基于边光滑有限元法的加筋板静力和自由振动分析

摘要

In this paper,the edge-based smoothed finite element method (ES-FEM) is presented for static and free vibration analysis of stiffened plates.In the ES-FEM model,the edge-based strain smoothing technique (E-SST) is employed to smoothen the original strain field.Due to the softening effect provided by the E-SST,the original overly-stiff FEM model can be properly softened and the stiffness of the obtained ES-FEM model is closer to the exact system stiffness than that of the FEM.Owing to the good adapt ability of the triangular element,a triangular mesh is used to discretize the problem domain.In order to avoid the transverse shear locking caused by the low-order Reissner-Mindlin plate element,the discrete shear gap technique for triangular element (DSG3) is employed here.From several numerical examples,it is demonstrated that the proposed ES-FEM possesses faster convergence property and higher computational efficiency,and can also provide more accurate solutions than the FEM for stiffened plates.%运用边光滑有限元法,研究分析了加筋板结构的静力和自由振动问题.在边光滑有限元法中,将基于边的应变光滑技术用于对原来的应变场进行光滑操作;由于应变光滑技术能够适当地软化原来过刚的有限元模型,从而能够得到更加接近于系统准确刚度的光滑有限元模型;鉴于三角形单元良好的适用性,选用三角形单元对模型进行网格划分;同时,为了解决低阶Reissner-Mindlin板单元弯曲过程中的横向剪切自锁问题,采用了一种新型的离散剪切间隙技术.算例的数值计算结果表明,与传统的有限元法相比,边光滑有限元法能够得到精度更高的计算结果,且收敛更快,计算效率更佳.