复合材料周期结构数学均匀化方法的一种新型单胞边界条件

Mathematical homogenization method (MHM) is one of the most effective methods for dealing with periodical structures, and its calculation accuracy and efficiency largely depend on the rationality of the unit cell boundary conditions which directly determines the accuracy of influence functions and perturbation displacements.In this paper, the influence function is treated as a virtual displacement firstly, and the real boundary conditions of a unit cell in the structure are obtained.The results show that clamped boundary condition is not fit as a boundary condition of a unit cell for a two-dimensional periodical structure.Secondly, for a two-dimension periodical structure, a super unit cell periodical boundary condition is proposed which effectively improves calculation accuracy of the influence functions and the virtual potential energy functional corresponding to the virtual displacement is proposed to verify the validity of the super unit cell's periodical boundary condition.Finally, numerical analysis is utilized to verify the accuracy of the mathematical homogenization method in the case of a super unit cell boundary condition and the necessity of second-order perturbation is emphasized.