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| 基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析 |
| Bending and natural frequency analysis of variable thickness stiffened plates on non-uniform elastic foundation based on meshless method |
| 投稿时间：2020-06-10 修订日期：2020-09-21 |
| DOI： |
| 中文关键词: 无网格法 弹性地基 加筋板 变厚度 固有频率 |
| 英文关键词:meshless method elastic foundation stiffened plate variable thickness natural frequency |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论，分析了变厚度加筋板在非均匀弹性地基上的弯曲和固有频率问题。首先，用节点对变厚度板和筋条分别进行离散，导出变厚度板和筋条的势能泛函；其次利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数，再将两者的势能泛函进行叠加得到变厚度加筋板的总势能泛函；最后，利用最小势能原理及Hamilton原理分别得到弯曲控制方程与振动控制方程。由于所采用的方法不能直接施加位移边界，故采用完全转换法处理位移边界。文中先计算非均匀弹性地基板、变厚度板的弯曲及固有频率验证方法的有效性；然后对不同非均匀弹性地基上变厚度板和变厚度加筋板进行了计算，并将计算结果与有限元结果进行了对比。结果表明所提出的方法计算所得结果与文献解、有限元结果之间的误差均小于5%，验证了该方法在计算非均匀弹性地基上变厚度加筋板弯曲与固有频率问题的有效性。 |
| 英文摘要: |
| The paper analyzed the bending and frequency problems of ribbed plate on the non-uniform elastic foundation with variable thickness by meshless method based on Moving Least-Squares(MLS) in conjunction with First-order Shear Deformation Theory(FSDT). First, nodes are used to discretize the variable thickness plates and ribs respectively, and the potential energy functional of the variable thickness plates and ribs is derived. Secondly, the displacement coordination conditions between the rib and the variable thickness plate are used to convert the nodal parameters of the rib to the nodal parameters of the plate, and then the potential energy functional of the two are superimposed to obtain the total potential energy functional of the variable thickness stiffened plate. Finally, the governing equations of bending and frequency were acquired using the minimum energy theory and Hamilton theory respectively. The full transformation method was used while the displacement boundary was solved because the method mentioned above cannot apply the boundary condition straightly. Bending and frequency of the variable plate above the non-uniform elastic foundation were validated by comparing the results of literatures. Variable thickness ribbed plate with different parameters were calculated, which was compared with FEM. The conclusion showed that the error between the results of meshless method and FEM and the error between the results of meshless method and literature are both less than 5%, which validate the effectiveness of the meshless method in calculating the bending and frequency of variable thickness ribbed plate above the non-uniform elastic foundation. |
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