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1

2 I (linear transformation) (matrix) (vector) (column vector) (row vector) (linearly dependent) (rank) (singularity) (Determinant) (product) (Dyad Product) (Orthogonal Matrix) (Inversed Matrix) (Coordinate Transformation) (Similar Transformation) (Congruent Transformation) (Orthogonal Transformation) (Linear Equation) (Gauss Elimination Method) (Choleski Method) (Eigenvalue Problem) (Eigenvalue) (Eigenvector) (Eigenvalue Problem of Second Order) (Differentiation) (Integration) (Numerical Method)

3 Lagrange Ritz Galerkin y = f(x) Frenet

4 Munier Gauss-Codazzi II Kirchhoff-Love Hooke Hamilton

5 (Principle of Virtual Work) (discretization) {b} {t} FEM ESO

6 7 A A A.2 ε i A.3 γ ij

7 [12] analysis chemical analysis

8 150 \ 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] [3] ESO

9 (GA, Genetic Algorithm) (Genetic Plans) Holland [2] Michigan Goldberg [1] GA 8.2 [9, 5, 5, 7, 6] (IA, Immune Algorithm) [13] 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

10 152 ƒ_ƒuƒ ƒœƒa [ Eƒgƒ ƒxƒh [ƒ ª ̃gƒ ƒx ƒvƒ ƒoƒ ƒœƒa [ EƒtƒŒ [ƒ ƒh [ƒ Fig. 8.2: GA

11 153 Step 1 Step 1 Step 2 Step 2 Step 3 iƒaƒxƒyƒnƒg : 2 j Step 3 iƒaƒxƒyƒnƒg : 4 j Step 1 Step 2 Step 3 iƒaƒxƒyƒnƒg : 8 j Fig. 8.3: ESO

12 von Mises ESO [10] 8.4 ESO m 42m von Mises ESO [10]

13 Fig. 8.4: 155

14 156 Fig. 8.5:

15 157 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:

16 158 Fig. 8.8:

17 [1] Genetic Algorithms in Search, Optimization and Machine Learning. Addison- Wesley Publishing Company. [2] Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. the MIT Press, Cambridge, Massachusetts, London, England, [3] M. P. Bendsoe and N. Kikuchi. Generating optimal topologies in structural design using a homogenization method. Computational Methods in Applied Mechanics and Engineering, Vol. 71, pp , [4] Y.M. Xie and G.P. Steven. Evolutionary Structural Optimization. Springer-Verlag, [5],.., No. 538, pp , [6],.., No. 555, pp , [7],,.., Vol. 47B, pp. 1 6, [8] [9],.., No. 520, pp , [10],. eso., No. 539, pp , [11],. eso., No. 552, pp , [12]. 5, pp , 40 43, ,

18 160 [13],,.., Vol. 49B,, [14],,.., No. 526, pp , 1999.

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