******* Pipes-Pagano Approximation Gr/Ep ******* ******************************************************************************** ENGINEERING ELASTIC CONSTANTS ******************************************************************************** E1= 0.2100E+07 E2= 0.2100E+07 E3= 0.2000E+08 G12= 0.8500E+06 G13= 0.8500E+06 G23= 0.8500E+06 NU12= 0.2100E+00 NU13= 0.2205E-01 NU23= 0.2205E-01 NU21= 0.2100E+00 NU31= 0.2100E+00 NU32= 0.2100E+00 ******************************************************************************** STIFFNESSES CALCULATED FROM ENGINERRING CONSTANTS ******************************************************************************** C11= 0.2213E+07 C22= 0.2213E+07 C33= 0.2024E+08 C12= 0.4771E+06 C13= 0.5648E+06 C23= 0.5648E+06 C44= 0.8500E+06 C55= 0.8500E+06 C66= 0.8500E+06 ******************************************************************************** STIFFNESSES CALCULATED FROM COMPLIANCES WHICH WERE CALC. FROM ENGR. CONSTANTS ******************************************************************************** C11= 0.2213E+07 C22= 0.2213E+07 C33= 0.2024E+08 C12= 0.4771E+06 C13= 0.5648E+06 C23= 0.5648E+06 C44= 0.8500E+06 C55= 0.8500E+06 C66= 0.8500E+06 ******************************************************************************** TOP LAYER, ANGLE (DEG.)= 0.750E+02 BOTTOM LAYER, ANGLE (DEG.)= 0.000E+00 BELOW ARE STIFFNESSES FOR BOTH LAYERS ******************************************************************************** ******************************************************************************** 0.1791E+08 0.5590E+06 0.1685E+07 0.0000E+00 0.4193E+07 0.0000E+00 0.5590E+06 0.2213E+07 0.4830E+06 0.0000E+00 0.2193E+05 0.0000E+00 0.1685E+07 0.4830E+06 0.2300E+07 0.0000E+00 0.3132E+06 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.8500E+06 0.0000E+00 0.0000E+00 0.4193E+07 0.2193E+05 0.3132E+06 0.0000E+00 0.1970E+07 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.8500E+06 ******************************************************************************** 0.2213E+07 0.4771E+06 0.5648E+06 0.0000E+00 0.0000E+00 0.0000E+00 0.4771E+06 0.2213E+07 0.5648E+06 0.0000E+00 0.0000E+00 0.0000E+00 0.5648E+06 0.5648E+06 0.2024E+08 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.8500E+06 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.8500E+06 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.8500E+06 ******************************************************************************** ******************************************************************************** MATRICES FOR EIGEN-VALUE PROBLEM FOR TOP/BOTTOM LAYERS ARE WRITTEN BELOW [A]/[AP] ******************************************************************************** 0.0000E+00 -0.1658E+01 0.0000E+00 -0.2107E+02 0.0000E+00 -0.4933E+01 -0.6368E+00 0.0000E+00 -0.9913E-02 0.0000E+00 -0.3842E+00 0.0000E+00 0.0000E+00 -0.2581E-01 0.0000E+00 -0.4933E+01 0.0000E+00 -0.2318E+01 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 ******************************************************************************** 0.0000E+00 -0.1561E+01 0.0000E+00 -0.2603E+01 0.0000E+00 0.0000E+00 -0.5998E+00 0.0000E+00 