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Name Index

AAbramovitz, M., 175Alexander, J. M., 109Alexandrov, A. V., 180Almroth, B. O., 41, 42Aron, H., xxvi

BBach, C., 95Bailey, R. W., 243, 246Baker, E. H., 55, 141, 277, 308Barber J. R., xxiiBatdorf, S. B., 23, 180Bassett, A., xxviBauschinger, J., xxv, 60, 180Becker, R., 245Beltrami, E., 94Benarjee, P. K, xxviiiBelloni, G., 15, 141, 171Belluzzi, O., 4, 23, 41, 51, 55, 58, 73, 109Bernasconi, G., 15, 240Bernoulli, G., 73Bessel, F. W., 175, 176Bickell, M. B., 1, 73Biezeno, C. B., xxviiBland, D. R., 245Boley, B. A., 141Boltzmann, L., 243Bones, J. A., 73, 179Boresi, A. P., xxiBresse, M., 29, 33Brownell, L. E., 321Bruhn, E. F., 23, 41, 55Brush, D. O., 41Budiansky, B., 180Burr, A. H., 1, 73, 109, 141Butterfield, R., xxviiiByrne, R., xxvii

CCarnot, L. N. M., 28Cauchy, A. L., xxviCaboni, F., 73, 109Capurso, M., 179Carslaw, H. S., 141Chaboche, J. L., 245Chajes, A., 41Chen, F. Y., 8Chong, K. P., xxiCicala, P., xxviiCoates, W. M., 336, 337, 339Codazzi, D., 311Colladine, C. R., 180Como, M., 55Cook, R. D., xxviii, 141Crossland, B., 73, 179Coulomb, C. A., 9, 181Crockcroft, R. D. H., 247

DDanielson D. A., xxviiDawson, V. C. D., 222De Iorio, A., 245Den Hartog, J. P., 73Desai, C. S., 15Dieter, G. E., 185Donnell, L., 283Dorn, J. E., 242, 243Dowling, N. E., 180Drucker, D., 41Dubbel, H., 109

EEichinger, A., 184Euler, L., 43, 44, 46Evans, R. W., 245

V. Vullo, Circular Cylinders and Pressure Vessels, Springer Series in Solidand Structural Mechanics 3, DOI: 10.1007/978-3-319-00690-1,� Springer International Publishing Switzerland 2014

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FFaupel, J. H., 217Feinberg, S., xxviFeodosyev, V., 122Filonenko-Borodich, M., xxiiFinnie, I., 245Flügge, W., 281Forsyth, A. R., 282Fourier, J. B. J., 154François, D., 180Furbek, A. R., 219

GGadolin, 122Galerkin, B. G., xxviGalileo, G., 8, 9Galimov, K. Z., xxviiGarro, A., 157Garofalo, F., 244, 245, 247Gauss, K. F., 311Geckeler, J., xxi, xxii, 340Gere, J. M., 10, 23, 26, 29, 33, 41, 56Giacosa, D., 157Gibbs, C. W., 157Giovannozzi, R., 96, 109, 141Godono, G., 245Golovin, H., 26Goodier, J. N., xxi, xxii, 4, 180Gola, M. M., 343Gol’denweizer, A. V., xxviGormann, D. J., 179Gromov, V. A., 41Graham, A., 245, 247Grammel, R., xxviiGrashof, F., 26Green, A. E., 398Guest, J. J., 9, 181

HHaddad, Y. M., 180Hankel, H., 175Hartmann, L., 185Haupt, P., xxiHeller, W. R., 247Henckey, H., 9Henderson, J., 247Hill, R., xxii, 41Hodge, P. G., 224Hoff, N. J., 41Hoffmann, O., 180Hooke, R., xxvi, xxviii, 44

Hospital, G. F. A. de l’, v. L’Hôpital, G. F. A.de , 261, 264

Houghton, D. S., 275Huber, M. T., 182

IIurzolla, E., 1, 73, 96, 109, 141, 211Ivanov, A. B., 311

JJaeger, J. C., 141Jorgensen, S. M., 73, 211Johnson, A. E., 247Johnson, J. B., 46Johns, R. H., 325, 326Juvinall, R. C., 188

KKachanov, L. M., 247Kahn, B., 247Kalnins, A., 211Karman, T. von, 51Kennedy, A. J., 244, 245Kil’chevskii, N. A., xxviKirchhoff, G. R., xxvi, 283Kline, M., 311Kogaev, V. P., 248Koiter, W. T., xxviiKrauss, F., xxviKrauthammer, T., 281, 299Krempl, E., 245Krylov, A. N., 295

LLagrange, J. L., 133Lamé, G., 9Lang, H. A. , 324, 325, 327Larson, F.R., 245Lebedeyev, O. G., 41Liguori, A., 179Lin, Y. J., 141Lévy, M., 61L’Hospital, G. F. A. de, 259, 262Linné, C., von (Linnaeus)., 241Lo Conte, A., 141, 171Love, A. E. H., xxvi, 283Lubliner, J., 180Lüders, W., 185Lucretius, T., Carus., 254

370 Name Index

Ludwik, P., 260Lur’e, A. I., xxvii

MMainardi, G., 311Manna, F., 241Manson, S. S., 247Marin, J., 188, 191, 247Mariotte, E., 5, 17Marriott, D. L., 245Maruyama, K., 247Maxwell, J. C., 182McVetty, P. G., 247Megyesy, E. F., 307Meissner, E., xxvi, 340Melnikov, Yu. A., 298Meyer, R. R., 275Michell, J. H., 80Miller, A. K., 245Miller, J., 245Mises, R., von , 9, 182, 185Moaveni, S., xxviiiMoradi, M., 212Mohr, O., 8, 181Moss, D., 307Mushtari, Kh. M., xxvii, 283

NNadai, A., 185Naghdi, P. M., xxviiNavier, C. L. M. H., 73Nordgren, R. P., xxviiNorton, F. H., 244Novozhilov, V. V., xxvi, 22, 283

OObodan, N. I., 41Ohji, K., 247Oikawa, H., 247Orange, T. W., 325, 327Orowan, E., 247Osgood, W. R., 64, 67Ostenfeld, A., 46Ovidius, P., Naso., 5

PPao, Y. H., 247Pearson, K., 26Perzyna, P., 245

Penny, R. K., 245Peterson, K. M., 311Peterson, R. E., xxi, 320Petrov, V. V., xxviiiPiercey, B. J., 247Pineau, A., 180Piobert, G., 185Poisson, S. D., xxviPotapov, V. D., 180Popov, E. P., 248Prager, W., 224Prandtl, L., 248Prosciutto, A., 73, 109

RRabotnov, Y. N., xxvii, 247Ramberg, W., 64, 260Rankine, W. J. M., 9, 35, 182Reddy, J. N., xxviiiRehfield, L. W., 41Reissner, H., xxviReissner, E., 340Résal, H., 26Reuss, A., 248Reyto, 188Roš, M., 184Ruiz, C., 1, 73Rutten, H. S., xxviii

SSaada, A. S., 73Sachs, G., 180Saint-Venant, Barré de, A. J. C., 4, 155, 163,

182, 200Salvini, P., 51Sanders, J. L. , xxviiSeigel, A. E., 224Serensen, S. V. , 248Shield, R., 41Shneiderovich, R. M., 248Sidebottom, O. M., 180Simmond, J. G., xxviiSim, R. G., 245Sirilwardane, H. J., 15Skrzypek, J. J., 245Smirnov, V., 176Smith, J. O., 180Soare, M., xxviiiSokolnikoff, I. S., xxiSouthwell, R. V., 38Steele, M. C., 267

Name Index 371

Stegun, I. H., 176Stewart, R. T., 33Steigelmann, W. H., 141, 154Swift, H. W., 260

TTabakman, H. D., 141Taira, S., 247Tanaka, C., 247Tanaka, K., 247Taylor, B., 145Tetmajer, L., 47Timoshenko, S. P., 29, 172, 299Tresca, H., 9, 181, 183Tricomi, F. G., 282Tsien, H.S., 51

VVentsel, E., 281, 299Vivio, F., 128, 210, 260Vlasov, V. Z., xxvii, 283Vullo, V., 128, 210, 260, 343

WWalles, K. F. A., 245, 247

Wan, C. C., 35Wang, G., 212Watts, G. W., 324, 325Weber, H., 175, 176Webster, G. A., 247Weiner, J. H., 141Westergard, H. M., 180Wilshire, B., 247Winkler, E., 26, 313Woinowsky-Krieger, S., 172, 281

