A new method of stiffness prediction for periodic beam-like structures

This paper presents a new method for stiffness prediction of periodic beam-like structures based on the selfequilibrium equation of the unit cell. In this method, actual displacements of a composite beam are separated into homogenized displacements and warping displacements. The effective stiffness matrix of a periodic heterogeneous beam is explicitly formulated based on the energy equivalence or the internal force equivalence of the unit cell at both macroscopic and microscopic levels, and it follows that these two approaches are equivalent in essence. In addition, six normalization constraints to determine the unique solution of the selfequilibrium equation of the unit cell are introduced and well elaborated from physical interpretations. Furthermore, a standard finite element formulation for calculating the warping displacements is derived by using the principle of the minimum potential energy. This method can be easily implemented in commercial software Comsol. Finally, numerical comparisons with the results in literature validate the effectiveness and accuracy of the proposed method.

Automated summary

This method presents a new approach for predicting stiffness of periodic beam-like structures based on the selfequilibrium equation of the unit cell. The effective stiffness matrix of a periodic heterogeneous beam is explicitly formulated, and six normalization constraints are introduced to determine the unique solution of the selfequilibrium equation of the unit cell. A standard finite element formulation for calculating warping displacements is derived using the principle of the minimum potential energy.