Radial Basis Function Based On PUM With Applications And Numerical Analysis Of Functionally Graded Plate

This paper mainly consists of two parts:radial basis function based on partition of unity method(RBF-PUM)and analysis of functionally graded(FG)structures.The RBF-PUM is used to investigate 2D elasticity and piezoelectric problems.In FG struc-tures,higher-order shear deformation theory(HOSDT)is used to analysis the bending of functionally graded plate(FGP)with a layer of piezoelectric fiber-reinforced com-posite(PFRC)material and nonlocal elastic theory is used to analysis the in-plane vibration of radial functionally graded annular nano-plate.Based on the partition of unity method and radial basis function interpolation,the RBF-PUM shape function is constructed and some properties are studied.The RBF-PUM shape function inherits all the good properties of the RBF shape function especially for the Kronecker delta function property and thus the essential boundary conditions can be imposed like the FEM and the RBF meshfree method.Unlike the RBF method,the RBF-PUM shape function is constructed using nodes in the patch domain where interpolation point is located and then the partition of unity weight functions are used for global approximation.The RBF-PUM doesn't need to search influence domain any more.The patch domain is not only used for the construction of nodal shape function but also used for the support domain of weight function.In order to insure all patch domains can cover problem domain and its boundary,the patch fill distance multiplied by a nondimensional parameter?_ris used for the patch size.The parameter?_rcan ensure effective coverage and also can ensure enough nodes in each patch domain and numerical precision.The numerical precision is not sensitive to the parameter?_r.Similar to the concept of the element free Galerkin method,the RBF-PUM shape function is used in the Galerkin method and form the partition of unity radial basis function meshfree method.Numerical results are more accurate and have high convergence rate comparing with the RBF results.In the FG structures,based on displacement assumption of continuum theory,the HOSDT is used for bending analysis of the FGP attached with a layer of PFRC material.The governing equations are derived by the principle of minimum potential energy.The Navier's procedure can be used for simply supported FGP based on reasonable assumption for electric potential through the PFRC layer.Some parameters,such as applied voltage,aspect ratio and graded parameter are studied to illustrate the control ability of the PFRC material.The present theory is very effective to predict the deformation of the FGP by comparing with 3D analytical theory and the FEM.In order to investigate small scale effect of micron/nano structures,the Eringen nonlocal elastic theory is used to study in-plane vibration of radial FG annular plate.This theory considers small scale effect and when nonlocal parameter is set to zero causing the nonlocal theory degenerates into the continuum theory.The equilibrium equations and generalized boundary conditions are derived by the Hamilton principle and the differential quadrature method is used to solve equations.Some parameters are studied using numerical examples and it's shown that the nonlocal effect decreases the stiffness of FGP so that the natural frequency decreases.The nonlocal effect is clearer for small outer radius by studying the size of FGP and nonlocal parameter.Moreover,according to the analysis of non-axisymmetry vibration mode,the vibration mode consists of radial and tangential vibration which is the same as the classical mechanics.