折板结构非线性弯曲分析的移动最小二乘无网格法

NONLINEAR BENDING ANALYSIS OF FOLDED PLATE STRUCTURES BY THE MOVING-LEAST SQUARE MESHFREE METHOD

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 square meshfree method to study the nonlinear bending behaviour of folded plate structures is introduced in this paper.A folded plate is simulated as an assembly of flat plates that lie in different planes.Based on von Karman＇s large deflection theory,the first-order shear deformation theory（FSDT） and the moving-least square approximation,the geometric nonlinear behaviour of the flat plates is investigated.By supposing the modified nonlinear stiffness matrices of the flat plates,the nonlinear stiffness matrix of the entire structure is derived and the nonlinear bending problem of the structure can then be solved.Because the constraint from mesh is removed,the proposed method can avoid remeshing due to mesh disorder.Several examples are employed to show the accuracy of the proposed method.The results given by the proposed method are found to be close to those from ANSYS FEM nonlinear analysis using shell elements.