A formulation of the multiquadric radial basis function method for the analysis of laminated composite plates

2003 ◽  
Vol 59 (3) ◽  
pp. 385-392 ◽  
Author(s):  
A.J.M. Ferreira
2014 ◽  
Vol 709 ◽  
pp. 153-156
Author(s):  
Guo Qing Zhou ◽  
Wei Ping Zhao ◽  
Song Xiang

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.


2014 ◽  
Vol 1082 ◽  
pp. 433-436
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao

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.


2014 ◽  
Vol 1082 ◽  
pp. 429-432
Author(s):  
Ying Tao Chen ◽  
Song Xiang ◽  
Wei Ping Zhao

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.


2018 ◽  
Vol 34 (3) ◽  
pp. 959-981 ◽  
Author(s):  
Nam Mai-Duy ◽  
Deepak Dalal ◽  
Thi Thuy Van Le ◽  
Duc Ngo-Cong ◽  
Thanh Tran-Cong

2020 ◽  
pp. 112067212090295 ◽  
Author(s):  
Gabor Nemeth ◽  
Laszlo Modis

Purpose: The aim was to assess the postoperative results of a biometric method using artificial intelligence (Hill–radial basis function 2.0), and data from a modern formula (Barrett Universal II) and the Sanders–Retzlaff–Kraft/Theoretical formula. Methods: Phacoemulsification and biconvex intraocular lens implantation were performed in 186 cataractous eyes. The diopters of intraocular lens were established with the Hill–radial basis function method, based on biometric data obtained using the Aladdin device. The required diopters of the intraocular lens were also calculated by the Barrett Universal II formula and with the Sanders–Retzlaff–Kraft/Theoretical formula. The differences between the manifest postoperative refractive errors and the planned refractive errors were calculated, as well as the percentage of eyes within ±0.5 D of the prediction error. The mean- and the median absolute refractive errors were also determined. Results: The mean age of the patients was 70.13 years (SD = 10.67 years), and the mean axial length was 23.47 mm (range = 20.72–28.78 mm). The percentage of eyes within a prediction error of ±0.5 D was 83.62% using the Hill–radial basis function method, 79.66% with the Barrett Universal II formula, and 74.01% in the case of the Sanders–Retzlaff–Kraft/Theoretical formula. The mean- and the median absolute refractive errors were not statistically different. Conclusion: Clinical success was the highest when using the biometric method, based on pattern recognition. The results obtained using Barrett Universal II came a close second. Both methods performed better compared to a traditionally used formula.


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