A Simplified analysis of cellular slabs including frame deformation and shear-lag

具有任意位置大孔洞的蜂窝板受弯曲变形和横向剪切变形的影响，同时受框架变形和剪切滞后的影响。框架变形定义为由顶板和底板以及蜂窝板中隔板组成的框架的弯曲变形。虽然有限元法对蜂窝板是有效的，但它需要大容量的计算机，而且计算成本高，耗时长。因此，在设计的初步阶段，采用有限元方法是不实用的。本文提出了一种考虑弯曲变形、横向剪切变形、框架变形和剪切滞后的具有任意位置孔洞的蜂窝板的通用简化方法。通过扩展狄拉克函数，将弯曲刚度和横向剪切刚度的不连续变化视为连续函数。本研究得到以下结果：提出了蜂窝板的一般理论，包括弯曲、剪切随框变形和剪切滞后。这里提出的理论包括Kirchhoff-Love理论和Mindlin Reissner理论，适用于一般板。利用所提出的一般理论，对蜂窝板的静力和动力问题，包括移动问题，提出了简化的分析方法。

Cellular slabs with arbitrarily-positioned large voids are affected by the bending and the transverse shear deformation along with the frame defomation, and shear-lag. The frame defomation is defined as the flexural defomation of frame composed of the top and bottom platelets and of partitions in the cellular plate.Although the finite element method is effective for a cellular plate, it needs a computer of great capacity and is both costy and time-consuming for computation. So, in the preliminary stage of design, the use of the finite element method is not practical. This study presents a general and simplified method for a cellular plate with anbitrarily-positioned voids, in which bending and the transverse shear deformation, along with the frame deformation, and shear-lag are considered. The discomtinuous variation of the bending and transverse shear stiffness is treated as a continuous function by means of the extended Dirac function. The following results of this research are obtained :1. The general theory of cellular plates including the bending, shear along with frame deformation, and shear-lag are proposed. The theory proposed here includes the Kirchhoff-Love theory and Mindlin Reissner theory and is applicable to general slabs.2. The simplified analytical method is presented for the static and dynamic problems including the moving problem of cellular slabs by means of the proposed general theory.