本論文主旨在最大化多種邊界條件之積層板的基礎頻率，文中利用有限元素法計算積層板的基礎頻率。就物理上來考量，平板彎曲時其外層板對剛度的影響大於內層板，因此本文乃提出積層板之二段式最佳化設計。第一階段以外層板的疊層角度為設計變數，假設其餘各層為等向性材料；第二階段再用全板N層之纖維角度為設計變數，用微調突變基因演算法對N維空間搜尋，找到最佳的解。除此，此方法亦可應用在最小化承受簡諧激振之複合材料積層板的振幅。
本文舉出數個數值範例，其最佳化的結果與使用簡單基因演算法的結果進行比較，以測試此二段式最佳化法的收斂性與正確性。

The main purpose of this thesis is to maximize the fundamental frequency of composite laminated plates with various boundary conditions. The fundamental natural frequency is evaluated by using the finite element method. Based on the physical consideration that the outer layer has more stiffening effect than the inner layer in the bending of plates, a two-stage optimal design for composite laminated plates is proposed. In the first stage, the fiber orientation angles of the outer layers are taken to be optimization design variables, and the inner layers are assumed to be isotropic materials. In the second stage, the fiber orientation angles of all N layers are taken to be design variables, and the genetic algorithms with fine-tunning mutation is applied to search for the optimal solutions in the N-dimensional space. In addition, the method is applied to minimize the amplitude of composite laminated plates to harmonic excitations. Several numerical examples are illustrated in the thesis. The performance of the proposed two-stage optimization technique on the convergence and the accuracy is tested by comparing the optimal solutions with those using simple genetic algorithms.

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