多尺度渐近展开方法是分析周期复合材料结构静动力学行为的一种有效方法。对于仅在轴向或者面内具有周期性的梁、板问题，已有工作主要是在三维理论框架下开展的。不同与此，本项目针对周期梁、板问题拟开展如下研究工作：在梁、板理论框架下，求解多尺度渐近展开解并利用双尺度收敛法证明其收敛性和给出严格的误差估计；根据单胞影响函数的性质建立用于求解梁、板单胞问题的周期边界条件和归一化条件；在宏观上将周期梁、板问题等效成均匀的梁、板问题进行求解，细观上通过调整渐近展开阶次和借助高维单胞等方式对宏观解进行修正以提高模拟精度。通过本项目的研究，可望为周期梁、板问题建立一种更加有效的多尺度分析方法，从而为该方法的应用提供更加宽广的力学基础。

The multiscale asymptotic expansion method is an effective way to analyze the static and dynamic behaviors of periodic composite structures. For beam and plate problems with periodicity only in the axial direction or in the plane, the existing work is mainly carried out under the three-dimensional theoretical framework. Taking a different approach, this project intends to carry out the following research work for the periodic beams and plates: obtain the multiscale asymptotic expansion solution under the theoretical framework of beam and plate, prove its convergence by using the two-scale convergence method and give a strict error estimation; establish the periodic boundary conditions and normalization conditions for solving unit cells of beam and plate problems according to the properties of influence functions; solve the equivalent homogeneous beam and plate problems at the macroscopic level, and make some local corrections based on the homogenized solutions by adjusting the asymptotic expansion order and utilizing high-dimensional unit cell to improve the simulation accuracy at the microscopic level. Through the research of this project, it is expected to establish a more effective multiscale analysis method for periodic beam and plate problems, thereby further provide a broader mechanical basis for the applications of this method.