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

Recommendations

Info

function Torsion Full(x, y, z, td, rho, cs) 211 pause; close % Make file for plotting with EasyPlot fout = fopen (‘tors.ezp’,’w’); fprintf (fout, ‘/et g “%s”\n’, tit); fprintf (fout, ‘/et x “t*Cs/R”\n’); fprintf (fout, ‘/og on\n’); fprintf (fout, ‘/sd off\n’); fprintf (fout, ‘/sm off\n’); fprintf (fout, ‘%15.5e%15.5e\n’, [tau;v]); fclose (fout); return
212 MATLAB programs function [] = Cavity3D(r, pois) % Spherical (3-D) cavity in a full, homogeneous space % subjected to a harmonic/impulsive pressure p % Arguments: % r = R/R0 = (distance to receiver)/(radius of cavity) % pois = Poisson’s ratio % % This program assumes p0=1 (unit pressure), and r0=1 (radius of cavity) % Basic parameters a2 = (2-2*pois)/(1-2*pois); a = sqrt(a2); % Cp/Cs R0 = 1; % Radius of cavity R = r*R0; % Receiver rho = 1; % mass density Cs = 1; % S-wave velocity Cp = a*Cs; % P-wave velocity mu = rho*Csˆ2; % shear modulus % Frequency and time vectors nf = 1024; wmax = 16*pi; dw = wmax/nf; w = [dw:dw:wmax]; tmax = 6; % maximum dimensionless time nt = 200; % No. of time steps dt = tmax/nt; % time step T = [0:nt]*dt; % dimensionless, delayed time (= t*Cp/R) % Response in frequency domain fac = 0.25*R0/mu; % assuming p=1 here w0 = w*R0/Cp; w1 = w0*r; G0 = 1+i*w0; G1 = 1+i*w1; G = fac*(G0./(G0-0.25*a2*w0.ˆ2)); % Cavity wall at R0 plot(w,real(G)); hold on; plot(w,imag(G),‘r’); grid on; tit = sprintf(... ‘T.F. for pressure in spherical cavity, R/R0=%5.4f, \\nu=%5.2f’,... r, pois); titx = ‘Frequency (rad/s)’; title (tit); xlabel(titx); H = G.*exp(-i*(r-1)*w0).*G1./G0/rˆ2; %Receiver at R plot(w,real(H),‘:’); plot(w,imag(H),‘r:’);
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 172 and 173: 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 220 and 221: function [ ] = Point Full(pois) 209
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?