Abstract
圓柱殼及圓球殼結構已廣泛地應用於管路、飛彈、航空器、潛水艇、壓力槽及核能反應器等方面。在不同的使用情況下，常須在殼結構上開孔，並承受各種不同的外力負荷。如此，殼結構可能發生挫曲現象而造成強度降低，甚或不堪使用。對以金屬材料製作之此類殼結構而言，挫曲現象常發生在材料進入塑性變形之後。本文即針對在軸向力及純彎矩作用下之鋁合金圓柱殼，和環狀力作用下之中碳鋼圓球殼，以非線性有限單元分析配合實驗的進行，研究其挫曲及挫曲後行為，並討論多種參數對其挫曲行為及挫曲模態之影響。在程式分析方面，以更新拉格朗治法及虛功原理推導非線性平衡方程式，並以退化殼單元將平衡方程式離散化；同時，配合塑性力學理論，建立疊代型有限單元分析模式，對彈塑性殼結構進行挫曲分析。在求解過程中，採用位移控制法，以避免挫曲點附近之數值發散現象。在實驗方面，建立軸向壓縮及彎矩實驗設備及數據收集系統，以進行挫曲實驗，並記錄殼結構之挫曲現象。此外，亦進行材料拉伸試驗，測定其材料常數以提供分析之用。由分析和實驗結果發現，對金屬類材料而言，必須考慮材料之彈塑性行為，方能正確分析厚殼結構之挫曲行為。而直徑—厚度比、製造不平整、開孔大小及開孔位置等，都會影響殼結構的挫曲行為及挫曲強度。圓柱殼在軸向力作用下，其挫曲模態受到開孔及邊界條件之影響。當圓柱殼沿軸向有厚度不平整之情況時，其軸向挫曲負載會降低，挫曲後之負荷—位移曲線也會改變。而厚度減少、開孔數增加及開孔加大時，軸向挫曲負載亦會降低。圓柱殼在純彎矩作用下，其挫曲模態則受到開孔及製造不平整之影響。當圓柱殼沿軸向或沿圓周方向有半徑不平整之情況時，其彎矩挫曲負載會隨之改變。而當厚度減少、沿軸向有厚度不平整、開孔加大及開孔位置自張力側移向壓力側時，彎矩挫曲負載會降低。對環狀力作用下之圓球殼而言，當直徑—厚度比較大、施力圓環較大及中央圓孔較小等情況下，圓球殼頂端在挫曲後保持鼓起，反之則出現下凹的挫曲模態。而直徑—厚度比及施力圓環加大時，無因次化之挫曲負載會提高。The buckling and postbuckling behavior of elastoplastic shellswas investigated analytically and experimentally. The circularcylindrical shell sconsidered were compressed axially or underpure bending, while the spherical shells considered were underring load. A finite element code based on the updatedLagrangian formulation was established by considering nonlineargeometric and material properties. For circular cylindricalshells under axial load, it was found that the buckling loadwas reduced by variation of initial thickness along the shellaxis. The boundary conditions caused varied postbucklingbehavior. The buckling load decreased as the ratio of diameterto thickness of the shell, size or number of cutout increased.For circular cylindrical shell under pure bending, it was foundthat the bending moment was correlated with ovalization of thecross section of shell. The limiting buckling moment decreasedas the ratio of diameter to thickness increased. The limitingbuckling moment was strongly influenced by the initial ovalityof the cross section and the initial radius variation along theshell axis. The influence of the size and the location of thecutout on the limiting buckling moment is discussed. Forspherical shells under ring load, ring loads of both line andstrip types were examined. The proper dimensionless bucklingload increased as the ratio of diameter to thickness of theshell or the diameter of the ring load increased. Theinfluence of the size of the apical circular cutout on thebuckling load is discussed. Convex and concave modes ofpostbuckling deformation around the apex were obtained inanalysis and observed in experiment for varied combination ofthe size of ring load, diameter of apical cutout, and ratio ofdiameter to thickness of the spherical shells.