Transverse shear stiffness of composite honeycomb core with general configuration

Based on the zeroth-order approximation of a two-scale asymptotic expansion , equivalent elastic shear coefficients of periodic structures can be evalu ated via the solution of a local function tau (kl)(ij)(y), and the homogeni zation process reduces to solving the local function tau (kl)(ij)(y) by inv oking local periodic boundary conditions. Then, effective transverse shear stiffness properties can be analytically predicted by reducing a local prob lem of a given unit cell into a 2D problem. In this paper, an analytical ap proach with a two-scale asymptotic homogenization technique is developed fo r evaluation of effective transverse shear stiffness of thin-walled honeyco mb core structures with general configurations, and the governing 3D partia l differential equations are solved with the assumptions of free warping co nstraints and constant variables through the core wall thickness. The expli cit formulas for the effective transverse shear stiffness are presented for a general configuration of honeycomb core. A detailed study is given for t hree typical honeycomb cores consisting of sinusoidal, tubular, and hexagon al configurations, and their solutions are validated with existing equation s and numerical analyses. The developed approach with certain modifications can be extended to other sandwich structures, and a summary of explicit so lutions for the transverse shear stiffness of common honeycomb core configu rations is provided. The lower bound solution provided in this study is a r eliable approximation for engineering design and can be efficiently used fo r quick evaluation and optimization of general core configurations. The upp er bound formula, based on the assumption of uniform shear deformation, is also given for comparison. Further, it is expected that with appropriate co nstruction in the displacement field, the more accurate transverse stiffnes s can be analytically attained by taking into account the effect due to the face-sheet constraints.