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.

瓦楞板的有效（均质）刚度是通过使用两步降维程序求解均质化理论的周期性单元边界值问题（BVP）来计算的。首先将三维（3-D）周期性单元BVP减少为板截面中的二维（2-D）问题。然后，假设板是薄的，则对于常微分方程（ODE）系统，将二维弹性问题简化为BVP，类似于曲线梁弯曲问题。

我们求解一维BVP，并根据ODEs解获得一些公式，用于计算波纹板的所有有效刚度。然后，我们发现ODEs解决方案与描述波纹曲线“内在”几何形状的公式之间存在相似性。通过使用这种相似性，我们根据波纹板的几何特性来表达波纹板的有效刚度。