0.0000E+00 0.0000E+00 -0.3842E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 -0.1000E+01 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.0000E+00 0.1000E+01 0.0000E+00 0.0000E+00 0.0000E+00 ******************************************************************************** TOP LAYER, CONVERGED= 0.852E-02 W(1)-0.477E-06 0.461E+01 Z(1) 0.937E+00 0.000E+00 Z(2)-0.121E-07 0.132E+00 Z(3) 0.243E+00 0.159E-07 Z(4) 0.195E-07-0.203E+00 Z(5) 0.287E-01 0.139E-08 Z(6) 0.470E-08-0.527E-01 W(2)-0.477E-06-0.461E+01 Z(1) 0.937E+00 0.000E+00 Z(2)-0.121E-07-0.132E+00 Z(3) 0.243E+00-0.159E-07 Z(4) 0.195E-07 0.203E+00 Z(5) 0.287E-01-0.139E-08 Z(6) 0.470E-08 0.527E-01 W(3)-0.298E-07 0.100E+01 Z(1)-0.177E+00 0.246E-06 Z(2)-0.253E-07-0.172E+00 Z(3) 0.664E+00 0.000E+00 Z(4) 0.256E-07 0.177E+00 Z(5)-0.171E+00 0.139E-07 Z(6) 0.232E-08-0.662E+00 W(4)-0.298E-07-0.100E+01 Z(1)-0.177E+00-0.246E-06 Z(2)-0.253E-07 0.172E+00 Z(3) 0.664E+00 0.000E+00 Z(4) 0.256E-07-0.177E+00 Z(5)-0.171E+00-0.139E-07 Z(6) 0.232E-08 0.662E+00 W(5) 0.939E-41 0.663E+00 Z(1) 0.711E-01-0.147E-06 Z(2) 0.168E-07 0.517E+00 Z(3)-0.182E+00-0.384E-07 Z(4)-0.239E-07-0.107E+00 Z(5) 0.780E+00 0.000E+00 Z(6) 0.491E-07 0.274E+00 W(6) 0.939E-41-0.663E+00 Z(1) 0.711E-01 0.147E-06 Z(2) 0.168E-07-0.517E+00 Z(3)-0.182E+00 0.384E-07 Z(4)-0.239E-07 0.107E+00 Z(5) 0.780E+00 0.000E+00 Z(6) 0.491E-07-0.274E+00 ******************************************************************************** BOTTOM LAYER, CONVERGED= 0.186E-01 WP(1) 0.000E+00 0.112E+01 ZP(1) 0.590E+00 0.000E+00 ZP(2) 0.000E+00 0.456E+00 ZP(3) 0.000E+00 0.000E+00 ZP(4) 0.000E+00-0.527E+00 ZP(5) 0.408E+00 0.000E+00 ZP(6) 0.000E+00 0.000E+00 WP(2) 0.000E+00-0.112E+01 ZP(1) 0.590E+00 0.000E+00 ZP(2) 0.000E+00-0.456E+00 ZP(3) 0.000E+00 0.000E+00 ZP(4) 0.000E+00 0.527E+00 ZP(5) 0.408E+00 0.000E+00 ZP(6) 0.000E+00 0.000E+00 WP(3) 0.000E+00 0.100E+01 ZP(1) 0.000E+00 0.000E+00 ZP(2) 0.000E+00 0.000E+00 ZP(3) 0.707E+00 0.000E+00 ZP(4) 0.000E+00 0.000E+00 ZP(5) 0.000E+00 0.000E+00 ZP(6) 0.000E+00-0.707E+00 WP(4) 0.000E+00-0.100E+01 ZP(1) 0.000E+00 0.000E+00 ZP(2) 0.000E+00 0.000E+00 ZP(3) 0.707E+00 0.000E+00 ZP(4) 0.000E+00 0.000E+00 ZP(5) 0.000E+00 0.000E+00 ZP(6) 0.000E+00 0.707E+00 WP(5) 0.000E+00 0.894E+00 ZP(1) 0.408E+00 0.000E+00 ZP(2) 0.000E+00 0.527E+00 ZP(3) 0.000E+00 0.000E+00 ZP(4) 0.000E+00-0.456E+00 ZP(5) 0.590E+00 0.000E+00 ZP(6) 0.000E+00 0.000E+00 WP(6) 0.000E+00-0.894E+00 ZP(1) 0.408E+00 0.000E+00 ZP(2) 0.000E+00-0.527E+00 ZP(3) 0.000E+00 0.000E+00 ZP(4) 0.000E+00 0.456E+00 ZP(5) 0.590E+00 0.000E+00 ZP(6) 0.000E+00 0.000E+00 ******************************************************************************** SUM FOR EQUATION NO.1 =-0.4438E+01 0.3642E+01 TOP LAYER SUM FOR EQUATION NO.1 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.2 =-0.3716E+00 0.2631E+02 TOP LAYER SUM FOR EQUATION NO.2 = 0.0000E+00-0.6250E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.3 =-0.5000E+00 0.9027E+00 TOP LAYER SUM FOR EQUATION NO.3 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** EIGEN-VALUE P(1)=-0.4768E-06 0.4612E+01 TOP LAYER NORMALIZED EIGEN-VECTOR