广义周期点阵结构的等效性能均匀化映射方法研究

Homogenization mapping method for equivalent properties of generalized periodic lattice structures

本文研究了广义周期点阵结构等效力学性能的均匀化计算问题,提出了计算等效弹性矩阵、等效热应力系数与热膨胀系数的均匀化映射方法,将广义周期均匀化问题映射转换为正方形单胞的经典周期均匀化问题,以此揭示了广义周期均匀化方法的内在映射机理,阐明了广义周期均匀化等效性能的基本性质.该方法极大降低了计算求解与编程难度.通过典型数值算例,分析比较了广义周期均匀化映射方法、经典周期均匀化方法与精细尺度有限元方法计算结果的差异.结果表明所提出的映射方法普适性与有效性强,对于静力学、热力耦合问题及动力学固有频率问题均具有良好的计算精度.

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.