Accurate boundary element analysis of plate-structures including rib-stiffened components and its applications

本文研究了一种有效的边界元法，用于精确分析由弹性板和双对称横截面肋组成的加筋板。在回顾前人研究的基础上，可以看出，它们可以分为两类：将加筋板近似为各向异性板，并考虑连接条件分别精确建模为板和肋。本文提出的方法属于后者，假定板与肋之间为线接触。迄今为止，对这一问题的数值分析方法有Rayleigh-Ritz法、有限元法、边界元法等，其中大多数方法都采用了将板上的等效剪力和弯矩分别视为肋上的线分布力和弯矩的Reynshenko理论。它们用板挠度表示，因此公式中最多出现板挠度的四阶导数。本文提出了一种新的加筋板的改进模型，将板与筋条之间的相互作用力和力矩视为线分布的未知载荷。在公式的数值实现中，这些力可以使用任何类型的插值函数来近似。详细介绍了配方和计算机代码的开发。计算机代码得到的数值结果进行了讨论，从而证明了所提出的解决方案的程序的有用性。

This study is concerned with development of an efficient boundary element method for accurate analysis of a stiffened plate which is composed of an elastic plate and ribs with doubly symmetrical cross section.Based on a state-of-the-art review of previous investigations, it can be seen that they are classified into the two groups: the stiffened plate is approximated as an anisotropic plate, and precisely modeled as a plate and ribs separately considering connectivity conditions. The method proposed in this paper belongs to the latter one, assuming a line contact between plate and rib. This problem has been so far analyzed numerically using the Rayleigh-Ritz method, FEM, BEM and so on. Most of these methods employ the Timoshenko theory where the equivalent shear force and the bending moment of the plate are considered as the line distributed force and a moment of the rib, respectively. They are expressed in terms of the plate deflection and hence at most fourth-order deriva-tives of the plate deflection appear in the formulation. This is a serious disadvantage of the theory, because at least fourth-order element must be used in numerical implementationA new advanced modeling of rib-stiffened plates is proposed, in which the interactive forces and moments between the plate and the stiffener are treated as line distributed unknown loads. In the numerical implementation of the formulation, these forces can be approximated using any type of interpolation functions. The formulation is presented in detail and a computer code is developed. The numerical results obtained by the computer code are discussed, whereby the usefulness of the proposed solution procedure is demonstrated.