V(1,1)=-0.9591E+00-0.9223E-07 V(2,1)= 0.6545E-08-0.1354E+00 V(3,1)=-0.2488E+00-0.2218E-07 ******************************************************************************** EIGEN-VALUE PP(1)= 0.0000E+00 0.1119E+01 BOTTOM LAYER NORMALIZED EIGEN-VECTOR VP(1,1)=-0.7911E+00 0.0000E+00 VP(2,1)= 0.0000E+00-0.6117E+00 VP(3,1)= 0.0000E+00 0.0000E+00 ******************************************************************************** ******************************************************************************** SUM FOR EQUATION NO.1 = 0.1250E+01-0.6260E+00 TOP LAYER SUM FOR EQUATION NO.1 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.2 = 0.4621E-01-0.9785E+00 TOP LAYER SUM FOR EQUATION NO.2 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.3 =-0.2500E+00-0.1075E+00 TOP LAYER SUM FOR EQUATION NO.3 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** EIGEN-VALUE P(2)=-0.2980E-07 0.1003E+01 TOP LAYER NORMALIZED EIGEN-VECTOR V(1,2)= 0.2505E+00-0.3619E-07 V(2,2)= 0.1974E-07 0.2423E+00 V(3,2)=-0.9373E+00-0.3279E-08 ******************************************************************************** EIGEN-VALUE PP(2)= 0.0000E+00 0.1000E+01 BOTTOM LAYER NORMALIZED EIGEN-VECTOR VP(1,2)= 0.0000E+00 0.0000E+00 VP(2,2)= 0.0000E+00 0.0000E+00 VP(3,2)=-0.1000E+01 0.0000E+00 ******************************************************************************** ******************************************************************************** SUM FOR EQUATION NO.1 =-0.2500E+00 0.2547E+00 TOP LAYER SUM FOR EQUATION NO.1 =-0.1250E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.2 =-0.2589E-01 0.4595E+00 TOP LAYER SUM FOR EQUATION NO.2 = 0.0000E+00-0.5000E+00 BOTTOM LAYER ******************************************************************************** SUM FOR EQUATION NO.3 =-0.6250E-01 0.2592E-01 TOP LAYER SUM FOR EQUATION NO.3 = 0.0000E+00 0.0000E+00 BOTTOM LAYER ******************************************************************************** EIGEN-VALUE P(3)= 0.9387E-41 0.6632E+00 TOP LAYER NORMALIZED EIGEN-VECTOR V(1,3)=-0.1286E+00 0.2863E-07 V(2,3)= 0.0000E+00-0.9355E+00 V(3,3)= 0.3292E+00-0.5896E-07 ******************************************************************************** EIGEN-VALUE PP(3)= 0.0000E+00 0.8936E+00 BOTTOM LAYER NORMALIZED EIGEN-VECTOR VP(1,3)=-0.6117E+00 0.0000E+00 VP(2,3)= 0.0000E+00-0.7911E+00 VP(3,3)= 0.0000E+00 0.0000E+00 ******************************************************************************** ******************************************************************************** T111-0.179E+08-0.169E+01 T112 0.421E+06-0.655E+00 T113-0.575E+06 0.265E+00 T121 0.756E+00-0.387E+07 T122 0.413E-01 0.420E+06 T123-0.161E-01-0.868E+06 T131-0.450E+07-0.428E+00 T132-0.801E+06-0.158E+00 T133 0.123E+06 0.387E-02 T211 0.756E+00-0.387E+07 T212 0.413E-01 0.420E+06 T213-0.161E-01-0.868E+06 T221 0.840E+06 0.158E+00 T222-0.418E+06 0.752E-02 T223 0.131E+07 0.147E-01 T231 0.188E+00-0.975E+06 T232 0.265E-01-0.799E+06 T233 0.332E-01 0.186E+06 T311-0.450E+07-0.428E+00 T312-0.801E+06-0.158E+00 T313 0.123E+06 0.387E-02 T321 0.188E+00-0.975E+06 T322 0.265E-01-0.799E+06 