加肋板自由振动的移动最小二乘无单元分析

Moving-least-square meshless analysis on free vibration behavior of ribbed plates

基于移动最小二乘近似,提出一种分析加肋板结构自由振动行为的无网格方法。将加肋板视为平板和肋条的集合,以梁模型来模拟肋条。从板和肋条位移场的移动最小二乘近似出发,先分别建立板和肋条自由振动情况下的势能泛函,再通过引入板和肋条之间的位移协调关系,将两者的势能叠加,建立描述整个加肋板自由振动行为的控制方程。该方法的无网格特性让肋条可以配置在板上的任意位置,而肋条位置的改变也不会像有限元那样导致板网格的重构,应用于加肋板的优化设计中可极大地减轻分析负担。文末通过算例将该方法解与ANSYS软件给出的有限元解及现有文献结果进行比较,验证该方法的准确性。

In order to study the free vibration behavior of ribbed plates,a meshless method based on moving-least-square approximation was proposed.A ribbed plate was considered as a composite structure of plate and ribs which were simulated as beams.The potential energy functional of the plate and those of the ribs were superposed by applying the displacement compatible conditions between them.The governing equation of the entire ribbed plate was then established in accordance with the potential energy functional of the entire structure.The meshless feature of the proposed method allows the ribs to be placed anywhere on the plate,and the remeshing is avoided when the stiffener positions are changd.A large amount of analysis burden is expected to be reduced if the proposed method is extended to the optimization design of ribbed plates.Some selected numerical examples were employed to compare the solutions by the proposed method with those given by ANSYS and existing literatures,which can prove the validity of the proposed method.