_num	636299460
open_access_boolean
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physical	XXV, 794 S. Ill., graph. Darst.
publishDate	2010
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publisher	CRC Press
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spelling	Bower, Allan F. Verfasser aut Applied mechanics of solids Allan F. Bower Boca Raton, Fla. [u.a.] CRC Press 2010 XXV, 794 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanics, Applied Solids Elasticity Strength of materials Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Festkörpermechanik (DE-588)4129367-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s DE-604 Festkörpermechanik (DE-588)4129367-8 s http://www.gbv.de/dms/weimar/toc/593899156_toc.pdf lizenzfrei Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018882673&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bower, Allan F. Applied mechanics of solids Mechanics, Applied Solids Elasticity Strength of materials Kontinuumsmechanik (DE-588)4032296-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd
subject_GND	(DE-588)4032296-8 (DE-588)4129367-8
title	Applied mechanics of solids
title_auth	Applied mechanics of solids
title_exact_search	Applied mechanics of solids
title_full	Applied mechanics of solids Allan F. Bower
title_fullStr	Applied mechanics of solids Allan F. Bower
title_full_unstemmed	Applied mechanics of solids Allan F. Bower
title_short	Applied mechanics of solids
title_sort	applied mechanics of solids
topic	Mechanics, Applied Solids Elasticity Strength of materials Kontinuumsmechanik (DE-588)4032296-8 gnd Festkörpermechanik (DE-588)4129367-8 gnd
topic_facet	Mechanics, Applied Solids Elasticity Strength of materials Kontinuumsmechanik Festkörpermechanik
url	http://www.gbv.de/dms/weimar/toc/593899156_toc.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018882673&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT bowerallanf appliedmechanicsofsolids

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