YYen, T. C., 141, 154Young, E. H., 325Young, T., 267Young, W. C., 141

ZZaoui, A., 180Zaslavsky, A., 4Zerna, W., 298Zhao, J., 212Zienkiewitcz, D. C., xxviiiZudans, Z., 141, 154

372 Name Index

Subject Index

AAbsolute maximum value, 83, 84, 87, 89Absolute value, 7, 24, 48, 82, 84, 85, 105, 120,

156, 158, 159, 167, 170, 183, 287, 293,286, 333, 343, 347, 350

Absolutely rigid built-in edge(s), 287, 288Absolutely rigid ring(s), 300Accordion-like waves, 42Accumulated creep strain, 244Activation energy, 243Actual length, 43, 51Additional bending moment(s), 309Additional radial displacement(s), 36Aeronautical and aerospace structures, 275Aeronautical, ship building, and submarine

industries, 275Aircraft fuselages, 51Allowable load, 48Allowable stress, 10, 32, 33, 48, 100Alloyed steel, 216Ambient temperature, 110, 189Analytical model(s), xxiAnalytical solution(s), xAngular acceleration, 115Angular coordinate, 20, 25, 55, 57, 74, 277,

281, 337Angular velocity, 127, 128, 210Annealing effect(s), 115Annular beam, 25, 27, 29, 31, 36, 39Approximate bending theory, xiiApproximate method(s), 45Aprioristic approach, 27ASME, 334Assembly temperature, 156Associated homogeneous equation, 29, 143,

280, 281, 295, 336Asymptotic approach, xxviiAsymptotic value(s), 39, 197

Autofrettage, 199, 200, 203, 204, 206,210–212, 215, 215–217, 221, 223, 236,228, 232–235

Autofrettage in a container, 200Autofrettage in closed-end conditions, 200Autofrettage pressure, 211–213, 217, 220–223,

225, 226, 234, 239Autofrettage pressure threshold, 221Autofrettage process, 199, 206, 211, 212, 215,

216, 222, 234, 252Autofrettage stress(es), xxvAutofrettage with a mobile seal equipment, 214Average shear stress, 345Axial compliance, 290Axial constraint(s), 156Axial coordinate, 3, 20, 55, 57, 172, 177, 282,

283, 293, 294, 302–304Axial dimension, 1, 74, 141, 142Axial direction, 6, 51, 71, 146, 166, 181, 278,

290Axial displacement, 11, 42, 152, 163, 164,

146, 164, 166, 288, 289Axial instability load, 68Axial membrane force(s), 278, 325Axial plane, 4, 44, 277–279, 281, 290, 301,

311, 313, 342Axial strain, 33, 60, 146, 163, 278Axial stress, 6–8, 15, 61–63, 66, 68, 71, 73, 80,

81, 83, 98, 151, 158, 161–163, 167, 172,198, 222, 290, 300, 314, 316, 317, 320,321, 327, 328

Axial stress resultant, 278, 324Axial symmetry, 21Axis of revolution, 20Axis of symmetry, 3, 31, 311Axis-symmetrically deformed shape, 25Axisymmetrical orthotropic material, 281Axisymmetric load(s), 294

V. Vullo, Circular Cylinders and Pressure Vessels, Springer Series in Solidand Structural Mechanics 3, DOI: 10.1007/978-3-319-00690-1,� Springer International Publishing Switzerland 2014

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BBach’s theory, 96Bailey-Popov relation, 246Bathyscaphes, 23Bauschinger effect, 60, 180, 213, 220, 222Beam on elastic foundation, 342Bellows joints, 11Beltrami’s theory, 96Bending contribution, 314Bending effect(s), 158, 334Bending load(s), 41, 275, 342Bending moment(s), 3, 31, 37, 60, 172, 210,

277–279, 282, 288, 290, 294, 295,296–298, 301, 302, 308, 309, 311–313,316–318, 320, 326–328, 331, 338, 342,345, 346

Bending problem(s), 341Bending stiffness, 23Bending theory, 172, 308, 309, 325, 326, 335,

336, 343Bending theory of circular cylindrical shells,

279Bending theory of shells, 337Bernoulli-Navier hypothesis, 73Bessel differential equation, 175Bessel function(s), 175, 176Beyond yielding, 179, 192Biaxial stress state, 11, 68, 70, 96, 182, 187,

189, 191, 192, 278, 315Bi-logarithmic coordinates, 64Blind hole method, 217Body force(s), 80, 115Boilers, 5, 17, 275Boltzmann’s constant, 243Boring-out method, 217Boundary condition(s), 1, 21, 22, 29, 31, 55,

57, 80, 132Boundary element method(BEM), xxviiiBresse’s formula, 33Brittle fracture, 185, 190, 191Brittle material(s), 189, 199Brittleness, 115Buckled shape, 25Buckling, 3, 24, 31, 43, 44, 49–51, 56, 59, 156,

190, 302Buckling deflection shape(s), 32Buckling mode, 50Buckling of circular cylinder(s), 51, 56, 58Buckling of circular ring(s), 3Buckling of cylindrical shell(s), 3Buckling of tube(s), 3Built-in edge(s), 38, 287–289, 301Burst(ing) pressure, 41, 66, 214, 232Bursting strength, 215

CCalculation example, 316, 320Carnot’s theorem, 28Cartesian reference system, 25, 276Causes of failures, 41Center of gravity, 25Centerline of the ring, 25Central angle, 36Central half-angle, 328Centrifugal direction, 153Centrifugal force, 126, 127Centrifugal heat flow, 157–159, 166, 167,

170–173Centrifugal load, 115, 126, 128Centripetal direction, 59, 112, 282Centripetal heat flow, 157, 158, 159, 166, 168,

171, 172Centroid, 27, 41Change in angle, 26Change in volume, 184Change(s) in curvature(s), 278, 279Characteristic parameter(s), 111, 172Chemical and nuclear industries, 115, 275Chemical composition, 235Circular axis, 24Circular centerline, 24, 27, 29Circular cylinder of finite length, 149, 163,

164, 171Circular cylindrical liner(s), 153Circular cylindrical shell(s), 32, 51, 53–60,

275–277, 280–283, 287–289, 293, 295,297, 298, 300–305, 308

Circular plate, 84, 171, 312Circular sector, 328, 330Circumferential angle, 19Circumferential bending moment(s), 277, 305,

340, 341Circumferential direction, 56, 63, 158Circumferential normal in-plane forces, 19Circumferential seam(s), 349Circumferential stiffeners, 38, 39, 275Clamped edge(s), 158, 287, 289, 290Clamped end(s), 11, 32, 142, 151, 155, 159,

174, 193, 195, 196Classical plasticity theory, 245Classical plate theory, 311Classical theory of the plates, xxviCleavage, 185Clockwise rotation(s), 310Closed section, 56Close end(s), 7, 17, 62, 66, 68, 80, 81, 83,

89–91, 93, 94, 97, 182, 205, 206Closure absolutely rigid, 313Closure deformable, 314, 317

374 Subject Index

Closure(s), 4, 23, 24, 38, 275, 278, 288, 290,307, 308, 310, 314–320, 323, 324

Coates’ theory, 158Coaxial cylinders, 116Codazzi-Mainardi-Peterson (conditions of),

311Coefficient of linear thermal expansion, 110Coefficient of the friction, 130Coefficient of thermal conductivity, 153, 154Coefficient of thermal expansion, 73, 141Cohesive bond(s), 185Colatitude angle, 19, 337, 341Cold-formed, 51Collapse pressure, 35, 38Collapsing strength, 23Combined expression, 242Combined load, 63Combined theories, 245Commutative relation, 242Comparison between the four yield theories,

256Compatibility equation(s), 1, 73, 76, 77, 142,

146, 202, 350Compatibility of deflections, 275Compatibility of displacements and rotations,

275, 308, 310, 315, 318, 321Complementary solution, 281–283, 295Complex integration constants, 281Compliance analysis, xxComposite concentric cylinders, 109Composite light, xxviiComposite material(s), 109Composite multilayer structure(s), 237Composite structure(s), 109, 112, 115, 116,

121, 122, 125, 126, 265, 271Composite two-component structure, 94, 95Compression stress(es), 7, 79, 166, 191Compression test, 34, 180, 186, 187Compressive strain history, xxvCompressive yielding, 213Compressive yield point, 215, 223, 225Compressive yield stress, 216, 219, 220Concentrated bending moments and forces, 280Concentrated line load, 290, 291Conceptual design, xxiConcertina buckling, 42, 51Concertina mode, 3, 42, 51Condition of plastic flow, 67Condition(s) of compatibility, 310Cone(s), 307Connecting rod, 44Connecting rod-crank mechanism, 44Conservative strength theory, 101, 108, 271Constant stress test, 240

