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**The static and free vibration analysis of a nonhomogeneous moderately thick plate using the meshless local radial point interpolation method.**
*(English)*
Zbl 1244.74237

Summary: A meshless local radial point interpolation method (LRPIM) for the bending and free vibration analysis of a nonhomogeneous moderately thick plate is presented in this paper. It uses a radial basis function coupled with a quadratic polynomial basis function as a trail function and a quartic spline function as a test function of the weighted residual method. The shape functions obtained in the trail function have the Kronecker delta function property, and the essential boundary conditions can be easily imposed. The present method is a true meshless method as it does not need any grids and all integrals can be easily evaluated over regularly shaped domains and their boundaries. In computational procedures, variations of material properties in the considered domain are modelled by adopting proper material parameters at Gauss points in integrations. Examples show that results obtained by the presented method are found to agree well with the existing solutions in the literature and with the results obtained by the finite element method, and the presented method has a number of advantages, such as high efficiency, quite good accuracy and easy implementation.

### MSC:

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

74K20 | Plates |

74H45 | Vibrations in dynamical problems in solid mechanics |

### Keywords:

meshless method; nonhomogeneous moderately thick plate; local radial point interpolation method; bending problem; free vibration
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\textit{P. Xia} et al., Eng. Anal. Bound. Elem. 33, No. 6, 770--777 (2009; Zbl 1244.74237)

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### References:

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