| Preface |
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xvi | |
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Single Degree of Freedom System - I |
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1 | (19) |
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1 | (1) |
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2 | (1) |
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2 | (1) |
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Single degree of freedom system |
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2 | (2) |
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Mathematical study of the SDOF system |
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4 | (1) |
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Influence of gravitational forces |
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5 | (1) |
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Solution of the differential equation |
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5 | (2) |
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Solution to the free vibration problem |
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7 | (1) |
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8 | (1) |
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Units used in dynamic analysis |
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9 | (1) |
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9 | (1) |
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9 | (2) |
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9 | (1) |
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10 | (1) |
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11 | (1) |
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11 | (1) |
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12 | (1) |
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13 | (2) |
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Summary of free vibration analysis |
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15 | (1) |
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Systems subjected to harmonic excitation |
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15 | (1) |
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Dynamic magnification factor |
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16 | (2) |
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17 | (1) |
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Response to base excitation |
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18 | (2) |
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Single Degree of Freedom System - II |
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20 | (30) |
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20 | (1) |
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20 | (1) |
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Laplace transform: examples |
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21 | (1) |
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Inverse Laplace transform |
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21 | (1) |
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Inverse Laplace transform: examples |
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21 | (1) |
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Laplace transform of derivatives |
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22 | (1) |
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Solution of differential equations |
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23 | (1) |
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23 | (4) |
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24 | (1) |
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24 | (2) |
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26 | (1) |
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27 | (1) |
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General solution of Duhamel integral |
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28 | (2) |
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Solution of Duhamel integral: specific examples |
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30 | (7) |
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30 | (1) |
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Rectangular impulse loading |
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31 | (2) |
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Triangular impulse loading |
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33 | (3) |
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Exponentially decaying force |
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36 | (1) |
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37 | (3) |
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37 | (1) |
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38 | (2) |
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Numerical evaluation of Duhamel integral |
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40 | (3) |
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43 | (3) |
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46 | (1) |
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Earthquake response spectra |
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46 | (4) |
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Introduction to Multiple Degree of Freedom Systems |
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50 | (34) |
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50 | (2) |
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52 | (13) |
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53 | (2) |
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55 | (1) |
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55 | (1) |
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Eigen-values of [ K-ω2 M]: examples |
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56 | (3) |
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Eigen-vectors of [ K-ω2 M] |
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59 | (6) |
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General and special eigen-value problems |
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65 | (2) |
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Conversion from general to special eigen-value problem |
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66 | (1) |
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Properties of eigen-values and eigen-vectors |
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67 | (5) |
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67 | (1) |
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Orthogonal property of eigen-vectors |
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68 | (2) |
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Arbitrary vector in terms of eigen-vectors |
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70 | (2) |
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Mode superposition method |
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72 | (8) |
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72 | (1) |
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Undamped forced response: Example |
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73 | (1) |
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Square root of the sum of the squares approximation |
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74 | (2) |
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76 | (1) |
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Damped forced response: Example |
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77 | (3) |
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Response to base acceleration |
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80 | (4) |
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Earthquake participation factors: Example |
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81 | (3) |
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84 | (23) |
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84 | (1) |
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84 | (1) |
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85 | (5) |
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Solution of simultaneous equations by Cholesky decomposition |
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86 | (2) |
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Converting a general to a special eigen-value problem |
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88 | (2) |
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90 | (3) |
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Solution of simultaneous equations by Crout decomposition |
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92 | (1) |
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Gaussian elimination method |
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93 | (4) |
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Gaussian elimination method: example |
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95 | (2) |
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97 | (1) |
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Determinant from Gaussian elimination |
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97 | (1) |
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Determinant from Cholesky factorisation |
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97 | (1) |
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Efficient storage schemes |
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98 | (3) |
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98 | (1) |
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98 | (3) |
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101 | (6) |
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101 | (1) |
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102 | (2) |
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104 | (3) |
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Solution Methods for the General Eigen-Value Problem |
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107 | (67) |
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107 | (1) |
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107 | (5) |
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Forward iteration: example |
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109 | (3) |
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Inverse iteration and higher frequencies |
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112 | (2) |
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Gram-Schmidt method of orthogonalisation |
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112 | (2) |
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Calculation of higher frequencies |
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114 | (3) |
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Calculation of higher frequencies: example |
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114 | (3) |
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117 | (1) |
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117 | (5) |
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118 | (2) |
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Higher frequencies and shift technique |
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120 | (2) |
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122 | (1) |
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Jacobi diagonalisation of the general eigen-value problem |
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123 | (9) |
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Calculation procedure for the Jacobi method |
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126 | (1) |
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General Jacobi method: example |
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126 | (4) |
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Determination of eigen-vectors |
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130 | (2) |
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Lanczos method of tri-diagonalisation |
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132 | (10) |
