关键词: 模块化, 子矩阵, 各向异性, 层合板, 屈曲, 有限差分法

Abstract: To obtain the buckling capability of anisotropic laminated plates accurately and efficiently. Firstly, the buckling governing differential equations and the boundary conditions were discretized by the finite difference method (FDM). The idea of modularization was utilized to classify and establish the related coefficient submatrices, which were then combined to a global coefficient matrix. One set of FDM equations was established with the deflection values in the mesh points as the unknown coefficients, and corresponding numerical procedures can be used for different numbers of mesh points and boundary conditions. The simply supported anisotropic laminated plates subjected to uniaxial loading condition was considered as the case study. Comparisons among the proposed FDM results, FEM results and analytical results show that the proposed FDM can get the buckling capability accurately and easily. And the coupled effect of the ply number, the aspect ratio, the ply angle and the stacking sequence on the buckling coefficient were also investigated. The study shows that the buckling coefficient increases first quickly and then slowly with respect to the ply number. The anisotropic laminated plates with aspect ratio less than one show better buckling capability, whereas the aspect ratio increases to some extent, the buckling coefficient is not sensitive to the aspect ratio. Reasonable laying angles can greatly improve the buckling behavior of the laminated plates, the optimal angle of stacking sequence for the symmetrical angle-ply laminated plates is around 60°, and antisymmetric angle-ply laminated plates have better buckling capacity than symmetrical angle-ply laminated plates.

Key words: modularization, submatrix, anisotropic, laminated plates, buckling, FDM