I 9 1 11 1.1..................................... 11 1.1.1 (linear transformation) (matrix) (vector)................................. 11 1.1.2 (column vector) (row vector)....... 12 1.1.3.............................. 12 1.1.4............................ 13 1.1.5 (linearly dependent) (rank) (singularity) (Determinant)........................... 14 1.2 (product)........................... 15 1.2.1.............................. 15 1.2.2 (Dyad Product)..................... 16 1.2.3 (Orthogonal Matrix)................. 17 1.2.4 (Inversed Matrix).................... 18 1.3 (Coordinate Transformation) (Similar Transformation) (Congruent Transformation) (Orthogonal Transformation).................................... 18 1.3.1.......................... 18 1.3.2................................. 19 1.4 (Linear Equation)......................... 19 1.4.1 (Gauss Elimination Method)............ 19 1.4.2 (Choleski Method)................... 20 1.5 (Eigenvalue Problem)....................... 20 1.5.1 (Eigenvalue) (Eigenvector).......... 20 1.5.2 (Eigenvalue Problem of Second Order)...... 21 1.6 (Differentiation) (Integration)........... 21 1.6.1.................... 21 1.6.2.................... 21 1.7 (Numerical Method)................ 22 1.7.1............................... 22 3
4 1.7.2............................... 22 2 23 2.1.................................. 23 2.1.1............................... 23 2.1.2.............................. 27 2.2................................ 29 2.2.1.................................. 29 2.2.2................................. 30 2.2.3............................ 31 2.2.4..................... 33 2.2.5 Lagrange............................ 34 2.2.6................................. 36 2.3.......................... 38 2.3.1.................................. 38 2.3.2.............................. 38 2.3.3................................... 38 2.3.4 Ritz.................................. 39 2.3.5 Galerkin............................... 41 2.3.6.................... 43 3 45 3.1................................. 45 3.1.1.......................... 45 3.1.2........................ 46 3.1.3........................ 47 3.2................................. 49 3.2.1........................ 49 3.2.2..................... 50 3.2.3..................... 50 3.2.4............................... 50 3.2.5.............................. 51 3.2.6....................... 53 3.2.7 y = f(x)..................... 55 3.3 Frenet.................................. 56 3.4....................................... 58 3.4.1........................ 58 3.4.2.............................. 60 3.4.3............................... 62
5 3.4.4............................... 63 3.4.5........................ 64 3.4.6 Munier..................... 67 3.4.7.......................... 67 3.4.8.................. 71 3.4.9 Gauss-Codazzi......................... 73 3.5................................... 73 3.6..................................... 74 3.6.1............................... 75 3.6.2............................... 76 3.6.3............................ 77 II 81 4 83 4.1...................................... 83 4.2............................. 84 4.3................................. 86 4.3.1................................... 86 4.3.2............................. 88 4.3.3 Kirchhoff-Love..................... 89 4.4........................ 94 4.4.1 Hooke.............................. 95 4.4.2................ 95 4.4.3............. 96 4.5................................... 97 4.5.1............ 97 4.5.2 Hamilton........... 100 4.6.......................... 105 4.6.1............................. 105 4.6.2............................... 107 4.6.3.......................... 109 4.6.4......................... 111 4.6.5............................... 113 5 115 5.1........................ 115 5.2.............................. 121 5.2.1.................... 121
6 5.2.2.................. 122 5.2.3.............. 123 6 127 6.1........................ 127 6.2.................. 127 6.3 3.......................... 129 6.4....................... 131 6.4.1........................ 131 6.4.2 (Principle of Virtual Work)......... 132 6.4.3..................... 134 6.5..................... 135 7 137 7.1................................. 137 7.2 (discretization)............................. 138 7.2.1.............................. 138 7.2.2............................. 139 7.2.3............................... 142 7.2.4............................... 142 7.2.5................................... 143 7.3..................... 143 7.3.1....................... 143 7.3.2.................... 144 7.3.3 {b} {t}..................... 144 7.3.4................... 145 7.3.5............................... 145 7.3.6................................... 147 7.4 FEM............................. 147 8 149 8.1.......................... 149 8.2................................. 150 8.2.1............... 151 8.2.2 ESO..................... 151 8.3...................... 151 8.3.1........................ 154 8.3.2............................ 154 8.3.3.......................... 154 8.4........................... 154
7 A - 161 A.1....................................... 161 A.2 ε i..................................... 163 A.3 γ ij.................................... 163
8 8.1 1990 [12] analysis chemical analysis 8.1 149
150 \ Œ` Ô ð Í Þ Œ` ó ŽxŽ ðœ d ðœ \ Œ` Ž \ Œ³ \ ð Í \ Œ` Ô n \ «\ ÏŒ` ž Í Ï Í ˆÀ S «Œo Ï «ü µ ³ Fig. 8.1: 8.2 [8] 19 1980 [3] ESO
151 8.2.1 (GA, Genetic Algorithm) (Genetic Plans) Holland [2] Michigan Goldberg [1] GA 8.2 [9, 5, 5, 7, 6] (IA, Immune Algorithm) [13] 8.2.2 ESO CA Cellular Automata 1940 von Neumann CA [14](ADFEM, Autonomous Decentralized Finite Element Method) [4] ESO, Evolutionary Structural Optimization ADFEM ESO 8.3 ESO [10, 11] 8.3
152 ƒ_ƒuƒ ƒœƒa [ Eƒgƒ ƒxƒh [ƒ ª ̃gƒ ƒx ƒvƒ ƒoƒ ƒœƒa [ EƒtƒŒ [ƒ ƒh [ƒ Fig. 8.2: GA
153 Step 1 Step 1 Step 2 Step 2 Step 3 iƒaƒxƒyƒnƒg ä @1 : 2 j Step 3 iƒaƒxƒyƒnƒg ä @1 : 4 j Step 1 Step 2 Step 3 iƒaƒxƒyƒnƒg ä @1 : 8 j Fig. 8.3: ESO
154 8.3.1 von Mises ESO [10] 8.4 ESO 8.3.2 8.5 8.3.3 400m 42m von Mises ESO [10] 8.6 8.4
Fig. 8.4: 155
156 Fig. 8.5:
157 ŠúŒ` Ô ŽxŽ ª B ðžn ß é ƒxƒpƒ ûœüœ` Ô É Ï» ÀŠÔ ûœüœ` Ô É à Ï» ÀŠÔ ûœüœ` Ô ªŒp ± I É Ï» \ ªŽŸ æ É ª» œši ª ¾ Ä É Ì pœ` Ô Fig. 8.6: S \ C[W Fig. 8.7:
158 Fig. 8.8: 8.8 21
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160 [13],,.., Vol. 49B,, 2003. [14],,.., No. 526, pp. 68 76, 1999.