Constant temperature and load, 240, 241Constant volume, 246Constant-volume strain condition, 70Constitutive equations, 32, 89Constitutive law(s), 142, 147, 239, 246, 247,

252, 258Constitutive stress-strain law(s), 76Constrained end(s), 38, 146, 152, 166Constraint condition(s), 44, 81, 133, 148, 277Constraint equation(s), 133, 134Constraint reaction(s), 275, 287, 288Constructive solution(s), 324Contact pressure, 110, 115, 120, 138, 139Contact thermal resistance(s), 115Continuous elastic Winkler foundation, 281Continuous support(s), 281Continuum mechanics, 184Control rods, xixConventional limit for thin-walled cylinders, 3Conventional strains, 67, 181Conventional upper limit, 3Core, 223, 225, 228, 229Corrugations, 51Coulomb yield theory (criterion), 181Coulomb-Tresca-Guest yield theory, 182Counterclockwise rotation(s), 310Cover plate(s), 307Crashworthiness strength, 51Creep, 190, 240–243, 247, 251Creep behavior, 240–242Creep rate, 241Creep strain(s), 240, 242–245Creep test(s), 240, 241Creep theory(ies), 241, 243Critical bending moment, 59Critical buckling load, 43Critical condition(s), 63Critical diameter ratio, 220, 221Critical length, 24, 38Critical limit, 185Critical load, 43, 44, 48, 50, 53, 55Critical pressure, 23, 24, 29, 32, 33, 39, 102,

135, 221Critical stress, 3, 32–35, 44–48, 52, 302Critical torque, 57Critical twisting moment, 57Critical unit load, 52, 53, 56Cross-sectional height, 26Cross-sectional ovalization, 3Cross-section area, 27, 41, 44, 48, 50, 58, 305Cross-section ellipticity, 3Cross-section ovalization, 3Cross-section plane, 4, 5Cubical dilatation, 248

Subject Index 375

Cubic hyperbola(s), 17, 78, 81, 83, 86Cusps, 239, 252Curvature(s), 19, 25–27, 279, 308, 311, 332,

336, 340, 341Curved beam, 24Curved pipe fitting, 4Curvilinear coordinate(s), 337–339, 346Curvilinear segment(s), 347Cusped curves, 265Cyclic re-pressurizing, xiCylindrical hinge, 44Cylindrical membrane shell, 1Cylindrical rod(s), 174, 176, 177

Dde L’Hospital’s theorem, 259, 262Decay distance, xiiDeflected centerline, 25Deflected shapes, 31Deflected surface, 310, 311, 313, 318Deflection curve, 25, 27, 29, 31, 32, 36, 44, 51,

53, 54, 287, 292, 297, 342Deflection mode, 51, 56Deflection(s), 23, 30, 33, 38, 42, 44, 49, 172,

190, 275, 280, 281, 294, 296–298, 300,326, 327

Deformable stiffening ring(s), 301Deformation(s), 1, 10, 15, 16, 25, 55, 56, 59,

60, 73, 76, 142, 180, 192, 206, 241, 242,246, 248, 277, 279, 290, 294, 309, 334

Deformed elastic line, 24, 25Degree of safety, 13Density, 127Design, 4, 5, 10, 11, 13, 15, 18, 22, 31, 35, 41,

46, 48, 49, 59, 65, 94, 98, 118, 119, 124,125, 128, 129, 153, 154, 159, 188–192,232, 233, 235, 238, 240, 241, 321, 324, 335

Design analysis, 2, 8, 10, 33, 41, 95, 96, 98,106, 242, 328, 349

Design analysis relation(s), 98, 106, 134Design axial load, 49Design considerations, 48, 92, 209Design function(s), 240Design objectives, 109Design optimization, 127Design purpose(s), 38, 170, 239, 240Design resistance, 49Developable surface(s), 276, 307Deviator invariant(s), 184, 185Diameter plane, 4Diameter ratio, 2, 157, 170, 193, 194, 198,

206, 208, 210–212, 216, 220–222, 225,226, 232–236, 256, 257, 264, 271

Diameter’s expansion, 15, 16Diametral interference, 111, 113, 129Differential element, 278, 279, 337, 338Differential equation, 25, 27, 29, 36, 51, 53, 78,

155, 248, 249, 252, 260, 280–282, 336, 338Differential operator, 64, 247Dimensionless external load, 264Dimensionless principal stress(es), 251Dimensionless ratio, 11, 13, 43, 81, 94, 100,

102, 194, 197, 209, 225, 273Dimensionless temperature, 157, 158, 171Dimensional tolerance(s), 115Directrix circumference, 277, 300Directrix(ices), 276, 277Discontinuity area(s), 275Discontinuity in shape, 308Discontinuity load(s), 275, 311, 318, 342, 343,

349, 350Discontinuity stresses, 308, 309, 325, 335Discontinuity stress resultants, 308, 309Discontinuity(ies), 314, 317, 325, 326, 335,

344–346Discontinuity(ies) in the stress gradient, 239Dished end(s), xiiDished head(s), 308, 332, 335, 336, 348Disk-shaped member(s), 127Dislocation(s), 185Displacement compatibility condition, 75Displacement field, 78, 91, 93, 143, 283, 285,

288, 291, 293, 308, 327Displacement(s), 1, 18, 21, 26, 28, 29, 36, 37,

42, 55, 57, 74, 76–78, 90–93, 111, 112,127, 128, 141, 142, 145, 147, 148, 164,166, 275, 277, 278, 283, 288, 294, 297,303, 309–311, 318, 319, 326, 329, 340, 350

Dissimilar material(s), 115Distillation columns, 275Distortion, 10, 96, 101, 103, 108, 116, 123,

125, 135, 137, 148, 156, 167, 181, 182,184–186, 188–193, 198, 201, 208–212,214, 220, 221, 226, 237, 238, 245, 255,257, 264, 265, 268–272, 274

Donnell-Mushtari-Vlasov theory, 283Dorn’s exponential function, 242Dorn’s observation, 243Double curvature surface(s), 337Double-walled composite structure, 120, 235,

236Double-walled structure, 113, 119, 124, 134Double-walled vessel(s), 299, 302Drill pipes, xixDuctile fracture, 185, 191Ductile material(s), 117, 198, 199Ductility, 62, 189

376 Subject Index

EEccentricity, 31, 317Eccentric load, 317Eccentric meridian forces, 309Edge bending moment, 172Edge condition(s), 308Edge effect differential equation, 336Edge effect(s), 172, 288, 290, 310, 314, 327,

330, 342, 344–346, 348, 351Edge(s), 41, 53, 163, 172–174, 282, 283, 285,

287, 288, 310–312, 314, 315, 318, 325,336, 342

Effective area, 27, 41, 44, 48, 50, 65, 203, 207,209, 307

Effective strain(s), 61Effective stress(es), 61, 239Elastic breakdown pressure, 192, 194, 195,

223, 237, 238Elastic imperfections of the material, 85Elastic instability response analysis, 32Elastic limit, 3, 32, 49, 68, 85, 116, 120, 125,

179, 180, 189, 202, 209, 239, 258Elastic limit stress, 74Elastic magnitude(s), 77, 80, 91, 93, 112, 258Elastic potential energy, 42Elastic recovery, 217Elastic region, 181, 204–206, 214, 218, 227,

254, 262Elastic strain(s), 61, 181, 240Elastic strength property(ies), 233Elastic-plastic boundary, 94, 264Elasto-plastic and plastic field, 45Elasto-plastic behavior, 240Elasto-plastic or plastic instability, 45Elasto-plastic state, 264Elbow pipe fitting, 4Elemental strip-beam, 281Elementary arc, 58, 339Elementary force(s), 74Elementary longitudinal strip, 51, 52Elementary radial force, 75Elementary slice of shell, 338Elementary tangential force, 75Ellipse of plasticity, 182, 186, 188Ellipse’s flattening factor(s), 331Ellipsoid(s), 311Elongation at failure, 62Empirical formulas, 45–47End closure(s), 288, 324, 331End constraint(s), 59, 156, 289, 312End face(s), 282, 288, 289, 297End(s), 4, 6, 7, 10, 17, 23, 31, 38, 43, 51, 54,

