弹性地基加肋功能梯度板自由振动分析的无网格法

Meshless method for free vibration analysis of stiffened functionally graded plates resting on elastic foundation

基于一阶剪切变形理论和移动最小二乘近似研究Winkler弹性地基上加肋功能梯度板的固有频率。假设功能梯度板的材料性质沿厚度方向按幂函数连续变化,基于物理中面和移动最小二乘近似分别推导功能梯度板和肋条的动能和势能,再通过引入位移协调条件,建立板和肋条节点参数转换关系,叠加两者的总能量,然后利用Hamilton原理推导加肋功能梯度板自由振动控制方程。采用完全转换法施加边界条件。通过将本文的计算结果与有限元以及文献的结果对比,验证方法的收敛性以及准确性。

Based on the first-order shear deformation theory(FSDT),the natural frequency of a stiffened functionally graded plate resting on a Winkler foundation is studied by moving-least-squares(MLS)approximation meshless method.It is assumed that the material properties of functionally graded plates change continuously in a power function along the thickness direction.The kinetic energy and potential energy of the functionally graded plate and those of its ribs are derived by the physical neutral surface and moving-least-squares approximation,respectively.The total energy of the plate and those of ribs were superposed by applying the displacement compatibility conditions.Then,the equation governing free vibration of the stiffened functionally graded plate is derived by Hamilton principle.The boundary condition is imposed by full transformation method.The convergence and accuracy of the method are verified by comparing the results of this paper with those of the finite element method(FEM)and the published literature.