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 軸對稱殼在很多工程中得到廣泛的應用，實際上它是一種軸對稱體，只是 厚度尺寸和其它軸對稱體之尺寸(例如曲率半徑)比較起來很小。如果利用 軸對稱體有限元素法對它進行分析，將遇到兩方面的問題:一是經濟方面 的，因為軸對稱實體元要求不同方向尺寸相差不應過大，而殼體結構厚度 方向尺寸很小，勢必要求在它的子午線方向劃分很多元素，結果導致計算 不必要之增加，另一是數值計算方面的，因為厚度方向和子午線方向之剛 度相差太大，使求解方程組病態，從而導致計算精度的劇烈下降。基於上 述原因，為了充分了解軸對稱殼體之力學分析，本文建立五種軸對稱殼元 素:(1)兩節點直線形之古典軸對稱殼有限元素法(2)兩節點直線形之 Mindlin軸對稱殼有限元素法(3)三節點曲線形之Mindlin軸對稱殼有限元 素法(4)兩節點直線形之超參數軸對稱殼有限元素法 (5)三節點曲線形之 超參數軸對稱殼有限元素法。本文除了探討軸對稱殼體之靜力分析外,又 完成了自由振動分析與臨界挫屈載重分析,以期進一步了解軸對稱殼體之 力學行為。
 The axisymmetric shell is frequently applied in the indu- stry, such as the pressure vessel, the cooling tower, et al. Actually, the axisymmetric shell is a kind of axisymmetric solid with much smaller thickness than the other dimensions ( for example the curvarures). There are two drawbacks for the axisymmetric solid finite elements, the first one is due to the economic consideration. The dimensions of the solid elem- ent should be in the same order for the accuracy requirement. However, the much smaller thickness will require a fine mesh in the ---- direction, and then the computation becomes a la- rge amount of work. The other consideration is due to the nu- merical accuracy. The stiffness through thickness is much st- iffer than that along the ---- direction,i.e, the global sti- ffness will be ill-conditioned. The accuracy is therefore not assured. In the present thesis, five axisymmetric shell elements are developed to investigate the analysis of axisymmetric sh- ell. They are two-node linear classical axisymmetric shell element, two-node linear Mindlin axisymmetric shell element, three-node curved Mindlin axisymmetric shell element,two-node linear degenerated axisymmetric shell element, and three- node curved degenerated axisymmetric shell element. A series of benchmark problems are proposed to illustrat- ed the performance of the axisymmetric shell elements. Accur- ate results and fast convergence are obtained. The reliabili- ty and efficiency are also shown in the benchmark tests. To further study the structural bevaviors of the axisymmetric shell, the free vibration and critical buckling load analysis are also provided for the classical axisymmetric shell elem- ent. Excellent results are presented.
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 1 密閉薄殼圓筒強度設計方法之研究

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