A Consideration on Application of Homogenization Theory to Beam and Plate Structures
Isao SAIKI, Michinori SANO, Akinori Nakajima, Michihiro Kitahara · Journal of Applied Mechanics · 2004
For cellular solids, exploiting its geometrical characteristics, authors have developed macroscopic continuum-microscopic frame multi-scale analysis. The planar cellular solids is subjected to out-of-plane bending as well as membrane loading when they are employed as box gabion or geogrid. In order to take the out-of-plane bending into account, we here develop a multi-scale, i. e. macroscopic thin plate-microscopic frame, method for planar cellular solids. For future extension to a class of nonlinear multi-scale analysis, we here propose a formulation based on the generalized convergence theory. To utilize the convergence theory for fourth order differential equation that is the governing equation of beam and plate, a functional which has deflection and rotation as its independent variable is defined.