T323 0.332E-01 0.186E+06 T331-0.139E+07-0.117E+00 T332 0.112E+05-0.559E-01 T333 0.186E+06 0.298E-01 ******************************************************************************** TP111-0.142E+07 0.000E+00 TP112 0.000E+00 0.000E+00 TP113-0.102E+07 0.000E+00 TP121 0.000E+00-0.127E+07 TP122 0.000E+00 0.000E+00 TP123 0.000E+00-0.114E+07 TP131 0.000E+00 0.000E+00 TP132-0.850E+06 0.000E+00 TP133 0.000E+00 0.000E+00 TP211 0.000E+00-0.127E+07 TP212 0.000E+00 0.000E+00 TP213 0.000E+00-0.114E+07 TP221 0.114E+07 0.000E+00 TP222 0.000E+00 0.000E+00 TP223 0.127E+07 0.000E+00 TP231 0.000E+00 0.000E+00 TP232 0.000E+00-0.850E+06 TP233 0.000E+00 0.000E+00 TP311 0.000E+00 0.000E+00 TP312-0.850E+06 0.000E+00 TP313 0.000E+00 0.000E+00 TP321 0.000E+00 0.000E+00 TP322 0.000E+00-0.850E+06 TP323 0.000E+00 0.000E+00 TP331-0.602E+05 0.000E+00 TP332 0.000E+00 0.000E+00 TP333 0.538E+05 0.000E+00 ******************************************************************************** L=1 T1 =-0.372E+00 0.270E+02 T2 = 0.000E+00 0.903E+00 T3 = 0.118E+03 0.536E+01 L=1 T1P= 0.000E+00-0.625E+00 T2P= 0.000E+00 0.000E+00 T3P=-0.625E+00 0.000E+00 ******************************************************************************** L=2 T1 = 0.462E-01-0.100E+01 T2 =-0.188E+00-0.108E+00 T3 =-0.188E+00-0.672E+00 L=2 T1P= 0.000E+00 0.000E+00 T2P= 0.000E+00 0.000E+00 T3P= 0.000E+00 0.000E+00 ******************************************************************************** L=3 T1 =-0.259E-01 0.375E+00 T2 =-0.391E-01 0.259E-01 T3 = 0.000E+00 0.272E+00 L=3 T1P= 0.000E+00-0.625E+00 T2P= 0.000E+00 0.000E+00 T3P=-0.688E+00 0.000E+00 ******************************************************************************** ******************************************************************************** IK= 1 K= 0.000010000 DET= 0.171677327E+01 IK= 2 K= 0.010009999 DET= 0.111024725E+01 IK= 3 K= 0.020009998 DET= 0.211749864E+01 IK= 4 K= 0.030009998 DET=-0.311088443E+01 IK= 5 K= 0.040009998 DET=-0.929969311E+01 IK= 6 K= 0.050009996 DET=-0.277408648E+01 IK= 7 K= 0.060009994 DET=-0.582746029E+01 IK= 8 K= 0.070009992 DET=-0.103270364E+01 IK= 9 K= 0.080009989 DET=-0.164812732E+01 IK= 10 K= 0.090009987 DET=-0.244692111E+01 IK= 11 K= 0.100009985 DET=-0.344394541E+01 IK= 12 K= 0.110009983 DET=-0.465089035E+01 IK= 13 K= 0.120009981 DET=-0.607640314E+01 IK= 14 K= 0.130009979 DET=-0.772587872E+01 IK= 15 K= 0.140009984 DET=-0.960176849E+01 IK= 16 K= 0.150009990 DET=-0.117033947E+01 IK= 17 K= 0.160009995 DET=-0.140270019E+01 IK= 18 K= 0.170010000 DET=-0.165662038E+01 IK= 19 K= 0.180010006 DET=-0.193117595E+01 IK= 20 K= 0.190010011 DET=-0.222518635E+01 IK= 21 K= 0.200010017 DET=-0.253723025E+01 IK= 22 K= 0.210010022 DET=-0.286567736E+01 IK= 23 K= 0.220010027 DET=-0.320868683E+01 IK= 24 K= 0.230010033 DET=-0.356424475E+01 IK= 25 K= 0.240010038 DET=-0.393017888E+01 IK= 26 K= 0.250010043 DET=-0.430419064E+01 IK= 27 K= 0.260010034 DET=-0.468386698E+01 IK= 28 K= 0.270010024 DET=-0.506674194E+01 IK= 29 K= 0.280010015 DET=-0.545025253E+01 IK= 30 K= 0.290010005 DET=-0.583183289E+01 IK= 31 K= 0.300009996 DET=-0.620890141E+01 IK= 32 K= 0.310009986 