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采用基于一阶剪切变形理论(FSDT)的无网格Galerkin方法分析不同荷载和边界条件下的带加劲肋和无加劲肋的折板弹性弯曲问题。折板由不同平面的板组合而成,这些板的刚度矩阵由无网格法给出。借用有限元概念,将每一块板都视为一个单元,整块板的整体刚度矩阵就可以通过这些单块板的刚度矩阵而得到。加劲板也同样如此,采用无网格法给出加劲板的刚度矩阵。比有限元方法优越的是,在确定板刚度矩阵的时候不需要网格,这意味着在折板或加劲肋位置变化处的大变形或者裂缝发展时,可以避免耗时过长,以及网格重组带来的对精度的影响。为验证此法的精确度和收敛性,本文采用此法及ANSYS对多个数学模型进行计算,结果表明两组结果非常一致。
The meshless Galerkin method based on the first-order shear deformation theory (FSDT) is used to analyze the flexural buckling of stiffened plates with or without stiffeners under different load and boundary conditions. The flaps consist of a combination of different planar plates whose stiffness matrix is given by the meshless method. By borrowing the concept of finite element, considering each panel as a unit, the overall stiffness matrix of the entire panel can be obtained from the stiffness matrix of the individual panels. The same is true of stiffened plates, using the meshless method to give the stiffener stiffness matrix. The advantage over the finite element method is that it does not require a grid when determining the stiffness matrix of the slab, which means that long delays and large deformations or fractures at flaps or stiffeners can be avoided, The impact of reorganization on accuracy. In order to verify the accuracy and convergence of this method, we use this method and ANSYS to calculate several mathematical models. The results show that the two groups are very consistent.