55, 59, 60, 62, 66, 68, 76, 81, 89–91, 94,98, 111, 146–149, 152, 153, 156, 158, 163,

164, 166, 167, 171, 199, 206, 222, 290,293, 295, 296–298, 307, 309

Energy losses per unit volume, 180, 258Energy method, 51Energy sinks, 153Energy sources, 153Energy theories, 96, 101, 125, 257, 270, 271Engineering strains, 142, 181Envelope, 186Equations of thermo-elasticity, 141Equatorial radius, 325, 334Equilibrium condition(s), 4, 17, 80, 147, 162,

171, 185, 277Equilibrium equation(s), 1, 73–75, 77, 79,

141–143, 146, 148, 202, 223, 229, 247,249, 252, 261, 277, 279, 339

Equilibrium method, 51Equivalent column length, 43–45, 50Equivalent combined stress-strain curve, 65Equivalent plastic strain, 61Equivalent quantity(ies), 245Equivalent residual stress, 213, 216, 219, 220,

223, 230Equivalent strain, 246, 247, 258Equivalent strain increment, 245Equivalent stress, 2, 8, 10, 11, 13, 16, 18, 24,

61, 65–67, 69, 85, 96–98, 102, 105, 106,116, 122, 132, 133, 179, 185, 192, 208,209, 220, 226, 227, 237, 245–248, 251,258, 265, 267, 268, 272, 273

Equivalent uniaxial problem, 245Euler buckling, 42, 51, 56Euler critical load, 43Euler instability, 11, 41, 42Euler’s critical buckling load, 43Euler’s cubic hyperbola, 45–47Euler’s formula, 43Euler’s relations, 44, 281, 295Euler’s stress, 47Evaporators, 23Even function, 296Expansion loops, 11Expansions of the variable(s), xxviiExpected service life, 240Experimental data, 182, 186, 188, 190–192,

240, 242–244, 265, 337Experimental evidence(s), 189, 191, 239, 244Experimental procedure(s), 309Experimental result(s), 117, 182, 188, 191,

192, 198Exponentially amplified trigonometric func-

tion(s), 283Exponentially damped trigonometric func-

tion(s), 283, 285, 346

Subject Index 377

Extension of the radius, 308External load per unit of length, 27External pressure, 1, 3–5, 7, 8, 10, 11, 13, 14,

16, 23, 29, 31–33, 35–38, 73, 82, 85, 87,88, 90–93, 95, 97, 98, 105, 106, 108, 111,113, 115, 138, 181, 183, 184, 192–196,197, 199, 210, 237, 238, 246, 249, 250,262, 265, 268, 275, 299, 302

Extinction length, xii

FFailure mechanics, 185Failure strength, 179Failure stress, 65Final temperature, 109Finite Difference Method (FDM), xxviiiFinite Element Method (FEM), xxviiiFirst invariant of the strain tensor, 90, 92, 148First invariant of the stress tensor, 148First loading beyond yielding, 202First-order approximation shell theory, xxviiFirst order differential equation, 75, 77, 202,

312First quadratic form of a surface, 311First stage creep, 243Fixed seal(s), 200Flange(s), xxFlanged connection(s), 179Flat end(s), xiiFlat-plate closure(s), 275, 309–311, 313, 321,

323Flattened semielliptical head, 333Flexural ovalization buckling, 58, 59Flexural rigidity, 23, 36, 58, 172, 297Flow rule(s), 61, 246Flow surface, 153Force-fit assembly, xiForce-fit pressure, 87Force fit(s), 109Formed closure(s), 307, 308Formed head(s), 23, 38, 275, 307–309Forth order differential equation, 51, 53, 342Foundation modulus, 338Fourier’s equation, 153, 154Fourier’s law, 153, 155, 159, 166, 174Fracture strength, 65, 191Free and unloaded ends, 10, 147Free closed ends, 10, 11, 13, 193, 195,

209–211, 217, 218, 220, 221, 223, 246,248, 249, 252, 257, 265, 277, 301, 302

Free end(s), 6, 63, 128, 142, 161, 163, 164,166, 167, 171, 172, 174

Free length, 43

Free open ends, 62, 193–196, 209, 218,220–222, 225, 300

Friction coefficient in torsion, 129Full autofrettage, 216, 219, 233Full overstrain, 216, 218Full plastic state, 248Full yield, 198, 247Fully plastic state, 179, 198, 204, 205,

207–210, 212, 214, 219, 220, 222, 226,239, 252, 254, 273

Fully yield, 222, 223Functions ;1; ;2; ;3 and ;4, 290Funicular curve, 31, 36Fuselage shell structures, 299

GGadolin’s conditions, 122Gage length, 62Garofalo’s hyperbolic sine function, 244Gauss (condition of), 311Gaussian curvature, 307General formulation, 344Generalized axisymmetry, 3, 4, 80, 142Generalized Hooke’s laws, 247Generalized Hooke’s relations, 15Generalized plane strain state, 4, 179General solution, 29, 281, 282, 295General theory of shells, 329General yielding, 198Generating meridian curve, 336, 338Generator(s), 7, 16, 21, 51, 53, 59, 276, 277,

279, 284, 286, 287, 298, 301–303, 308,310, 325, 335, 339, 349

Geometric assumption, 283Geometrical axisymmetry, 1Geometrical cylindrical axisymmetry, xixGeometrical discontinuity(ies), xxGeometrical non-linearity, 27Geometrical pitch, 57Geometric parameter, 280Global instability, xiGoverning differential equation, 280, 295, 336Grain boundary(ies), 185Green’s functions, 294Gross cross-sectional area, 50Guest yield theory (criterion), 181

HHalf-wavelength, 285, 286Hamburg formula, 2, 12, 101–103, 198Hand holes, 307Hankel function(s), 175

378 Subject Index

Hardness, 115Hartmann’s lines, 185Head(s), 4, 6, 307, 308, 324–326, 328–331,

334, 336, 339, 345Heat conduction, 141Heat exchanger tubes, 23, 153Heat exchanger(s), 275Heat flow, 81, 115, 141, 153, 154, 156, 166,

167, 171, 174, 177Heat transfer, 141Heat treatment(s), 94, 115, 118, 126, 192, 216,

217Hemisphere(s), 311, 313, 328, 343Hemispherical dished head(s), 324, 331, 335Hemispherical meridian curve, 324Hencky yield theory (criterion), 182Hexagon of plasticity, 184, 188Higher-order approximation shell theory, xxviiHigher-order buckling deflection curves, 31Higher-order infinitesimal(s), 75, 174High performance structure(s), 212High strength-to-weight ratio, 109Hinge(s), 44, 312, 314History of deformation, 240Hole(s), 85, 94, 179, 190Homogeneous and isotropic material(s), 76,

109, 110, 142, 145, 148, 309Homogeneous equation, 281–283, 338, 339Homogeneous material(s), 153, 190Homogeneous second order differential equa-

tion, 28, 77Hooke’s law(s), 44, 152, 259, 278, 315Hooke’s relations, 78Hoop membrane force, 325Hoop normal stress, xxiiHoop strain, 60–62, 278Hoop stress, 4, 5, 7, 8, 15, 17, 18, 24, 61–63,

66, 68, 71, 73, 82–85, 87, 88, 105, 116,117, 122, 156, 158, 159, 167, 173, 182,183, 185, 202, 204, 205, 212, 213, 222,225, 227, 251, 261, 287, 297, 300, 304,305, 316, 320, 328, 330, 332–335, 348, 349

Hoop stress ratio, 88, 89Hoop stress resultant, 304, 305, 325, 327Hooping sleeve, 223–225Horizontal asymptote, 81, 83, 86, 101, 270Huber yield theory (criterion), 182Hull(s), 23, 275, 302Hydraulic and pneumatic cylinders, 4Hydroelectric powerplants, 275, 299Hydrostatic head, 4Hydrostatic stress state, 184, 185

Hyperstatic unknown(s), 111, 113, 287, 289,291, 303, 310, 313, 315, 316, 318–320,322, 327, 342–344, 350, 351

Hypervelocity launchers, 212Hysteresis cycle, 180, 258

IIdeal stress, 2, 185Idealized clamped edge(s), 288, 290Idealized constraint(s), 287Immaterial surface, 85Impact absorbers, 51Imperfection factor, 50Incompressibility condition, 60Incompressible material, 246Incremental plastic flow theory, 246Indefinitely large wall-thickness, 84, 85Inertia force(s), 141Inextensional condition, 30Infinitesimal angle, 75Infinitesimal elementary portion, 75Inflection point(s), 43, 44Influence functions, 294Initial condition(s), 60, 67, 175Initial curvature, 25, 27, 36Initial deformation, 61, 62Initial dimension(s), 61, 62Initial ductile yielding, 190Initial ellipticity, 35, 36Initial geometrical imperfections, 35Initial out-of-roundness, 35Initial temperature, 109, 110Initial yielding, 198, 199, 201, 212, 221, 222,