DET=-0.657890797E+01 IK= 33 K= 0.320009977 DET=-0.693933105E+01 IK= 34 K= 0.330009967 DET=-0.728771687E+01 IK= 35 K= 0.340009958 DET=-0.762169361E+01 IK= 36 K= 0.350009948 DET=-0.793902588E+01 IK= 37 K= 0.360009938 DET=-0.823755360E+01 IK= 38 K= 0.370009929 DET=-0.851532078E+01 IK= 39 K= 0.380009919 DET=-0.877049541E+01 IK= 40 K= 0.390009910 DET=-0.900140572E+01 IK= 41 K= 0.400009900 DET=-0.920660210E+01 IK= 42 K= 0.410009891 DET=-0.938481617E+01 IK= 43 K= 0.420009881 DET=-0.953497982E+01 IK= 44 K= 0.430009872 DET=-0.965624332E+01 IK= 45 K= 0.440009862 DET=-0.974796009E+01 IK= 46 K= 0.450009853 DET=-0.980972481E+01 IK= 47 K= 0.460009843 DET=-0.984134007E+01 IK= 48 K= 0.470009834 DET=-0.984280968E+01 IK= 49 K= 0.480009824 DET=-0.981437588E+01 IK= 50 K= 0.490009815 DET=-0.975646782E+01 IK= 51 K= 0.500009835 DET=-0.966974449E+01 IK= 52 K= 0.510009825 DET=-0.955502701E+01 IK= 53 K= 0.520009816 DET=-0.941332340E+01 IK= 54 K= 0.530009806 DET=-0.924582672E+01 IK= 55 K= 0.540009797 DET=-0.905389309E+01 IK= 56 K= 0.550009787 DET=-0.883899975E+01 IK= 57 K= 0.560009778 DET=-0.860278797E+01 IK= 58 K= 0.570009768 DET=-0.834698105E+01 IK= 59 K= 0.580009758 DET=-0.807337475E+01 IK= 60 K= 0.590009749 DET=-0.778394413E+01 IK= 61 K= 0.600009739 DET=-0.748061848E+01 IK= 62 K= 0.610009730 DET=-0.716545582E+01 IK= 63 K= 0.620009720 DET=-0.684048843E+01 IK= 64 K= 0.630009711 DET=-0.650777817E+01 IK= 65 K= 0.640009701 DET=-0.616940308E+01 IK= 66 K= 0.650009692 DET=-0.582738781E+01 IK= 67 K= 0.660009682 DET=-0.548372889E+01 IK= 68 K= 0.670009673 DET=-0.514038563E+01 IK= 69 K= 0.680009663 DET=-0.479923773E+01 IK= 70 K= 0.690009654 DET=-0.446207523E+01 IK= 71 K= 0.700009644 DET=-0.413061285E+01 IK= 72 K= 0.710009634 DET=-0.380645823E+01 IK= 73 K= 0.720009625 DET=-0.349108815E+01 IK= 74 K= 0.730009615 DET=-0.318586063E+01 IK= 75 K= 0.740009606 DET=-0.289202237E+01 IK= 76 K= 0.750009596 DET=-0.261065626E+01 IK= 77 K= 0.760009587 DET=-0.234271193E+01 IK= 78 K= 0.770009577 DET=-0.208899641E+01 IK= 79 K= 0.780009568 DET=-0.185015452E+01 IK= 80 K= 0.790009558 DET=-0.162669408E+01 IK= 81 K= 0.800009549 DET=-0.141897297E+01 IK= 82 K= 0.810009539 DET=-0.122718787E+01 IK= 83 K= 0.820009530 DET=-0.105140173E+01 IK= 84 K= 0.830009520 DET=-0.891532707E+01 IK= 85 K= 0.840009511 DET=-0.747362232E+01 IK= 86 K= 0.850009501 DET=-0.618543196E+01 IK= 87 K= 0.860009491 DET=-0.504606724E+01 IK= 88 K= 0.870009482 DET=-0.404968643E+01 IK= 89 K= 0.880009472 DET=-0.318940544E+01 IK= 90 K= 0.890009463 DET=-0.245738339E+01 IK= 91 K= 0.900009453 DET=-0.184492910E+01 IK= 92 K= 0.910009444 DET=-0.134260845E+01 IK= 93 K= 0.920009434 DET=-0.940354538E+01 IK= 94 K= 0.930009425 DET=-0.627586460E+01 IK= 95 K= 0.940009415 DET=-0.393321848E+01 IK= 96 K= 0.950009406 DET=-0.226293993E+01 IK= 97 K= 0.960009396 DET=-0.115068686E+01 IK= 98 K= 0.970009387 DET=-0.481595325E+01 IK= 99 K= 0.980009377 DET=-0.141388774E+01 IK= 100 K= 0.990009367 DET=-0.174782121E+01 APPROXIMATION FOR ROOT, K BETWEEN 0.0 AND 1.0 KR(1)= 0.20010E-01 aaa= 0.20010E-01 bbb= 0.30010E-01 EXACT ROOT TO WITHIN 5 SIGNIFICANT FIGURES bbb= 0.29388E-01