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Lanczos method of tri-diagonalisation: example |
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135 | (3) |
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Comments on convergence of Lanczos method |
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138 | (3) |
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Selective orthogonalisation |
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141 | (1) |
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142 | (10) |
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Interleaving of eigen-values: example |
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146 | (1) |
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Sturm sequence property and sign counts |
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147 | (3) |
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150 | (1) |
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Isolating a specific eigen-value by root bisection |
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151 | (1) |
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152 | (5) |
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QR factorisation: example |
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154 | (3) |
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Gerschgorin limits on eigen-values |
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157 | (1) |
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Gerschgorin limits: example |
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157 | (1) |
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158 | (16) |
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159 | (6) |
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165 | (4) |
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169 | (5) |
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Solution of Large-Scale Eigen-Value Problems |
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174 | (39) |
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174 | (1) |
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Simultaneous iteration method |
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174 | (12) |
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174 | (3) |
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Implementation of the simultaneous iteration method |
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177 | (2) |
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Example of the simultaneous iteration method |
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179 | (7) |
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Subspace iteration method |
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186 | (9) |
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186 | (3) |
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Implementation of the subspace iteration method |
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189 | (2) |
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Subspace iteration method: example |
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191 | (4) |
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195 | (3) |
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Superposition of Ritz vectors |
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195 | (1) |
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Generation of Ritz vectors |
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196 | (1) |
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Generation of Ritz vectors: example |
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196 | (2) |
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198 | (3) |
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Generation of Lanczos vectors: example |
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199 | (1) |
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200 | (1) |
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201 | (12) |
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201 | (6) |
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207 | (6) |
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213 | (43) |
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213 | (1) |
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Bar element: differential equation |
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213 | (3) |
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Natural frequency and mode shapes of bar element |
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216 | (2) |
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Beam element: flexural deformations only |
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218 | (3) |
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Natural frequency and mode shapes of beam element |
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221 | (4) |
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Simply supported beam: mode shapes |
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221 | (2) |
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Cantilever beam: mode shapes |
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223 | (2) |
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Standards results for beam vibration |
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225 | (1) |
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Beam element with shear deformation included |
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225 | (3) |
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Effect of axial load on natural frequency of beams |
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228 | (3) |
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231 | (3) |
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Approximate shape functions and stiffness coefficients |
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234 | (1) |
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Approximate dynamic stiffness matrix for a bar element |
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234 | (2) |
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Derivation of approximate dynamic stiffness matrix |
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236 | (1) |
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Method of minimum total potential |
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237 | (14) |
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Approximate bar element dynamic stiffness matrix |
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237 | (2) |
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Approximate beam element dynamic stiffness matrix including flexural deformation only |
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239 | (3) |
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Approximate beam element dynamic stiffness matrix including flexural and shear deformations |
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242 | (7) |
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Approximate beam-column element dynamic stiffness matrix |
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249 | (2) |
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Approximate dynamic stiffness matrix of a shaft element |
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251 | (1) |
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Galerkin's weighted residual method |
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251 | (5) |
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Undamped free longitudinal vibrations |
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252 | (1) |
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Undamped free flexural vibrations including bending deformations only |
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253 | (3) |
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256 | (42) |
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256 | (1) |
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Summary of results from the Theory of Elasticity |
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256 | (3) |
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257 | (1) |
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Strain-stress relationship |
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257 | (1) |
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Stress-strain relationship |
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258 | (1) |
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258 | (1) |
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Strain-displacement relationship |
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258 | (1) |
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Equilibrium equations in terms of displacements |
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258 | (1) |
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A plane stress rectangular element: shape functions |
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259 | (2) |
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Galerkin's weighted residual method |
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261 | (4) |
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Integrals of shape functions |
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264 | (1) |
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Explicit K and M matrices |
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265 | (1) |
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Derivation of K and M matrices by minimisation of total potential |
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265 | (2) |
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265 | (1) |
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Loss of potential by external loads |
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265 | (1) |
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Loss of potential by inertial forces |
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266 | (1) |
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267 | (1) |
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Concept of mapping and isoparametric elements |
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267 | (7) |
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Change of variables and implicit functions |
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271 | (2) |
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Cartesian derivatives of shape functions |
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273 | (1) |
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Numerical integration by Gaussian quadrature |
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274 | (2) |
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Evaluation of K and M matrices of isoparametric elements |
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276 | (2) |
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In-plane quadratic isoparametric element |
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278 | (1) |
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Summary of results from the Theory of Thin Plates |
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278 | (3) |
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279 | (1) |
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Moment-curvature relationship |
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279 | (1) |
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280 | (1) |
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Equations of equilibrium in terms of displacements |
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280 | (1) |
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Frequencies of vibration of a simply supported plate |
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280 | (1) |
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A Kirchoff rectangular plate-bending element: shape functions |
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281 | (4) |
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Conditions that displacement functions must satisfy |
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285 | (1) |
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Galerkin's weighted residual method |
