Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method
Free Vibration Analysis of Folded Plate Structures by the FSDT Mesh-free Method
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DOI：
10.1007/s00466-006-0070-9
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发表时间：
2007-02
影响因子：
4.1
通讯作者：
L. Peng;S. Kitipornchai;K. Liew
中科院分区：
文献类型：
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作者：
L. Peng;S. Kitipornchai;K. Liew
本文基于一阶剪切变形理论，提出了一种无网格伽辽金法，用于加筋和非加筋折板及板结构的自由振动分析。折叠板或板结构被建模为由平板组成的复合结构。基于无网格法推导了平板的刚度矩阵和质量矩阵。为了避免直接叠加的失败，引入了修改刚度矩阵和质量矩阵的处理。然后，通过叠加修改后的平板刚度和质量矩阵，得到整个折板或板结构的整体刚度和质量矩阵。加筋折板或板结构的分析以类似的方式进行，因为它们被视为加筋和非加筋平板的复合结构。用无网格法给出了加筋平板的刚度矩阵和质量矩阵。由于在推导刚度矩阵和质量矩阵时不使用网格，因此该方法在研究有限元法不可避免地需要重新划分网格的问题时更加灵活。数值算例验证了该方法的准确性和收敛性。结果表明，与其他研究人员和ANSYS的解决方案，已经给出了很好的一致性。
Based on the first-order shear deformation theory, a mesh-free Galerkin method for free vibration analysis of stiffened and un-stiffened folded plates and plate structures is presented in this paper. The folded plate or plate structure is modelled as a composite structure that consists of flat plates. The stiffness and mass matrices of the flat plates are derived based on the mesh-free formulation. To avoid the failure of direct superposition, a treatment is introduced to modify the stiffness and mass matrices. The global stiffness and mass matrices of the entire folded plate or plate structure are then obtained by superposing the modified stiffness and mass matrices of the flat plates. The analysis of the stiffened folded plates or plate structures proceeds in a similar fashion, as they are regarded as composite structures of stiffened and un-stiffened flat plates. The stiffness and mass matrices of the stiffened flat plates are also given by the mesh-free method. As no meshes are used in deriving the stiffness and mass matrices, the proposed method is more flexible in studying problems for which remeshing is inevitable with the finite element methods. Several numerical examples are computed with the proposed method to demonstrate its accuracy and convergence. The results show good agreement with the solutions that have been given by other researchers and ANSYS.