Research On Meshless Local Natural Neighbour Interpolation Method For Free Vibration Analysis Of Moderately Thick Functionally Graded Plate

The meshless local natural neighbour interpolation method is a new numerical method,which is widely used in all engineering fields and applied science.In this paper,the basic principle of meshless local natural neighbour interpolation method and the basic theory of moderate thick functionally graded plate are studied.Then,the natural frequencies in the free vibration are calculated numerically in detail.First of all,the development history,the research status and the research trend of moderately thick functionally graded plates and meshless method are discussed respectively.Then,the equations of motion for moderately thick functionally graded plate are obtained according to the theory of first-order shear deformation.In addition,based on the natural neighbour interpolation method,the local weighted residual method is used to derive the free vibration governing equation of the moderately thick functionally graded plate and obtain the corresponding discrete governing equation.Finally,a large number of computational procedures for the free vibration problem of the functionally graded plate are written.The numerical examples show that the meshless local natural neighbour interpolation method is very effective for free vibration analysis of moderately thick functionally graded plates.The meshless local natural interpolation method is a meshless local Petrov-Galerkin method based on natural neighborhood interpolation.This method has the following advantages: Firstly,this method can take advantage of local Petrov-Galerkin method;Secondly,the natural neighbour interpolation does not involve the complex computation of matrix inversion and require no artificial parameters;Thirdly,the trial functions are constructed by the natural neighbour interpolation,which makes the constructed shape functions possess Kronecker delta property and thus no special techniques are required to enforce the essential boundary conditions;Fourthly,the order of integrands involved in domain integrals is reduced due to the use of threenode triangular FEM shape functions as test functions.