基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...

HIGH-ORDER RIGID-FLEXIBLE COUPLED DYNAMIC MODEL OF ROTATING MINDLIN PLATE BASED ON RADIAL POINT INTERPOLATION METHOD

The radial point interpolation method(RPIM) is proposed for dynamic analysis of rotating hub-Mindlin plates. Considering the shear deformation and non-linear coupling deformation which means the in-plane longitudinal shortening terms caused by transverse deformation, retaining all of the high-order terms related to the non-linear coupling deformation in the kinetic energy, the high-order rigid-flexible coupled(HOC) dynamic model is established via employing Lagrange’s equations of the second kind with floating coordinate system and the first-order shear deformation theory which means Mindlin plate theory. This model can avoid the shear locking issue by constructing high-order shape functions. And it can not only deal with thin plate problems but also thick plate problems. The highorder shape functions can be constructed easily by adding high-order polynomial basic functions in RPIM. The static results show that it is enough to avoid shear locking issue by adding 15 polynomial basic functions for RPIM. The simulation results for dynamic analysis of a rotating hub-rectangular plate are compared with those obtained by using first-order approximation coupled(FOAC) dynamic model and zero-order approximation coupled(ZOAC) dynamic model. The results show that the ZOAC dynamic model can only be applied to the case with low rotating speed because of its theoretical defects(neglecting the non-linear coupling deformation), the FOAC and HOC dynamic models can be applied to both low rotating speed and high rotating speed cases. It also shows the results using HOC are more accurate and have wider scope of application, especially in the situation of large deformation. The results are also compared with those obtained by assumed mode method(AMM) and finite element method(FEM), which shows the accuracy of RPIM. It is also demonstrated that the RPIM as a flexible discrete method has more advantages in the same computational condition and can be extended in the field of multibody system dynamics.