226, 233–235Innermost cylinder (or liner), 130Innermost fiber(s), 82, 192, 193, 195, 201Inner plastic region, 211Inner radius, 2, 5, 7, 17, 21, 74, 81–85, 87–90,

92, 94, 98, 103, 106, 111, 116, 125, 126,131, 133, 135, 152–154, 156–158, 166,167, 169–172, 174, 179, 183, 189,192–198, 201, 202, 206, 208, 211, 213,215–221, 223, 229, 238, 267, 268, 273

In-plane circumferential force(s), 277In-plane displacement(s), 279In-plane meridian stress resultant(s), 278, 338In-plane resultant forces, 19In-plane stress resultants, 277, 324Inside diameter, 2, 5, 6, 10, 15, 60, 68Instability, 3, 13, 32, 35, 38, 41, 42, 45, 46, 48,

50, 51, 54–56, 60, 6971

Subject Index 379

Instability condition, 64, 66, 69, 70Instability of columns, 3Instability pressure, 63Instantaneous plastic strain, 245Instantaneous value(s), 60, 62Integration constant(s), 22, 29, 31, 78, 79, 81,

90, 96, 98, 105, 143, 150, 154, 163, 202,249, 253, 260, 282, 283, 292, 295, 312,315, 339, 340, 342

Interaction between structural components,275

Interface, 110, 111, 115, 116, 127–129, 138,198, 217, 218, 223, 224, 229–231, 239,252, 267, 290, 302–304, 325, 330, 349

Interface circumference(s), 326Interface pressure, 117, 132Interface radius, 118Interference fit, 109, 110, 116, 120, 121, 212Interference shrink-fit(s), 126Internal force(s), 141, 277Internal friction yield theory, 188, 191, 199Internal pressure, 2–5, 7, 10, 11, 13, 16–19, 41,

60, 63, 66–68, 71, 82, 85, 87, 90–95, 98,100, 101, 105, 106, 108, 111, 113,119–126, 134, 135, 137, 138, 179,182–184, 189, 193, 195–202, 204–207,210–212, 214, 215, 217, 218, 223, 226,228–232, 235, 238, 246, 250, 252, 254,267, 275–277, 284, 287–289, 295, 297,299, 300, 302–305, 308, 310–314, 318,324, 328, 330, 331, 339, 342, 344, 346–351

Irregularity(ies), xx, xxiIsochronous stress-strain curve(s), 241Isothermal conditions, 244, 245Isotropic material(s), 153

JJacket, 23Jacketed vessels, 23Johnson’s formula, 47Junction interface, 327, 335Junction plane(s), 309–311, 313–315,

317–321, 323–326, 331, 334, 336, 338,343, 346–349

KKind(s) of instability, 41Kinematic relations, 278Kinematics of deformation, xxviiKirchhoff-Love assumptions, xxviiKirchhoff’s plate theory(s), 309, 311, 321Krylov’s functions, 295

LLagrange multipliers, 133Lagrange’s method, 133Lagrangian strains, xxiiiLamé-Rankine yield theory, 9, 182Lamé’s constant, 148Lamé’s equations, 78, 262Lamé’s relations, 253, 315Large deformations assumption, 181Large strains assumption, xxiiiLateral contraction, xxiiiLatitude angle, 337, 341Law(s) of heat transfer, 141Limit analysis design, xixLimit-design factor, 209, 210Limiting autofrettage pressure, 221, 222Limiting curve, 186, 192, 199, 222Limiting design condition, 221Limiting diameter ratio, 220, 221Limit of proportionality, 32, 33, 44, 45, 47, 49,

51, 53, 54, 57, 68, 116, 125, 180, 209, 239,259, 260, 265

Limit(s), 2, 13, 33, 34, 42, 45, 47, 49, 62, 63,68, 81, 83, 84, 88, 93, 101, 123, 157, 159,170, 174, 186, 197, 213, 240, 242–244,255, 257, 264, 266, 266, 272, 273, 298,308, 313, 321, 334, 343, 348

Linear elastic field, 1, 3, 19, 76, 80, 97, 119,142, 145, 146, 152

Linear elastic range, 141, 147, 208, 233, 275,278, 309, 344

Linear elastic stress state, xxLinear elastic-perfectly plastic behavior, 32,

180, 214, 252, 257, 258Linear formulas, 46, 47Linear velocity, 127Liner (or innermost cylinder), 157Linnaeus’ dictum, 239Loaded edge, 283, 286Load history, 258Loading and unloading process, 258Loading operation, 258Loading process, 258Load ratio(s), 82, 88, 89, 257Local bending, 283, 326, 328Local instability, 3, 42, 45, 51, 54, 55, 65Localized areas, 275Localized bending moment(s), 171–174, 275,

287, 325Localized shearing force(s), 288Local strain, 4Local stress, 4, 171Local stress resultant(s), 294, 304, 308, 309,

330, 331, 348, 349, 351

380 Subject Index

Logarithmic strain(s), xxLog-log coordinates, 64Long circular cylinder(s), 33, 38, 142, 149,

153, 156Long circular cylindrical shell(s), 282, 285,

286, 290, 291, 293, 295, 298, 299Long circular pipe, 282Long cylindrical shell(s), 294, 336Longitudinal direction, 38Longitudinal equilibrium, 247Longitudinal plane, 58Longitudinal stress, 4, 7, 17, 23, 97, 156, 164,

166, 218, 225, 248, 261, 287, 304, 305Long thin-walled circular cylinder(s), 283Long tube(s), 299Loosening, 128, 130Lucretius’ dictum, 254Lüders’ bands, 185Lüders’ lines, 185Ludwik’s law, 260

MMachining process(es), 115, 121Macrostructure, 185Main deflection, 31Main deformation, 58Major semi-axis, 331, 333, 334, 337Manholes, 56, 307Manufacturing drawings, 129Mariotte’s formulas, 5, 17Material constant(s), 242, 243, 245Material’s actual behavior, xxv, 241, 305Material’s elastic properties, 3, 281Material’s mechanical properties, xxi, xxii, 3,

277Material’s microstructure, 243Material’s stress-strain curve, 179, 180, 201,

260, 261Maximum bending moment, 37, 293Maximum deflection, 292Maximum distortion energy equivalence the-

ory, 2, 65–69, 101, 117, 121, 132, 135, 206,249

Maximum distortion energy strength theory, 2,65, 67, 68, 100, 117, 135

Maximum distortion energy yield theory, 181,182, 184, 191, 193, 210, 216, 228

Maximum internal pressure, 123Maximum modified strain energy theory, 96Maximum normal strain strength theory, 2, 10Maximum normal strain yield theory, 182, 186Maximum normal stress strength theory, 2

Maximum normal stress yield theory, 181,182, 186

Maximum octahedral shear stress yield theory,184, 185, 189, 191

Maximum performance, 116, 320Maximum principal stress, 67, 68, 70, 182Maximum shear stress equivalent theory, 245Maximum shear stress strength theory, 120,

135, 249Maximum shear stress yield theory, 181, 182,

184, 202, 210, 211Maximum shearing force, 293Maximum strain energy theory, 101Maximum stress, 8, 82, 84, 105, 314, 317, 320,

321, 328, 333, 349Maximum theoretical residual stress(es), 216,

219Maximum thickness, 101, 103, 271Maxwell yield theory (criterion), 9, 182Maxwell-Huber-von Mises-Hencky yield the-

ory, 182Mean circumference, 15, 16, 308Mean curvature, 307Mean generator(s), 326Mean meridian curve, 326Membrane circumferential force(s), 281, 312Membrane contribution, 304, 314Membrane of revolution, 19Membrane shearing force(s), 277Membrane stress(es), 158, 277, 284, 308, 314,

328, 330, 332, 344, 346Membrane stress state, 21Membrane theory, 21, 275, 308, 309, 324, 325,

331, 334, 343, 347Membrane theory of shell(s), 19, 21Membrane theory’s limits, 325Meridian angle, 19Meridian curve, 20, 328–330, 337–339, 347Meridian plane, 19, 20, 326, 335, 337, 338,

