矩形加肋板线性弯曲分析的移动最小二乘无网格法

提出了一种求解矩形加肋板线性弯曲问题的移动最小二乘无网格法。将矩形加肋板模拟成平板与肋条组成的复合结构。先基于一阶剪切变形理论,由移动最小二乘近似建立板和肋条的位移场,再利用板与肋条叠合处的位移协调条件,推导肋条与板的节点参数转换方程,最后利用此方程将板与肋条的应变能叠加,推导出整个加肋板的刚度方程。由于本文提出的加肋板无网格模型中不涉及到网格,肋条不必像有限元那样必须沿网格线布置,肋条位置的改变也不会导致板网格的重新划分。文末算例表明由本文方法得到的解与采用实体单元得到的ANSYS有限元解吻合良好,证明了本文方法的准确性。

Bending analysis of rectangular ribbed plates by the moving-least square meshfree method

A moving-least square meshfree method for bending analysis of rectangular ribbed plates is proposed in this paper. A rectangular ribbed plate is considered as a composite structure of a plate and rib(s). Based on the first-order shear deformation theory (FSDT) and the moving-least square approximation,the displacement fields of the plate and rib(s) are established. Employing the displacement compatible condition between the plate and rib(s),an equation that transforms the nodal parameters of the rib(s) to those of the plate is derived. With the help of the equation,the strain energy of the plate and rib(s) can be superimposed to derive the stiffness equation of the entire structure. Because there is no element involved in the meshfree model,the rib(s) need not to be placed along the meshes,as is done in the FEM. Any change of the location of the rib(s) will not lead to the re-meshing of the plate.Numerical examples show good agreement between the solutions given by the proposed method and ANSYS,using solid elements,which proves the validity of the proposed method.