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.

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.

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.

Natural Frequency of Laminated Composite Plates Using a Sinusoidal Theory

2014 ◽  
Vol 709 ◽  
pp. 148-152
Author(s):  
Guo Qing Zhou ◽  
Ji Wang ◽  
Song Xiang
Keyword(s):  
Differential Equations ◽  
Analytical Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Composite Plates ◽  
Simply Supported ◽  
Sinusoidal Shear Deformation Theory

Sinusoidal shear deformation theory is presented to analyze the natural frequencies of simply supported laminated composite plates. The governing differential equations based on sinusoidal theory are solved by a Navier-type analytical method. The present results are compared with the available published results which verify the accuracy of sinusoidal theory.

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.

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.

Buckling of Laminated Composite and Sandwich Plates Using Radial Basis Function Collocations

2015 ◽  
Vol 15 (01) ◽  
pp. 1540002 ◽  
Author(s):  
Sandeep Singh ◽  
Jeeoot Singh ◽  
Karunesh Kumar Shula
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Present Method ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Finite Point ◽  
Optimal Value ◽  
Radial Basis

In this paper, buckling analysis of isotropic, orthotropic, laminated composite and sandwich plates utilizing trigonometric shear deformation theory and meshless method based on the finite point formulation using thin plate, polynomial and inverse multiquadric radial basis function is presented. The convergence of the present method is studied for isotropic and laminated composite plates for different radial basis functions with optimal value of shape parameter. Numerical examples of laminated and sandwich plates subjected to various types of in-plane loads are solved to demonstrate accuracy and applicability of present method. Several new results for variety of composite and sandwich plates are presented. The present results are observed to be in good agreement with those available in literature. The effects of orthotropy ratio of material, span to thickness ratio, number of layers, core thickness and lamination scheme on the critical load of plates are also presented.

Global Gaussian Collocation Method for Free Vibration Analysis of Laminated Composite Plates

2013 ◽  
Vol 785-786 ◽  
pp. 244-247
Author(s):  
Jiang Wu ◽  
Song Xiang
Keyword(s):  
Free Vibration ◽  
Collocation Method ◽  
Present Method ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Composite Plates ◽  
Laminated Composite Plates

In the present paper we used the global Gaussian collocation method and trigonometric shear deformation theory to analyze free vibration of laminated composite plates. Natural frequencies computed by the present method are found to agree well with those from some available published results.

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