340, 341Meridian stress resultant, 324Method of successive approximations, xxviiiMethod of successive loadings, xxviiiMethod of superposition, 120, 138, 144, 150,

152, 223, 229, 278, 327, 344Method of variation of arbitrary constants, 286Method of variation of parameters, 282Michell’s theorem, 80Microstructure, 185Middle cross-section, 296, 297Middle diameter, 24Middle fiber, 24–26, 345Middle generator(s), 42

Subject Index 381

Middle meridian curve, 325Middle plane(s), 288, 300, 302, 310–312, 315,

317, 318, 320, 323, 324Middle surface, 51, 276, 278, 279, 299, 302,

307–309, 314, 318, 324, 331, 337–339,341, 348

Minimum creep rate, 243Minimum elastic potential energy configura-

tion, 334Minimum principal stress, 195Minimum total energy principle, 59Minimum weight, xxMinor semi-axis, 331, 334Mises yield theory (criterion), 181Missiles, 243, 279Mobile mandrel, 199Mobile piston(s), 4Mobile seal(s), 199Modified Beltrami’s theory, 96Modulus of elasticity in tension, 77Mohr’s cyrcle(s), 8, 184, 186, 187, 198Mohr’s plane, 184, 186, 187Mohr’s yield theory, 181, 186Moment of inertia of area, 44, 58, 59Moment of inertia of the effective cross-sec-

tional area, 27Mono-bloc-type construction, 124Monobloc-type structure, 125, 126, 235Monochromatic classes of solutions, xxviiMonolithic structure, 94, 119Multiaxial problem, 245Multiaxial stress state, 185, 245Multiaxial stress system, 245Multilayer composite structure, 223, 238Multilayer cylindrical structure(s), 130Multilayer structure(s), 117, 130, 132, 134,

135, 137, 238, 270, 271, 272Multilayer tanks, xixMultiply-connected body, 80

NNatural half-wave length, 53, 54Natural logarithm, 61Natural strain(s), 60, 181Necking down, 65Neutral axis, 26, 58, 59Neutral equilibrium, 29Neutral fiber, 345Nominal dimension(s), 110Nominal strain(s), 62Nominal unit elongation(s), 62Non-developable surface(s), 307Non-dimensional slenderness, 50

Non-hardening linear elastic behavior, 241Non-homogeneous forth order differential

equation, 284, 285, 340Non-linear problem(s), xiNonlinear theories, xxviiNon-linearity, xxviiNon-load edge, 287Non-rotating solid disk, 315Non-strain hardening behavior, xxvNon-zero Gaussian curvature, 307, 337, 338Normal compressive force, 27Normal strain(s), 2, 10, 16, 77, 95, 147, 149Normal stress(es), 77, 78, 80, 81, 94, 146, 147,

184, 284, 314, 320, 328, 338Norton’s power law, 242Notch effect(s), 190Notch(es), 179, 190Nozzles, 56Nuclear vessel(s), xix, 279Numerical model(s), xx

OOctahedral plane(s), 184Offset yield strength, 46, 233Oil refineries, 275Omega method, 49One-dimensional heat flow, 153One-dimensional problem, xxiiOne-dimensional tensile creep test(s), 241Onset of plastic flow, 192, 195–197, 199, 204,

205, 209, 210, 212, 217, 218, 262Onset of the plastic state, 125, 126, 189, 201,

210Onset of yield, 126, 235, 236Open cross-section(s), 56Open end(s), 62, 80, 83, 89, 91, 92, 95, 116Openings, 56Operating condition(s), 190Optimal geometry, 116, 117Optimal interference, 121Optimal thickness ratio, 325Optimization criterion, 116Optimized design, 116, 120Optimized preliminary pre-stressing process,

xiOptimum internal pressure, 123Optimum structure design, 133Osculating circumference, 186Osculating sphere, 333Outer elastic region, 208, 211Outer radius, 7, 17, 32, 82–85, 87–90, 92–95,

102, 103, 106, 111, 116, 126, 127, 131,135, 142, 151–154, 156–158, 163, 164,

382 Subject Index

166, 167, 170–174, 183, 199, 200,202–204, 207, 208, 211–214, 216, 218,220, 223, 227, 231, 238, 268, 276, 284,309, 314, 315, 317, 318, 327, 328, 345, 346

Outermost fiber(s), 37, 82Out-of-plane load(s), 314Out-of-plane radial displacement(s), 283Out-of-plane stress resultant(s), 330Outside diameter, 2, 4, 6Oval of plasticity, 188Overall buckling, 54Overall instability, 42, 44, 45, 48, 49, 51Overloading, 41Overspeeding, 210Overstrain, 216, 219, 226, 233, 234Overstressing, 211, 216Overstressing pressure, 211, 216

PParabolic formula, 46Parabolic function, 314, 345Parallel circle, 22, 333, 338Parallel plane, 277, 337Partial differential equation, 55, 57, 64, 69, 174Partial factor for resistance, 50Partially plastic state, 212, 252, 265Partial overstrain, 218Partial plasticization, 257Partial vacuum, 23Partial yield, 265Particular formulation, 344Particular integral, 281–283, 295Particular solution, 29, 282Penstocks, 275, 299Percentage autofrettage, 216, 234Percentage overstrain, 216, 234Perfect circular form, 35Perfectly elastic behavior, 180, 214Perfectly plastic behavior, 180Perfectly plastic material, 179, 212Peripheral velocity, 127Permanent plastic strain, 180, 258Permanent residual deformation(s), xxiiiPermanent residual strain(s), xxiii, xxivPermanent set, 46, 191, 211, 233Permissible error, 286Permissible stress, 290Perturbations at the edges, 4, 155Physical absurdity, 239, 252Physical constant(s), 243Physical non-linearity, xxviiPinned-end column, 43Piobert effect, 185

Piobert’s bands, 185Pipeline(s), xixPiping, 11, 153, 156Plane stress state, 71, 80, 126, 142, 146, 150,

171, 198Plastic adaptation, 257Plastic boundary, 211, 231, 252, 263Plastic constitutive laws, 61Plastic deformation(s), 61, 128, 185, 229Plastic-elastic interface, 181, 202, 204–208,

213, 214, 218–220, 222, 239, 256, 267Plastic expansion, 41Plastic flow, 41, 62, 64, 65, 70, 94, 115,

192–197, 209, 211, 212, 215, 217, 220,223, 232, 251, 257

Plastic flow equation, 66Plastic flow instability, 63, 64, 68Plastic flow laws, 67Plastic hinge, 210Plastic instability, 41Plastic material(s), 212, 265Plastic range, 63, 185, 203, 208, 247, 255, 258,

263Plastic region, 181, 202, 206, 208, 212–214,

218, 232, 261, 264Plastic reserve, 199, 209, 210, 215Plastic strain(s), 181, 240, 245Plate’s flexural rigidity, 311Point function, 45, 258Points of inflection of the deflection curve, 43,

44Poisson’s ratio(s), 77, 141, 268, 280, 296Polar coordinate reference system, 25Polynomial correlation, 258Post-buckling curvature, 26Power series, 153Power series expansion, 18, 168, 297Prandtl-Reuss laws, 246Press fit(s), 109Pressure equipment(s), 307Pressure load(s), 179, 344Pressure vessel(s), 2, 13, 210, 275, 307–309,

314, 316, 317, 319, 321, 322, 324, 328,330, 331, 335, 348, 349, 351

Pre-stressing procedure, xxivPrimary creep stage, 241Principal curvature(s), 311, 307, 340Principal direction(s), 1, 4, 146, 181, 245Principal plane(s) of curvature, 22, 315, 341,

342, 343, 350, 351Principal radius of the meridian, 19Principal radius of the parallel circle, 19Principal radius(ii) of curvature, 22, 311,

337–339, 346, 347

Subject Index 383

Principal strain(s), 10, 14, 15, 67, 68, 70, 71,90–92, 94, 148, 246, 247, 207

Principal stress(es), 3, 4, 7, 8, 10, 16, 21, 60,,82, 90, 98, 106, 151, 157, 158, 163, 164,166, 168, 170, 171, 181, 184, 185, 190,195, 198, 200, 202, 206, 208, 226, 229,239, 246, 247, 250, 251, 252, 263, 264

Principal true strain(s), 60Principal true stress(es), 63Principal unit elongation(s), 89, 91, 93, 205Processes control(s), 115Production cycle, 211Profiles, 276Pronounced yield point, 34Proof stress, 46Proof testing to failure, 179Proportional limit, 32, 33, 44, 45, 47, 49, 51,

