On the effective stiffnesses of corrugated plates of various geometries

The effective (homogenized) stiffnesses of the corrugated plate are calculated by solving the periodicity cell boundary-value problems (BVPs) of homogenization theory using a two-step dimension reduction procedure. The three-dimensional (3-D) periodicity cell BVPs first are reduced to two-dimensional (2-D) problems in the plate cross-sections. Then, provided that the plate is thin, the 2-D elasticity problems are reduced to a BVP for a system of ordinary differential equations (ODEs), similar to the problem of curvilinear beam bending. We solve the 1-D BVPs and obtain some formulas for computation of all effective stiffnesses of the corrugated plate in terms of ODEs solutions. Then, we find similarities between the ODEs solutions and the formulas describing the “intrinsic” geometry of the corrugation curve. By using this similarity, we express the effective stiffnesses of the corrugated plate in terms of the geometric characteristics of its corrugation.