基于周期均匀化理论的瓦楞板等效力学模型研究

Equivalent models for corrugated panels based on periodic homogenization theory

瓦楞板在建筑结构中有广泛应用,在对瓦楞结构进行力学分析及优化设计中,需要高精度的等效模型来简化计算。本文将瓦楞板等效为经典正交各向异性板,并基于复合材料中的周期均匀化理论,建立了瓦楞板的高精度分析模型。本方法基于单周期波纹的几何形状和尺寸以及原始板材(压型成瓦楞板前的原始板材)的刚度特性,给出了等效正交各向异性板的显性刚度表达式;该表达式具有形式简约且精度高的特点,可应用于任何形状的瓦楞结构,具有普适性。

Corrugated pands are widely used in civil engineering. High-precision equivalent model is necessary for the mechanics analysis and optimization. Based on the periodic homogenization theory, a corrugated panel is equivalent to a classic orthotropic plate with high-precision equivalent stiffness properties. This method,which could be used for any corrugation shape,is based on a simplified geometry for a unit-cell, has the stiffness properties of original sheet and shows the universal simply form and very high precision.