FEM formulation of homogenization method for effective properties of periodic heterogeneous beam and size effect of basic cell in thickness direction

• The FEM formulation of AH method for periodic beam structures is established.
• The algorithm is simply implemented by using commercial software as a black box.
• Complicated microstructures are modeled with various kinds of elements.
• Size effect in thickness direction is studied and compared with 3D AH method.

This paper applies the asymptotic homogenization method to predict effective properties of periodic heterogeneous beam structures. A improved FEM formulation and algorithm of the unit cell problems is developed. The effective properties are rewritten in terms of the nodal quantities of the FEM model of the unit cell. With this approach, periodic beam structure of complicated microstructure can be modeled by various elements and modeling techniques and solved by using the commercial software as a black box. Numerical examples illustrate the versatility and efficiency of the method. Finally, the size effect of basic cell in thickness direction is studied.