Generalized Multiquadrics with Optimal Shape Parameter and Exponent for Deflection and Stress of Functionally Graded Plates

2014 ◽  
Vol 709 ◽  
pp. 121-124 ◽  
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao
Keyword(s):  
Genetic Algorithm ◽  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Shape Parameter ◽  
Optimal Shape ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Radial Basis ◽  
Meshless Collocation

Deflection and stress of simply functionally graded plates are calculated by the meshless collocation method based on generalized multiquadrics radial basis function. The generalized multiquadric radial basis function has the shape parameter c and exponent which have the important effect in the accuracy of the approximation. The deflection and stress of simply functionally graded plates are calculated using the generalized multiquadrics with optimal shape parameter and exponent which is optimized by the genetic algorithm.

Inverse Multiquadrics with Optimal Shape Parameter for Stress Analysis of Functionally Graded Plates

2014 ◽  
Vol 1082 ◽  
pp. 383-386
Author(s):  
Yu Liang ◽  
Song Xiang ◽  
Wei Ping Zhao
Keyword(s):  
Genetic Algorithm ◽  
Radial Basis Function ◽  
Stress Analysis ◽  
Basis Function ◽  
Meshless Method ◽  
Shape Parameter ◽  
Optimal Shape ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Radial Basis

Stress of simply functionally graded plates is predicted by the meshless method based on inverse multiquadrics radial basis function. The genetic algorithm is utilized to optimize the shape parameter of inverse multiquadrics radial basis function. The stress of simply functionally graded plates is calculated using the inverse multiquadrics with optimal shape parameter and compared with the analytical results of available literatures.

Vibration of Laminated Composite Plates by Generalized Multiquadrics with Optimal Shape Parameter and Exponent

2014 ◽  
Vol 1082 ◽  
pp. 429-432
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Shape Parameter ◽  
Laminated Composite ◽  
Composite Plates ◽  
Optimal Shape ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Radial Basis ◽  
Meshless Collocation

Meshless collocation method based on generalized multiquadrics radial basis function is used to study the free vibration of simply supported laminated composite plates. The generalized multiquadric radial basis function g=[r2+c2]q has the exponent q and shape parameter c that play an important role in the accuracy of the approximation. Genetic algorithm is utilized to optimize the shape parameter and exponent of generalized multiquadrics radial basis function. The natural frequencies of simply supported laminated composite plates are calculated using the generalized multiquadrics with optimal shape parameter, exponent and compared with the analytical solutions.

A novel local radial basis function collocation method for multi-dimensional piezoelectric problems

2021 ◽  
pp. 1045389X2110572
Author(s):  
Amir Noorizadegan ◽  
Der Liang Young ◽  
Chuin-Shan Chen
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Shape Parameter ◽  
Piezoelectric Medium ◽  
The Finite Element Method ◽  
Mechanical Field ◽  
Radial Basis ◽  
2D And 3D

The local radial basis function collocation method (LRBFCM), a strong-form formulation of the meshless numerical method, is proposed for solving piezoelectric medium problems. The proposed numerical algorithm is based on the local Kansa method using variable shape parameter. We introduce a novel technique for the determination of shape parameter in the LRBFCM, which leads to greater accuracy, and simplicity. The implemented algorithm is first verified with a 2D Poisson equation. Then, we employed LRBFCM in a numerical simulation for 2D and 3D piezoelectric problems involving mutual coupling of the electric field and elastodynamic equations for mechanical field. The presented meshless method is verified using corresponding results obtained from the finite element method and moving least squares meshless local Petrov–Galerkin method. In particular, the 2D piezoelectric problem is verified with an exact solution.

Shape Parameter Optimization of Gaussian Radial Basis Function Using Genetic Algorithm for Natural Frequencies of Laminated Composite Plates

2014 ◽  
Vol 709 ◽  
pp. 153-156
Author(s):  
Guo Qing Zhou ◽  
Wei Ping Zhao ◽  
Song Xiang
Keyword(s):  
Genetic Algorithm ◽  
Radial Basis Function ◽  
Basis Function ◽  
Shape Parameter ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Radial Basis

Natural frequencies of simply supported laminated composite plates are calculated by the meshless global collocation method based on Gaussian radial basis function. The accuracy of meshless global radial basis function collocation method depends on the choice of shape parameter of radial basis function. In present paper, the shape parameter of Gaussian radial basis function is optimized using the genetic algorithm. Gaussian radial basis function with optimal shape parameter is utilized to analyze the natural frequencies of simply supported laminated composite plates. The present results are compared with the results of available literatures which verify the accuracy of present method.

Shape Parameter Optimization of Inverse Multiquadrics Radial Basis Function for Vibration of Laminated Composite Plates

2014 ◽  
Vol 1082 ◽  
pp. 433-436
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Shape Parameter ◽  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Radial Basis

Free vibration of simply laminated composite plates is studied by the global collocation method based on inverse multiquadrics radial basis function. The choice of shape parameter of radial basis function has the important effect on the accuracy of meshless radial basis function collocation method. Genetic algorithm is used to optimize the shape parameter of inverse multiquadrics radial basis function. The natural frequencies of simply supported laminated composite plates are calculated using the inverse multiquadrics radial basis function with optimal shape parameter and compared with the analytical solutions.

scholarly journals The Optimal Shape Parameter for the Least Squares Approximation Based on the Radial Basis Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1923
Author(s):  
Sanpeng Zheng ◽  
Renzhong Feng ◽  
Aitong Huang
Keyword(s):  
Radial Basis Function ◽  
Least Squares ◽  
Basis Function ◽  
Shape Parameter ◽  
Optimal Parameter ◽  
Optimal Shape ◽  
Least Squares Approximation ◽  
Scattered Data Approximation ◽  
Least Squares Problem ◽  
Radial Basis

The radial basis function (RBF) is a class of approximation functions commonly used in interpolation and least squares. The RBF is especially suitable for scattered data approximation and high dimensional function approximation. The smoothness and approximation accuracy of the RBF are affected by its shape parameter. There has been some research on the shape parameter, but the research on the optimal shape parameter of the least squares based on the RBF is scarce. This paper proposes a way for the measurement of the optimal shape parameter of the least squares approximation based on the RBF and an algorithm to solve the corresponding optimal parameter. The method consists of considering the shape parameter as an optimization variable of the least squares problem, such that the linear least squares problem becomes nonlinear. A dimensionality reduction is applied to the nonlinear least squares problem in order to simplify the objective function. To solve the optimization problem efficiently after the dimensional reduction, the derivative-free optimization is adopted. The numerical experiments indicate that the proposed method is efficient and reliable. Multiple kinds of RBFs are tested for their effects and compared. It is found through the experiments that the RBF least squares with the optimal shape parameter is much better than the polynomial least squares. The method is successfully applied to the fitting of real data.

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