【摘要】 船体外壳基本上是由加筋板构成的 ,这种结构可能由于受面内压力作用而屈曲。为充分利用板的承载能力 ,减轻结构重量 ,有时将板设计得比较薄 ,使其工作于后屈曲状态。对大量的加筋板进行非线性有限元计算是一件非常费时的工作 ,在船体的初步设计阶段这样做很不经济。为此需先分析板的后屈曲特性 ,然后把板按某一折减宽度计入到加筋的剖面中去 ,再对加筋板进行整体屈曲分析。这就需要得到对任意边长比和初挠度均适用的应力和应变之间的显式关系 ,而目前尚缺乏这方面的研究。有鉴于此 ,应用von K rm n大挠度薄板方程 ,对承受单向面内压力、四边简支的有初挠度矩形板进行后屈曲特性分析 (其中挠曲函数取为双傅氏级数展开式的前三项 )。首先对边长比小于等于 2的板进行分析 (初挠度根据已有的大量实测结果取为双傅氏级数的一项 )。将有关变量化为无量纲量 ,以无量纲载荷作为小参数 ,用参数摄动法求解非线性代数方程组 ,得到受压边最大应力与平均压应力之间、平均压应力与平均应变之间的显式函数式。分析了不同边长比和初挠度对矩形板后屈曲特性的影响 ,结果表明初挠度的存在会明显降低板的面内刚度。继而将这些结论推广应用到边长比大于 2的情况。更多还原

【Abstract】 The outer shell of shiphull is basically made up of stiffened plates. Such type of structure may buckle due to in plane compression. For the sake of utilizing the carrying capacity of plates to the utmost and lightening the structure, engineers want the thickness of plate to be as small as possible. Therefore, the plate may be in the state of postbuckling. It is a time consuming work to carry through nonlinear finite element method analysis for a large number of stiffened plates. It is costly for primary design. In order to solve this problem, the postbuckling behavior of plate should be analyzed first. Afterwards, the width of buckled plate can be reduced accordingly. Whereafter, buckled plates can be taken for attached flange of the stiffener, then overall buckling of stiffened plate can be analyzed by linear finite element method. Therefore, the explicit expressions for edge stress, average strain and stiffness of rectangular plate with arbitrary aspect ratio and initial deflection have to be derived. However, such research is scarce up to now. Wherefore, in this paper, the postbuckling behavior of a simply supported rectangular plate with initial deflection loaded along two opposite straight edges is analyzed using von Krmn equations. Firstly, the rectangular plate with the aspect ratio smaller than 2 is analyzed. The first three terms of the double Fourier series are taken as the deflection function. The first term of the double Fourier series is taken as the initial deflection function based on the Kmiecik’s data acquired by measuring a great deal of ship plates in shipyard. Whereafter, the relative variables are transformed to non dimensional variables. Then the non dimensional load is taken as perturbation parameter. Afterward, the non linear algebraic equations generated are solved approximately using a perturbation technique, which facilities the development of explicit expressions for edge stress, average strain and stiffness of rectangular plate with arbitrary aspect ratio. The effect of initial deflection and aspect ratio on the postbuckling behavior is also studied. It is evinced that initial deflection can reduce the in plane stiffness of the plate distinctly. With the concept of "equivalent rectangular plate" and "deflection method" proposed by Ueda, all the results acquired above can be easily spread to the plate with aspect ratio larger than 2.更多还原