53, 54, 68, 116, 120, 125, 180, 209, 238,257–259

Proportional range, 185, 259Pure shear, 84, 187, 198Pythagorean theorem, 28

QQuadratic formulas, 46Quasi-cylindrical portion, 339

RRadial and hoop stresses, 80, 83–87, 97, 111,

113, 131, 135, 152, 155, 159, 162, 164,314, 317, 320

Radial deflection(s), 29Radial direction, 74, 75, 146, 310Radial displacement(s), 16, 21, 25, 29–31, 75,

77, 80, 90, 92, 111, 126, 142, 144, 151,152, 155, 159, 163, 164, 172, 206, 250,282, 286, 287, 291, 292, 294, 296, 297,299, 300, 301, 303, 304, 310, 314, 315,318, 325, 326, 328, 334, 335, 338, 339

Radial equilibrium, 238, 247Radial expansion, 199, 217, 287, 301Radial heat flow, 142, 143Radial interference, 111, 117, 118, 123, 127,

129, 130Radial interference fit, 109, 110Radial strain, 18, 60, 70, 75, 278Radial stress, 4, 7, 8, 15–18, 32, 61, 68, 81–84,

116, 138, 152, 156, 157, 159, 166, 168,183, 198, 202, 204, 205, 212, 214, 217,222–224, 229, 248, 261–263, 315, 321

Radius of curvature, 25, 158Radius of gyration, 43, 48

Radius of the parallel circle, 19, 20Ram, 199Ramberg and Osgood formula, 64, 67Ramberg and Osgood’s law, 260Range of uniform flow, 65Range of unstable flow, 65Rankine’s formula, 35Rate of deformation, 240Rate-independent plasticity, 245Reactive circumferential membrane force(s),

281Reactor liner(s), xixReciprocating machines, 153Recoverable elastic strain, 258Redistribution of stresses, 179, 190Reduction factor for the relevant buckling

mode, 50Reduction of area, 62Reference system, 276, 283, 325, 336Reference temperature, 156, 166, 174Reinforced vessels, 23Residual internal stress(es), 179Residual state of coaction, 179Residual stress(es), 115, 179, 192, 195, 199,

212, 213, 216–223, 225–227, 229, 230,235, 239

Residual stress state, 212, 213, 215, 217, 220Response analysis, 2, 10, 33, 41, 48, 98, 106Response analysis relation, 134Restoring moment, 29Reverse yielding, 212, 214, 217, 220–223,

225–228, 231, 234Reverse-yield boundary, 223, 225, 228Reyielded core, 223, 226, 227Reyielded region, 225, 229Reyielding, 220, 223, 231Rhombus of plasticity, 186Ribbed hulls, 299Ribbed monocoque fuselages, 275Ribbed structures, 279Ring attachment(s), 302Ring frames, 299Ring(s), 1, 23, 25–27, 30, 31, 38, 141–143,

146, 149, 304, 305Risk of failure, 8, 189Roll formed tubular segments, 351Roš-Eichinger-Nadai yield theory, 184Rotating disk, 210, 315Rotational equilibrium, 27Rotational speed(s), 128Rotation angle, 58, 303, 310, 311, 313Rotation axis, 19, 20Rotation of the normal, 286, 311, 315, 318,

327, 341

384 Subject Index

SSafety factor, 32, 33, 35, 47, 48, 129, 156, 167,

192, 199Safety requirement(s), xxSaint-Venant’s principle, 4Saint-Venant’s yield theory, 182Secondary creep stage, 241, 243Secondary deflection, 48Secondary deformation, 58, 59Second degree algebraic equation, 255Second moment of area, 44, 58Second order differential equation, 77, 143,

148, 175Second quadratic form of a surface, 311Second stage creep, 241, 243Second-order approximation shell theory,

xxviiSelf-diffusion, 243Self-hooping, 199, 211Self-hooping force, xxivSemielliptical dished head(s), 332, 334, 335,

339, 341, 342, 344–348Semielliptical meridian curve, 331, 332,

335–338, 348, 349Semi-infinite circular cylindrical shell(s), 290Separable variable, 202, 312Separation criterion, 242Serensen’s relation, 246Series expansion(s), 145, 169, 175–177Service condition(s), 119, 192, 212, 239, 246Service load(s), 115, 195, 199Shear stress(es), 4, 8, 57, 116, 118, 120, 147,

184, 185, 189, 201, 209, 238, 314Shear stress resultant, 280Shearing strain(s), 4, 76Shearing stress(es), 76, 85Shell(s) of revolution, 21, 276, 307, 308, 325,

336Shell’s flexural rigidity, 36, 52, 53, 279Short circular cylindrical shell(s), 295, 298Short cylindrical shell(s), xiiShort-life items, 241Shrink fit(s), 109, 111, 112, 114, 115, 118,

121, 124, 126, 128, 210Shrink-fit assembly(ies), 115, 117, 118, 120,

126–128, 130Shrink-fit diameter(s), 110Shrink-fit interface, 111, 121, 130Shrink-fit pressure, 87, 110, 111, 113, 114,

119–123, 128–130Shrink-fit process, 110, 115, 217Shrink-fit shaft/hub assembly(ies), 111, 113,

129

Shrinking, 109Sign convention(s), 279, 303, 310, 313, 315,

319, 343, 349, 350Significant quantities, 292, 295Significant strain(s), 61Significant stress(es), 61, 347Simple support, 315, 318Simple tensile creep test(s), 240, 241Simplified Mohr’s criterion, 186Simplifying assumption(s), 4, 141, 239, 265,

308Simply plasticity theory, 245Simply supported edge(s), 38, 55, 57, 287, 288Single-walled structure, 120, 124, 125Singularity problem(s), 81, 255, 269, 315Singularity(ies), 81, 82, 145, 152, 164, 270Sinusoids, 51Slender column(s), 42, 44Slenderness ratio, 43–45, 47–49Slip band(s), 185Slip limit, 129Slip plane(s), 185, 188Slope, 64, 287Slope of the deflection curve, 286, 290, 294,

310Small deformation(s), 181, 247Small deformations assumption, 181Small displacement assumption(s), 42, 283,

315Small displacement(s), 42, 279, 311Small element, 4, 17, 20, 25, 26, 36, 74, 153,

238, 277, 278, 290, 337, 338Small-parameter method, xxviiSmall strains assumption, 181, 249Small terms, xxviiSmokestacks, 153, 167Solid circular cylinder, 87, 152, 159, 164, 174Solid circular plate(s), 309–312, 315, 318, 319Solid fuel elements, xixSolid shaft, 118, 119, 129Southwell’s formula, 35Sphere(s), 328Spherical coordinate(s), 19, 337Spherical shape, 334Spherical surface, 311Spiral layers, 265Square of plasticity, 186Stabilization heat treatment, 235Stable equilibrium, 29Standard specimen, 34, 64, 180, 190, 239, 242State of coaction, 211, 265, 273, 274Static assumption, 279Static equivalent load system, 321

Subject Index 385

Steady-state condition(s), 153, 154, 247Steady-state creep, 241, 243Steady-state creep rate, 241, 243Steady-state viscous behavior, 246Steady-state viscous creep, 246Steady-state viscous flow, 250, 251Steady-state viscous state, 251, 257Steel grade(s), 51, 62Stiffener(s), 23, 24, 300, 302Stiffening ring effect, 54Stiffening ring(s), 23, 38, 39, 275, 299–305Stiffness response, 308Straight beams, 27Strain components, 142, 147Strain gage measurement(s), 309Strain hardening, 180, 185, 214, 235, 245Strain hardening behavior, 179–180, 216, 248Strain hardening material(s), 222, 258Strain hardening phenomenon, 258Strain hardening plastic behavior, 246Strain hardening theory, 244Strain offset, 46, 233Strain state, 1, 6, 14, 21, 73, 76, 81, 89–92,

111, 128, 142, 144, 146, 147, 162, 164,171, 181, 205, 217, 248, 250, 264

Strain-aging effect, 216, 235Strain-hardening coefficient, 64Strain-hardening material, 240Strength, 2, 3, 7, 8, 11–14, 16, 46, 83, 96–98,

100–103, 105, 106, 108, 116, 118, 120,122, 125, 135, 137, 156, 211, 216, 232,233, 235, 269, 271, 272, 274

Strength coefficient, 64Strength criterion(s), 8, 96Strength limit stress, 238Strength limit value, 3Strength property(ies), 194, 216Strength theory(ies), 8, 10, 12–14, 18, 96, 101,

