对称层合折板结构自由振动分析的移动最小二乘无网格法

Free vibration solving of a symmetrically laminated folded plate with moving-least square meshfree method

提出了一种求解对称层合折板结构自由振动问题的移动最小二乘无网格法。以提出的折板无网格模型为基础,将对称层合折板结构视为由不同平面上对称层合板组成的复合结构。先基于一阶剪切变形理论,由移动最小二乘近似推导出各对称层合板的刚度和质量矩阵,再利用板与板间的位移协调条件,将各板的刚度和质量矩阵叠加得到整个结构的刚度和质量矩阵,推导出描述层合折板结构自由振动行为的控制方程。文末算例表明由该方法得到的解与采用壳单元得到的ANSYS有限元解吻合良好,证明了该方法的准确性。

A moving-least square meshfree method for solution to free vibration of a folded symmetrically laminated plate was proposed here. Employing the meshfree folded plate model proposed by the author, a folded laminated plate was considered as a composite structure of laminates lying in different planes. Based on the first-order shear deformation theory （FSDT） and the moving-least square approximation, the stiffness and mass matrices of laminates were derived and the stiffness and mass matrices of the entire structure were obtained by using displacement compatible conditions among the laminates and superposing the stiffness and mass matrices of all the laminates. The governing equations of free vibration of the folded laminated plate were derived. Because of meshfree characteristic, no mesh was involved to determine the stiffness and mass matrices of the laminates. Hence the troublesome remeshing problems as large deformation of folded laminated plates. Numerical examples solutions given with the proposed method and ANSYS using shell elements. The verified. was removed completely from such showed good agreement between the validity of the proposed method was