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

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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.