Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

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Fundamental Solutions in Elastodynamics A Compendium EDUARDO KAUSEL Massachusetts Institute of Technology iii
CAMBRIDGE UNIVERSITY PRESS Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge CB2 2RU, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridg e.org /9780521855709 © Eduardo Kausel 2006 This publication is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format ISBN-13 978-0-511-14700-5 eBook (NetLibrary) ISBN-10 0-511-14700-7 eBook (NetLibrary) ISBN-13 978-0-521-85570-9 hardback ISBN-10 0-521-85570-5 hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Page 2 and 3: FUNDAMENTAL SOLUTIONS IN ELASTODYNA
Page 6 and 7: Contents Preface page ix SECTION I:
Page 8 and 9: Contents vii SECTION V: ANALYTICAL
Page 10 and 11: Preface We present in this work a c
Page 12 and 13: SECTION I: PRELIMINARIES 1 Fundamen
Page 14 and 15: 1.1 Notation and table of symbols 3
Page 16 and 17: 1.3 Coordinate systems and differen
Page 24 and 25: 1.4 Strains, stresses, and the elas
Page 38 and 39: 2 Dipoles In most cases, we provide
Page 40 and 41: 2.2 Line dipoles 29 z z z y y y x x
Page 42 and 43: 2.5 Blast loads (explosive line and
Page 44 and 45: 2.6 Dipoles in cylindrical coordina
Page 46 and 47: SECTION II: FULL SPACE PROBLEMS 3 T
Page 48 and 49: 3.3 SH line load in an orthotropic
Page 50 and 51: 3.4 In-plane line load (SV-P waves)
Page 52 and 53: 3.5 Dipoles in plane strain 41 0.6
Page 54 and 55:
3.6 Line blast source: suddenly app
Page 56 and 57:
3.7 Cylindrical cavity subjected to
Page 58 and 59:
3.7 Cylindrical cavity subjected to
Page 60 and 61:
4.2 Point load (Stokes problem) 49
Page 62 and 63:
4.2 Point load (Stokes problem) 51
Page 64 and 65:
4.3 Tension cracks 53 given earlier
Page 66 and 67:
4.5 Torsional point source 55 Spher
Page 68 and 69:
4.6 Torsional point source with ver
Page 70 and 71:
4.8 Spherical cavity subjected to a
Page 72 and 73:
4.8 Spherical cavity subjected to a
Page 74 and 75:
4.9 Spatially harmonic line source
Page 76 and 77:
Page 78 and 79:
Page 80 and 81:
SECTION III: HALF-SPACE PROBLEMS 5
Page 82 and 83:
5.3 Half-plane, SV-P source and rec
Page 84 and 85:
5.4 Half-plane, SV-P source on surf
Page 86 and 87:
5.4 Half-plane, SV-P source on surf
Page 88 and 89:
5.5 Half-plane, line blast load app
Page 90 and 91:
6.1 3-D half-space, suddenly applie
Page 92 and 93:
6.2 3-D half-space, suddenly applie
Page 94 and 95:
6.3 3-D half-space, buried torsiona
Page 96 and 97:
6.3 3-D half-space, buried torsiona
Page 98 and 99:
SECTION IV: PLATES AND STRATA 7 Two
Page 100 and 101:
7.2 Stratum subjected to SH line so
Page 102 and 103:
7.3 Plate with mixed boundary condi
Page 104 and 105:
Page 106 and 107:
Page 108 and 109:
SECTION V: ANALYTICAL AND NUMERICAL
Page 110 and 111:
8.1 Summary of results 99 Plane str
Page 112 and 113:
8.2 Scalar Helmholtz equation in Ca
Page 114 and 115:
8.3 Vector Helmholtz equation in Ca
Page 116 and 117:
8.4 Elastic wave equation in Cartes
Page 118 and 119:
8.4 Elastic wave equation in Cartes
Page 120 and 121:
8.6 Vector Helmholtz equation in cy
Page 122 and 123:
8.7 Elastic wave equation in cylind
Page 124 and 125:
Page 126 and 127:
Page 128 and 129:
8.8 Scalar Helmholtz equation in sp
Page 130 and 131:
8.9 Vector Helmholtz equation in sp
Page 132 and 133:
8.10 Elastic wave equation in spher
Page 134 and 135:
8.10 Elastic wave equation in spher
Page 136 and 137:
9 Integral transform method The int
Page 138 and 139:
9.1 Cartesian coordinates 127 In pa
Page 140 and 141:
9.1 Cartesian coordinates 129 Writi
Page 142 and 143:
9.2 Cylindrical coordinates 131 Fou
Page 144 and 145:
9.2 Cylindrical coordinates 133 Hen
Page 146 and 147:
9.2 Cylindrical coordinates 135 Oth
Page 148 and 149:
9.3 Spherical coordinates 137 √
Page 150 and 151:
9.3 Spherical coordinates 139 ∫
Page 152 and 153:
10.1 Summary of method 141 special
Page 154 and 155:
10.2 Stiffness matrix method in Car
Page 156 and 157:
Page 158 and 159:
Page 160 and 161:
Page 162 and 163:
Page 164 and 165:
Page 166 and 167:
Page 168 and 169:
Page 170 and 171:
10.3 Stiffness matrix method in cyl
Page 172 and 173:
Page 174 and 175:
Page 176 and 177:
Page 178 and 179:
Page 180 and 181:
Page 182 and 183:
Page 184 and 185:
Page 186 and 187:
10.4 Stiffness matrix method for la
Page 188 and 189:
Page 190 and 191:
Page 192 and 193:
Page 194 and 195:
Page 196 and 197:
SECTION VI: APPENDICES 11 Basic pro
Page 198 and 199:
11.2 Spherical Bessel functions 187
Page 200 and 201:
11.3 Legendre polynomials 189 1.0 P
Page 202 and 203:
11.4 Associated Legendre functions
Page 204 and 205:
11.4 Associated Legendre functions
Page 206 and 207:
12.1 Fourier transforms 195 b) Wave
Page 208 and 209:
12.3 Spherical Hankel transforms 19
Page 210 and 211:
function [ ] = SH2D Full( ) 199 fun
Page 212 and 213:
function [ ] = SVP2D Full(x, z, poi
Page 214 and 215:
function [ ] = SVP2D Full(x, z, poi
Page 216 and 217:
function [ ] = Blast2D(pois) 205 Ur
Page 218 and 219:
function [ ] = Cavity2D(r, r0, pois
Page 220 and 221:
function [ ] = Point Full(pois) 209
Page 222 and 223:
function Torsion Full(x, y, z, td,
Page 224 and 225:
function [ ] = Cavity3D(r, pois) 21
Page 226 and 227:
function [ ] = SH2D Half(xs, zs, xr
Page 228 and 229:
function [T, Ux, Uz] = Garvin(x, z,
Page 230 and 231:
function [T, Uxx, Uxz, Uzz] = lamb2
Page 232 and 233:
Page 234 and 235:
Page 236 and 237:
function [T, Uxx, Utx, Uzz, Urz] =
Page 238 and 239:
function [T, Uxx, Utx, Uzz, Urz] =
Page 240 and 241:
function [ ] = Torsion Half(r, z, z
Page 242 and 243:
function [ ] = Torsion Half(r, z, z
Page 244 and 245:
function [ ] = SH Plate(x, z, z0) 2
Page 246 and 247:
function [ ] = SH Stratum(x, z, z0)
Page 248 and 249:
function [ ] = SH Stratum(x, z, z0)
Page 250 and 251:
function [ ] = SVP Plate(x, z, z0,
Page 252 and 253:
Page 254 and 255:
Page 256 and 257:
function [ztors, zspher] = spheroid
Page 258 and 259:
function [ztors, zspher] = spheroid
Page 260 and 261:
function [si] = cisib(x) 249 functi
Page 262:
function [el3] = ellipint3(phi, N,
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Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

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