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285 | (5) |
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Derivation of K and M matrices by minimisation of total potential |
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290 | (2) |
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290 | (1) |
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Loss of potential by external loads |
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290 | (1) |
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Loss of potential by inertial forces |
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291 | (1) |
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291 | (1) |
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A conforming rectangular thin plate element |
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292 | (1) |
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Mindlin-Reissner isoparametric quadratic thick plate-bending element |
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292 | (3) |
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Isoparametric quadratic flat shell element |
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295 | (1) |
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296 | (2) |
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298 | (23) |
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298 | (1) |
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Bending finite strip with simply supported ends |
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298 | (4) |
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In-plane finite strip with simply supported ends |
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302 | (3) |
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Auxiliary nodal line technique |
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305 | (5) |
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Thin plate-bending strip with an auxiliary nodal line |
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306 | (2) |
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In-plane strip with an auxiliary nodal line |
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308 | (2) |
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Mindlin-Reissner plate-bending finite strip |
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310 | (3) |
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Cubic spline strip method |
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313 | (6) |
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313 | (2) |
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315 | (1) |
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Incorporation of boundary conditions |
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316 | (3) |
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K and M matrices for cubic spline finite strip |
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319 | (2) |
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In-plane cubic spline finite strip |
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319 | (1) |
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Cubic spline plate-bending finite strip |
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319 | (2) |
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321 | (16) |
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321 | (1) |
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Member axis stiffness matrix of line elements |
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321 | (2) |
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Member axis stiffness matrix of finite elements |
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323 | (1) |
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323 | (1) |
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Plate-bending finite elements |
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323 | (1) |
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Flat shell finite elements |
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323 | (1) |
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Member axis stiffness matrix of finite strip elements |
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324 | (1) |
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Member axis to global axis stiffness matrix |
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324 | (6) |
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Two-dimensional pin-jointed member |
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324 | (1) |
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Two-dimensional rigid-jointed member |
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325 | (2) |
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327 | (1) |
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328 | (2) |
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Structural stiffness matrix |
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330 | (4) |
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Automatic assembly of structural stiffness matrix |
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334 | (2) |
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336 | (1) |
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337 | (23) |
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337 | (1) |
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Direct numerical integration |
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337 | (9) |
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Linear acceleration method |
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338 | (1) |
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339 | (5) |
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344 | (1) |
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The central difference method |
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345 | (1) |
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Explicit and implicit integration schemes |
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346 | (1) |
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Stability of integration schemes |
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346 | (1) |
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Accuracy of integration schemes |
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347 | (1) |
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347 | (2) |
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Non-linear analysis: the Wilson-θ method |
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347 | (1) |
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Non-linear analysis: Newmark method |
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348 | (1) |
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349 | (1) |
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349 | (11) |
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349 | (5) |
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354 | (3) |
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357 | (3) |
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360 | (74) |
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360 | (1) |
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Terminology used in the programs |
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360 | (1) |
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Subroutines for data input |
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361 | (3) |
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361 | (1) |
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362 | (1) |
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363 | (1) |
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Subroutines to determine the size of stiffness matrix |
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364 | (3) |
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364 | (1) |
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365 | (1) |
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365 | (2) |
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Subroutines for Cholesky factorisation |
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367 | (2) |
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367 | (1) |
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Subroutine Backsub (A,B,C) |
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368 | (1) |
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Subroutine Forwsub (A,B,C) |
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369 | (1) |
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Stiffness matrices of line elements |
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369 | (4) |
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370 | (1) |
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371 | (2) |
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Consistent mass matrices of line elements |
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373 | (6) |
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373 | (1) |
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374 | (2) |
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376 | (3) |
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379 | (5) |
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379 | (5) |
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Subroutines for Sturm sequence check |
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384 | (3) |
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384 | (1) |
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385 | (2) |
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387 | (3) |
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Finite element analysis: plate bending |
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390 | (7) |
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390 | (7) |
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397 | (3) |
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Subroutines for direct integration |
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400 | (7) |
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400 | (1) |
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401 | (1) |
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402 | (1) |
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402 | (1) |
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403 | (3) |
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406 | (1) |
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407 | (1) |
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Finite strip method: plate bending |
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407 | (5) |
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407 | (2) |
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409 | (3) |
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412 | (12) |
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412 | (1) |
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413 | (1) |
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414 | (6) |
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420 | (4) |
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424 | (4) |
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Data preparation for programs |
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428 | (6) |
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Data input to program Frasim.F90 |
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428 | (3) |
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Data input to program Dplsim.F90 |
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431 | (1) |
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Data input to program Splnsim.F90 |
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431 | (2) |
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Data input to program Frastep.F90 |
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433 | (1) |
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Data input to program Dplstep.F90 |
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433 | (1) |
| Selected References |
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434 | (3) |
| Index |
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437 | |
