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

Recommendations

Info

function [ ] = Point Full(pois) 209 hold on; plot (Ws,imag(CHI),‘r’); grid on; title(tit); titx = ‘Dimensionless frequency w*r/Cs’; xlabel(titx); ylabel(‘\chi’); hold off; EasyPlot(‘CHI-3D-FD.ezp’, tit, titx, Ws, CHI, ‘c’); pause; % Time domain clear G* tp = r/cp; % arrival time of P waves ts = r/cs; % arrival time of SV waves ts2 = tsˆ2; T = [0:dt:tmax]; Tp = T.*(T>=tp)/ts2; Ts = T.*(T>=ts)/ts2; PSI = Ts-Tp; CHI = -3*PSI; jp = ceil(tp/dt)+1; js = floor(ts/dt); amax = 10*max(abs(PSI)); % to simulate a Dirac delta mm = length(PSI); PSI = [0,0,0,PSI(jp),PSI(jp:js),PSI(js),amax,0,0]; CHI = [0,0,amax,CHI(jp),CHI(jp:js),CHI(js),- amax,0,0]; tp1 = 0.5*(T(jp-1)+T(jp)); ts1 = 0.5*(T(js)+T(js+1)); T = [0,tp1,tp1,tp1,T(jp:js),ts1,ts1,ts1,tmax]; plot (T, PSI); tit = sprintf(‘\\psi in full 3D space, \\nu=%5.2f’,pois); title(tit); titx = ‘Dimensionless time, t*Cs/r’; xlabel(titx); grid on; axis([0 tmax -1.5 0.5]); EasyPlot(‘PSI-3D-TD.ezp’, tit, titx, T, PSI, ‘r’); pause; plot (T, CHI); tit = sprintf(‘\\chi in full 3D space, \\nu=%5.2f’,pois); title(tit); titx = ‘Dimensionless time, t*Cs/r’; xlabel(titx); axis([0 tmax -0.5 5]); grid on; EasyPlot(‘CHI-3D-TD.ezp’, tit, titx, T, CHI, ‘r’); pause; close; return
210 MATLAB programs function Torsion Full(x,y,z,td,rho,cs) % Computes the response of a full 3D space to a torsional % point source with time variation (pi/2/td)*sin(pi*t/td), 0
Page 2 and 3:
FUNDAMENTAL SOLUTIONS IN ELASTODYNA
Page 4 and 5:
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 18 and 19:
Page 20 and 21:
Page 22 and 23:
Page 24 and 25:
1.4 Strains, stresses, and the elas
Page 26 and 27:
Page 28 and 29:
Page 30 and 31:
Page 32 and 33:
Page 34 and 35:
Page 36 and 37:
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 186 and 187: 10.4 Stiffness matrix method for la
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 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 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 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,
show all

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

Create successful ePaper yourself

Delete template?

Save as template?