幾何參數對復合材料圓柱殼折減因子的影響

摘要： 對于彈箭體結構中常見的復合材料圓柱殼結構，在計算其軸壓屈曲載荷時需要對理論線性解進行折減，從而彌補實際含缺陷產品與理想的完美結構之間的差別。目前，雖然可以基于非線性有限元分析得到較為精確的折減因子數值，但是折減因子隨結構幾何參數變化而變化的具體規律尚未厘清。針對這一問題，研究當復合材料圓柱殼的長度、半徑、單層厚度等幾何參數的變化對折減因子的影響，發現無論鋪層方式如何，折減因子總是與半徑和單層厚度呈近似線性的正相關，而與結構長度間呈近似線性的負相關。在初始設計階段應用這一結論，可以減少非線性有限元分析的次數，提高設計效率。

關鍵詞： 復合材料；圓柱殼；折減因子；屈曲；有限元分析；幾何參數

中圖分類號： V421.3" " " " 文獻標志碼： A

doi：10.3969/j.issn.2095-1248.2023.02.001

Influence of geometric parameters on knock-down factor of composite cylindrical shells

HE Dan1，2， WANG Yu-long 1

（1. Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and

Simulation，Shenyang Aerospace University，Shenyang 110136，China；

2. Hunan InnoChina Advanced Material Co.，Ltd.，Yueyang 414000，China）

Abstract： Composite cylindrical shells are commonly used in missile and rocket structures.When calculating the axial compression buckling load，the analytical linear solution needs to be knocked down to compensate for the difference between the actual as-built product and the ideal perfect structure.Although the knock down factors can be obtained from nonlinear finite element analysis，the regularity of the knock down factors varying with the structural geometric parameters has not been clarified.To this issue，the influence of the geometric parameters，such as length，radius，and monolayer thickness，on the knock down factors was investigated.It is showed that the knock-down factors are always approximately linear，positively correlated with the radius and monolayer thickness，and approximately linear negatively correlated with the structural height，regardless of the stacking sequence.By applying these conclusions into the primary design phase，the numbers of finite element analysis can be reduced hence the design efficiency can be improved.

Key words： composite；cylindrical shells；knock-down factors；buckling；finite element analysis；geometric parameters

碳纖維增強復合材料圓柱殼廣泛應用于航天運載器結構，其薄壁特性導致其在使用中易于發生軸壓屈曲，需要準確地預測其極限屈曲載荷從而保證結構安全。此類結構對幾何缺陷非常敏感［1-3］，表現為結構軸壓屈曲的實驗值往往顯著低于其理論解析解。結構實際承載能力與理論解之間的比值被稱為折減因子（Knock-down Factor，KDF［4］），因此KDF視為是對結構幾何缺陷敏感性的定量描述［5-6］。

20世紀60年代，NASA基于大量的實驗結果給出了薄壁非加筋/加筋圓柱殼KDF的建議值［5］。進入21世紀后，隨著材料、工藝等技術的不斷進步，人們發現傳統的KDF嚴重低估了結構的承載力，導致結構質量的冗余。……