A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells.

*(English)*Zbl 1217.74143Summary: A formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method (RPIM). The deflection fields are approximated using the RPIM shape functions which possess the Kronecker delta property for easy impositions of essential boundary conditions. Three types of smoothing domains, which are also serving as the numerical integrations domains, are constructed based on the background three-node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential boundary conditions of rotations are imposed in the process of constructing the curvature field, and the translation boundary conditions are imposed as in the standard FEM. A number of numerical examples, including both static and free vibration analysis, are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures. The results show that the present formulation can obtain very stable and accurate solutions, even for the extremely irregular background cells.

##### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74K20 | Plates |

##### Keywords:

numerical method; meshfree method; generalized smoothed Galerkin weak form; gradient smoothing; radial point interpolation method (RPIM); thin plate
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\textit{X. Y. Cui} et al., Int. J. Numer. Methods Eng. 85, No. 8, 958--986 (2011; Zbl 1217.74143)

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