臺灣博碩士論文加值系統

複合材料之應用日廣，對非均向之複材而言，其力學分析繁雜與艱深，非三維彈性理論能完全求得其解。積層複材平板、曲殼等結構，不同纖維方向之各層剛性不同，為此各層之變形位移宜分層設置，即所謂層化（Layerwise），各層產生其獨自之應變與應力，由連體力學觀之，各層介面須保持應力與位移連續，即橫向應力σzz、σyz、σxz，位移u、v、w 須完全相等。在彈性理論中，除計算各項勢能外，本論文位移場以雷建德多項式（Legendre polynomials）展開，並以雷建德多項式滿足各式邊界條件為研究重點，並引用六類拉氏乘子（Lagrange's multipliers），迫使各層介面之橫向應力與位移連續，達到表面三維邊界條件之滿足，而由能量變分，總勢能最小化，完成周邊與表面外力平衡、層間介面連續之目的，經由高低階變數轉換，建立靜態控制方程，再予求分析各項問題。有關平板之自由振動，所得結果與現有文獻之理論及實驗數據互相評比，精確可信，十分合理，可資學術研究之參考，及工程設計分析之採用。

The composite material have been finded ever increasing applications in aerospace, vehicle and marine structures, electronic packaging, armour safety device, and sporting goods. Composites, made of reinforcement fibers and matrix, are anisotropic in mechanical properties. Three-dimensional elasticity is a necessity in a good mechanics analysis. Since the stiffness differs in each direction from layer to layer, layerwise displacements must be assumed, in which stresses and strains are independent in the individual layers from a micro-point of view. However, the transverse stress σzz、σyz、σxz and the 3-D displacements u、v、w must be continue at the layer interfaces. Three-dimensional displacement fields are assumed according to various edge boundary conditions in term of Legendre polynomials. In the linear/nonlinear theories six types of Lagrange's multipliers are used to implement the interlaminar continuity and lateral surface conditions in addition to the various potentials via the augmented 3-D energy variational approach and dynamic governing equations are set up for solutions to the associate problems. The free vibrational of plates are compared well with the exact solutions and experiments in existing literature.

中文摘要 i
ABSTRACT ii
誌謝 iv
目錄 v
表目錄 vii
圖目錄 viii
符號說明 ix
第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 3
1.3 文獻回顧 4
第二章 三維彈性理論 5
2.1 層間連續性 5
2.2 側向表面條件 7
2.3 位移場設置方法 8
2.3.1 完全自由邊界 9
2.3.2 簡支邊界 9
2.3.3 固定邊界 10
2.4 異向積層之應變與應力 11
2.5 應變能 12
2.6 非保守功 13
2.7 表面邊界條件與介面連續條件之虛工 14
2.8 動能 14
2.9 三維能量變分 15
第三章 數值實例與模態分析20
3.1 何謂模態 20
3.2 完全自由邊界振動模態分析 20
3.3 組合邊界振動模態分析 22
3.3.1 正交積層板對厚度的影響 23
3.3.2 角交積層板對厚度的影響 23
第四章 結論與未來研究方向 44
4.1 結論 44
4.2 未來研究方向 45
參考文獻 46

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