Homogenization of thin structured sheet metals by using FEM

Abstract

Thin structured sheet metals promise high potential concerning lightweight design in industrial applications regarding the classical mechanical engineering and vehicle construction as well as the aeronautics. Compared to flat, unstructured sheet metals the component stiffness and buckling behavior can significantly be improved by structuring especially in out of plane direction. To be able to calculate the elastic behavior of large structures from structured sheet metals a mechanical surrogate model is developed which describes effectively average material parameters based on processes of homogenization. For the surrogate properties symmetry and antisymmetry boundaries and periodic boundaries respectively are contemplated on elementary cells whose structural mechanical behavior is decisive. By using an energetic approach [3] the stiffnesses of large plate and shell structures can be determined by a cooperatively small amount of finite elements. By means of these material properties elastic behavior can easily be calculated. With it an efficient numerical design is guaranteed. This explained analysis can be applied to other periodically built up plate structures.