A simplified analysis of rectangular cellular plates

This paper presents a general analytical method for rectangular cellular plates with arbitrarily-positioned large voids, in which the bending and the transverse shear deformations along with the frame deformation are considered. The frame deformation is defined as the flexural deformation of frame composed of the top and bottom platelets and of partitions in the cellular plate. The discontinuous variation of the bending and transverse shear stiffnesses due to the voids is expressed continuously by the use of a specific function, defined to exist continuously in a prescribed region. The bending stiffness is given by the actual bending stiffness at each point. The transverse shear stiffness per void is given by an equivalent transverse shear stiffness, which is calculated from the stiffness of a frame and partitions, like shear walls surrounding each void, and depends on the shape of each void. The governing equations are formulated by means of Hamilton’s principle. Neglecting the effect of voids, the proposed governing equations reduce to the Mindlin theory. Static and dynamic solutions are obtained by the Galerkin method. The approximate solution for dynamic plates is proposed. The numerical results obtained from the proposed theory for simply-supported and clamped cellular plates show good agreement with results obtained from the finite element method. The theory proposed here includes the Mindlin and Reissner theories, and Takabatake’s theory [Takabatake, H. (1991). Static analyses of elastic plates with voids. Int. J. Solids Structures 28, 17991961 based on the Kirchhoff-Love hypothesis.