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提出了一种研究折板结构非线性弯曲行为的移动最小二乘无网格法。先将折板结构模拟成不同平面上平板的集合体,再基于冯.卡门的大挠度理论,使用一阶剪切变形理论和移动最小二乘近似先分析各平板的几何非线性行为,最后将通过修正的各板的非线性刚度矩阵叠加得到整个折板结构的非线性刚度矩阵,研究整个结构的几何非线性行为。由于摆脱了网格的束缚,该文方法可以避免网格扭曲引起的网格重构问题。文末通过几个算例将该文方法与使用壳单元的ANSYS有限元非线性分析进行对比,发现两者的计算结果接近。
A moving least squares meshless method is proposed to study the nonlinear bending behavior of the folded plate structure. Firstly, the folded plate structure is modeled as an assembly of flat plates on different planes. Based on the large deflection theory of von Karmen, the geometric nonlinear behavior of each plate is first analyzed by using the first-order shear deformation theory and the moving least square approximation. Finally, The nonlinear stiffness matrix of the entire folded plate structure is obtained through the superposition of the modified nonlinear stiffness matrices, and the geometric nonlinear behavior of the whole structure is studied. Due to the shackles of the grid, this method can avoid the problem of grid reconstruction caused by grid distortion. At the end of this paper, several examples are used to compare the proposed method with ANSYS nonlinear analysis using shell elements, and the results of the two methods are close to each other.