基于一阶剪切变形理论和移动最小二乘近似的加肋板屈曲临界荷载求解

CRITICAL BUCKLING LOAD CALCULATION OF RIBBED PLATES BY THE FIRST-ORDER SHEAR DEFORMATION THEORY AND THE MOVING-LEAST SQUARE APPROXIMATION

针对加肋板屈曲临界荷载的求解,提出了一种基于一阶剪切变形理论和移动最小二乘近似的无网格方法。该方法将加肋板的肋条和平板分开考虑,肋条用梁模型来模拟,按照一阶剪切变形理论和移动最小二乘近似给出平板和肋条的无网格近似位移场,再利用板和肋条交界上的位移协调条件推导出将肋条的节点参数转换成板节点参数的公式,最后通过转换公式,将板和肋条的势能叠加,由最小势能原理得到描述整个加肋板线性屈曲行为的控制方程。该文方法相对有限元的优势在于加肋板肋条不必沿网格线布置,即使肋条位置改变也不需要网格重构。文末通过几个算例比较了该文方法解和采用实体单元的ANSYS有限元解,两者较为接近,证明了该文方法的准确性。

In order to obtain the critical buckling load of fibbed plates, a meshfree method based on the first-order shear deformation theory （FSDT） and the moving-least square （MLS） approximation is introduced. The plate and the fibs of a ribbed plate are considered separately and the ribs are simulated with a beam model. The approximated displacement fields of the plate and the fibs are determined according to the FSDT and MLS approximation. Employing the displacement compatible conditions along the interface between the plate and ribs, the formula that transforms the nodal parameters of the ribs to those of the plate is derived. Superposing the potential energy of the plate and fibs, the governing equation for the buckling behavior of the entire fibbed plate is established by the principle of minimum potential energy. Compared with the FEM, the introduced method has such advantages that the ribs need not to be fitted along the mesh lines of the plate and remeshing is avoided if the rib position changes. The solutions given by the proposed method about several numerical examples are compared with those from ANSYS using solid elements. A close agreement has been observed, which proves the validity of the introduced method.