广义周期点阵结构的等效性能均匀化映射方法研究

This paper investigates the homogenization computing of equivalent mechanical properties for generalized periodic lattice structures. A mapping method is proposed for computing the equivalent elastic matrix, equivalent thermal stress coefficients, and thermal expansion coefficients. This method transforms the problem of generalized periodic homogenization into the classical periodic homogenization problem of the square unit cell. The underlying mapping mechanism of the generalized periodic homogenization method is thus revealed and the basic property related to the equivalent properties of the generalized periodic homogenization is highlighted. This method greatly reduces the complexity of the computation and programming. Through typical numerical examples, the differences between the results obtained by the generalized periodic homogenization mapping method, classical periodic homogenization method, and fine-scale finite element method are investigated and compared. The results indicate the strong generality and effectiveness of the proposed mapping method. It demonstrates excellent computational accuracy for static, thermomechanical and dynamic natural frequency problems.