| 摘要: | 本文係研究同平面邊界受限制而不可移動但非同平面邊界為彈性支撐之有缺陷複合層板在均勻溫度場下之熱挫屈分析。在分析過程中, 採用簡單高階剪力變形複合層板理論, 另將缺陷量考慮在厚板非線性理論之應變-位移關係式中, 並以能量法推導出複合層板受熱而挫屈的統御方程組及邊界條件。簡單高階剪力變形複合層板理論能滿足表面無剪力邊界條件, 因此不需修正係數配合使用。其次應用適合邊界條件的廣義雙重傅立葉級數, 代入無因次化後的統御方程組, 形成一組代數方程組, 而熱挫屈分析即是求解這組方程組具有非零解的最小特徵值, 而此最小特徵值即為複合層板在均勻溫度場下的臨界挫屈溫度。本文將詳細探討複合層板之各種參數如疊層數, 疊層角度, 長寬比, 模數比, 熱膨脹係數比, 缺陷量及非同平面的彈性支撐邊界條件對熱挫屈的影響。經比較, 所得結果與相關文獻成果間有良好的一致性, 因此驗證了簡單高階剪力變形複合層板理論分析的結果合理。此外, 經由複合層板之缺陷量、幾何參數、材料參數及非同平面邊界對熱挫屈溫度的效應的系統化整理與歸納, 將可提供設計者參考而能採用合乎熱挫屈強度的複合層板結構物。
The thermal buckling of an initially imperfect and moderately thick laminated composite plate with in-plane immovable and out-of-plane elastic restrains in a uniform temperature field is studied in the thesis. In the thermal buckling analysis, a simple higher-order shear deformation plate theory is applied and the initial imperfection is considered in the strain-displacement relations accordingly. With the use of energy method, governing equations and boundary conditions for the composite plate are then derived. After the introduction of non-dimensional parameters and the use of double Fourier series displacement functions which satisfy the boundary conditions, a set of non-linear algebra equations is obtained. The thermal buckling temperature can then be found by obtaining the lowest eigen-value of the non-linear equation set. Finally, the effects of various quantities of laminated composite plates, such as number of layers, lamination angles, aspect ratios, thickness- to-length ratios, modulus ratios, thermal expansion coefficients, initial imperfections, and out-of-plane elastically restrained boundary conditions on the thermal buckling are thoughtfully examined. |