102, 103, 108, 116, 117, 137, 156, 167,189, 237, 250, 265, 268–271, 274

Stress and strain state, 1, 115, 130, 141, 171,174, 176, 201, 240, 245, 246, 275, 278,295, 308, 309, 336

Stress components, 147Stress concentration factor, 111, 190, 320, 321Stress concentration(s), 189, 190, 228, 308Stress distribution(s), 113, 121, 200, 201, 206,

208, 275, 314Stress field, 84, 87, 105, 171, 179Stress intensifications factors, 351, 352Stress peak(s), 83, 84, 87, 189, 325Stress resultants per unit length, 281Stress state, 1, 8, 18, 19, 68, 73, 81, 83, 84, 89,

94–96, 110, 111, 113, 119, 120, 132, 142,

144, 146, 149, 151, 152, 155, 156, 158,159, 161, 163, 164, 166, 167, 171, 177,179, 184–186, 189–191, 197–200,202–204, 206, 207, 212, 214, 215, 223,229, 249, 250, 253, 254, 261–263, 286,293, 302, 315, 317, 320, 346

Stress-strain law, 240Structural collapse, xxStructural strength, 82Structure of revolution, 74Submarines, 23, 299Successive maxima and minima, 286Successive yield cycles, 212Summation function, 133Surface force distributions, 152, 163, 164Surface force(s), 22, 74, 76, 81, 84, 85, 88,

141, 144, 146, 149, 150, 152, 164, 246,282, 315

Swage autofrettage, 200Swift’s law, 260Symmetrical deformation, 280Symmetry conditions, 31, 277System of orthogonal curvilinear coordinate,

307

TTangential direction, 277Tangential displacement(s), 30, 76, 90, 277,

278Tangential force per unit of surface area, 129Tangential strain, 75, 94, 95, 151Tangent modulus, 34, 45, 53, 258Technical theory of the shells, xxviiTemperature distribution(s), 141, 149, 153,

155, 157–159, 164, 166, 168, 171, 176Temperature gradient, 148, 150–153, 163, 164,

171, 174, 247Tensile strain history, xxvTensile strength, 103, 167Tensile stress(es), 59, 79, 116, 156, 157, 166,

167, 170, 179, 190, 229, 314, 317, 327,330, 348

Tensile test, 64, 117, 180, 190, 191, 233, 239Tensile yield point, 215Tensile yielding, 213Tensor invariant(s), 184Tertiary creep stage, 241Test temperature, 240Tetmajer’s formula, 47Theorem of minimum work, 59Theoretical circular shape, 35Theoretical method(s), xTheoretical model(s), 182, 189, 243

386 Subject Index

Theories for creep, 242, 243Theory(ies) of failure, 8Theory(ies) of the shells, 19, 21, 280, 329,

335, 341Theory of curved beams, 26Theory of plasticity, 321Thermal gradients, 115Thermal load(s), 7, 11, 17, 76, 81, 142, 146,

155, 156, 159, 161, 163, 164, 166, 167,171, 173, 174

Thermal stress(es), 73, 80, 115Thermoelasticity relation(s), 142, 147–150Thermoelastic stress-strain relations, 15Thermomechanical magnitude(s), 149Thickness, 1–4, 7, 10, 13, 14, 16, 17, 22, 24,

27, 38, 44, 48, 51, 60, 63, 66–68, 70, 73,78, 83–86, 89, 93, 94, 100, 101, 102, 103,106, 116, 119, 126, 135, 142, 145, 157,158, 168, 170–172, 198, 208, 211, 212,214, 215, 217, 218, 220–222, 225, 226,232, 233, 264, 265, 272, 273, 276, 288,300, 302, 308–310, 312–314, 314, 315,324, 325, 328, 331, 345, 349

Thickness discontinuity, 349, 351Thickness ratio(s), 321Thick-walled circular cylinder(s), 2, 13, 18,

19, 34, 35, 80, 89, 94, 95, 97, 98, 101–103,106, 179, 181–183, 189, 199, 201, 210,227, 241, 248

Thick-walled tubes, 189Thick-walled vessel(s), 210Thin-walled annular ring(s), 33Thin-walled circular cylinder(s), 1–4, 6–8, 10,

11, 13, 14, 16, 17, 19, 23, 35, 38, 41, 44,58, 60, 63, 80, 96, 100–103, 108, 171, 198,210, 276

Thin-walled circular ring(s), 1, 32Thin-walled rings, 24Thin-walled structures, 41, 56, 309Third order differential equation, 316Third stage creep, 243Threshold value(s), 220, 221, 240Time-dependent magnitude(s), 141Time-dependent strain(s), 242Time hardening theory, 244Tolerable limits, 35Torsional buckling, 3, 56, 57Torsional rigidity, 56Total critical load, 52Total radial displacement(s), 36, 152, 342Total radial interference, 112Total strain, 240, 241Transient thermal load, 141Transitional region, 265

Transmittable torque, 129Transverse displacement(s), 312, 321Transverse shearing force(s), 277–279, 312,

337Tresca yield theory (criterion), 181Triaxial stress state, 4, 10, 65, 95, 96, 97, 128,

135, 147, 181, 191, 199, 201, 202, 247Trigonometric functions, 281, 299True hoop stress, 60, 62True radial stress, 60True strain(s), 45, 63, 64, 181True stress(es), 64, 192True stress-true strain curve, 64Tubing, 33, 153, 156Tubular shell structure(s), 275Tubular structure(s), 1, 41, 44, 48, 82, 179Twist, 279Twisting couple, 56Twisting moments, 21, 277Two-dimensional problem, xxviTwo-walled composite structure, 125

UUltimate limit state, 65Ultimate strain, 62Ultimate stress, 46, 64, 65, 179, 199, 214Ultimate tensile strength, 62Unalloyed steel, 216Uniaxial stress state, 18, 198Uniaxial tensile test, 243Uniaxial tension stress-strain curve, 65Uniform axial translation, 146, 147, 162, 164,

171Uniform normal pressure per unit of length, 27Uniform plastic flow, 65Unitary axial length, 17, 36, 153, 174Unit elongation(s), 30, 146, 206, 207Unit normal elongation(s), 80, 149Unit shear strain(s), 4Unloading and loading cycle, 180Unload open ends, 4Unstable elastic equilibrium, 43, 85Unstable equilibrium, 29

VVacuum columns, 23Vacuum condensers, 23Vacuum crystallizers, 23Variable plastic compliance, xixVerification analysis, 8, 10, 95Vertical asymptote, 81Virgin material, 202, 215, 217

Subject Index 387

Virgin state, 258Viscous behavior, 240Viscous flow, 247, 251Viscous flow theory of creep, 246Viscous range, 247Viscous state, 248, 253, 259Volume element, 74, 75, 130Volume expansion, 60, 148, 206, 248

WWavelength, 42, 51, 54, 285Wave(s), 31, 38Weber function(s), 175Wedge-shaped layers, 265Weld beads, ix, xxiWelded junction, 308Welded seam, 308, 351Winkler’s beam, 26, 285Winkler’s theory, 96Winkler-type foundation, 285, 51Work, 3, 42, 115Working conditions, 48, 137, 217, 240Working pressure, 7, 119, 120, 179, 195, 212,

215, 217, 233, 307Working stress(es), 13, 98, 212Wrinkles, 56Wrinkling, 51

YYield criterion, 181, 186–188, 190, 191, 202,

205Yield ellipse, 183, 189Yield hexagon, 184, 189Yielding, 14, 37, 60, 179, 181, 184–186, 191,

192, 198, 201, 210, 215, 217, 220, 221,235, 239, 263, 292

Yielding onset, 186Yield point, 23, 24, 32, 116, 125, 179, 185,

238, 240Yield-point stress, 34, 37, 41, 48, 64, 68, 180,

209, 213, 214, 221–223, 226, 258, 321Yield rhombus, 186Yield square, 186Yield strength, 62, 65, 94, 117, 119, 123, 124,

126, 179, 180, 189, 216, 227, 230, 232–236Yield stress, 37, 47, 65, 93, 115, 125, 156, 182,

199, 206, 208, 220, 238Yield theory, 179, 181–183, 185, 188–193,

195, 196, 198, 199, 208, 210, 212–214,216, 220, 221, 223, 226, 229, 231, 238,254, 256, 257, 264

Young’s modulus, 27, 34, 43, 45, 53, 141, 258

ZZero Gaussian curvature, 276, 307, 337

388 Subject Index