Preface |
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xiii | |
Acknowledgment |
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xv | |
PART 1 BASIC COMPUTATIONAL TOOLS |
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Linear Systems and Matrices |
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3 | (24) |
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3 | (1) |
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4 | (1) |
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4 | (4) |
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4 | (2) |
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6 | (2) |
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Condition of Matrix Systems |
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8 | (2) |
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Techniques for Matrix Solution |
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10 | (11) |
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10 | (8) |
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18 | (3) |
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Mixed Boundary Conditions |
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21 | (1) |
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22 | (5) |
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22 | (1) |
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22 | (5) |
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27 | (20) |
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27 | (1) |
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28 | (1) |
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28 | (10) |
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Method of Successive Approximations |
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28 | (3) |
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31 | (2) |
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Method of False Position (regula falsi Method) |
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33 | (4) |
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Locally Convergent Methods |
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37 | (1) |
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38 | (3) |
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Matrix Newton-Raphson Method |
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38 | (2) |
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Approximate Jacobian Formulation |
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40 | (1) |
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41 | (6) |
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42 | (1) |
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42 | (1) |
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42 | (5) |
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Approximation, Interpolation, and Curve Fitting |
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47 | (30) |
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47 | (1) |
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47 | (1) |
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48 | (4) |
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52 | (4) |
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Least-Squares Polynomial Fit |
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56 | (4) |
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Least-Squares Chebyshev Polynomial Fit |
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60 | (1) |
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Fourier Series of Discrete Systems |
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61 | (3) |
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64 | (8) |
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64 | (2) |
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66 | (6) |
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72 | (5) |
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73 | (1) |
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74 | (3) |
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77 | (18) |
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77 | (1) |
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77 | (1) |
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Simple Integration Formulas |
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78 | (4) |
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Integration of Cubic Splines |
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82 | (1) |
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Gauss-Legendre Integration |
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83 | (4) |
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Comparison of Methodologies |
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87 | (1) |
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88 | (7) |
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88 | (1) |
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89 | (6) |
PART 2 COMPUTATIONAL TOOLS FOR APPLICATIONS |
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Finite-Difference Techniques |
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95 | (14) |
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95 | (1) |
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95 | (1) |
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96 | (3) |
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Error and Mesh Considerations |
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99 | (2) |
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101 | (5) |
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106 | (1) |
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106 | (1) |
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107 | (2) |
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108 | (1) |
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108 | (1) |
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109 | (22) |
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109 | (1) |
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109 | (1) |
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Initial Increments with a Taylor Series |
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110 | (2) |
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Taylor Series Method for Implicit Systems |
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112 | (1) |
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112 | (4) |
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Euler Forward-Integration Method |
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116 | (3) |
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119 | (3) |
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Optimum Step-Size Considerations |
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122 | (1) |
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123 | (2) |
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125 | (6) |
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126 | (1) |
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126 | (5) |
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Ordinary Differential Equations |
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131 | (14) |
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131 | (1) |
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131 | (1) |
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Iterative Solutions of Boundary-Value Problems |
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132 | (1) |
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Matrix Solutions of Linear Boundary-Value Problems |
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133 | (5) |
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133 | (3) |
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Example in Structural Mechanics |
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136 | (2) |
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Matrix Solutions of Nonlinear Boundary-Value Problems |
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138 | (4) |
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142 | (3) |
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142 | (1) |
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142 | (3) |
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Partial Differential Equations |
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145 | (20) |
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145 | (1) |
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146 | (1) |
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Classification of Partial Differential Equations |
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146 | (1) |
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Modeling of Partial Differential Equations |
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147 | (1) |
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Example in Heat Conduction |
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148 | (5) |
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Example in Structural Mechanics |
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153 | (7) |
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160 | (5) |
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160 | (1) |
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160 | (5) |
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Energy Methods and Minimization |
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165 | (24) |
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165 | (1) |
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166 | (1) |
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167 | (3) |
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170 | (2) |
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Examples in Structural Analysis |
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172 | (3) |
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175 | (2) |
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Heat Transfer Formulations |
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177 | (4) |
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181 | (8) |
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182 | (1) |
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182 | (7) |
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189 | (26) |
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189 | (1) |
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189 | (1) |
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Philosophy of Element Selection |
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190 | (1) |
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Structural Finite-Element Analysis |
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191 | (9) |
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Other Structural Finite-Element Method Approximations |
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200 | (3) |
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Finite-Element Structural Example |
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203 | (2) |
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Thermal Finite-Element Analysis |
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205 | (4) |
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209 | (1) |
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210 | (5) |
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210 | (1) |
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210 | (1) |
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211 | (4) |
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Dynamic Methods in Applied Mechanics |
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215 | (20) |
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215 | (1) |
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215 | (1) |
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216 | (6) |
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Modal Extraction by Lumped Parameters |
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222 | (1) |
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Modal Extraction by Finite Elements |
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223 | (3) |
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Dynamic Analysis by Finite-Element Methods |
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226 | (2) |
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228 | (7) |
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229 | (1) |
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229 | (1) |
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229 | (6) |
PART 3 ADVANCED COMPUTATIONAL TOOLS |
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Method of Characteristics |
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235 | (20) |
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235 | (1) |
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236 | (1) |
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Classification of Partial Differential Equations |
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236 | (3) |
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Investigations in Engineering |
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239 | (1) |
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Applications in Structural Analysis |
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240 | (8) |
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240 | (4) |
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Discontinuities in the Variables |
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244 | (4) |
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Application in Fluid Mechanics |
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248 | (2) |
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250 | (5) |
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250 | (1) |
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250 | (1) |
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250 | (5) |
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255 | (18) |
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255 | (1) |
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256 | (1) |
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257 | (7) |
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Dynamic Analysis of a Spherical Cavity |
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260 | (2) |
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Dynamic Analysis of a Timoshenko Beam |
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262 | (2) |
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Control Volume Analysis in Fluid Flow |
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264 | (4) |
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268 | (5) |
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268 | (1) |
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269 | (1) |
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269 | (4) |
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Biomechanical Applications |
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273 | (20) |
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273 | (1) |
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Analysis of Orthodontic Appliances |
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273 | (3) |
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Prediction of Tooth Movement |
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276 | (12) |
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Orthopedic Applications of the Finite-Element Method |
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288 | (2) |
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290 | (3) |
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291 | (2) |
Index |
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293 | |