Papers by Keyword: Shape Parameter

Abstract: In the study of polydisperse materials, most of the experimental particle size distributions were obtained on bounded intervals. In these cases, it is also desirable to use bounded models with different shapes to simulate the results of studying polydisperse and powder materials. The beta distribution is often used to approximate results due to the fact that this distribution contains many forms for displaying realizations on a limited interval. With the development of computer technology, there has been an increased interest in the use of beta distribution in the modern practice of analyzing results. Meanwhile, there remains a limitation in the use of the beta distribution that is associated with the choice of distribution shape. The possibilities of using known shape measures for mapping beta distribution in this paper is discusses. On the example of the space of shape measure of kurtosis and skewness, the limited use of only probabilistic measures of shapes is illustrated. It is proposed to use the entropy coefficients as an additional informational parameter of the beta distribution shape. On the base of a features comparison of the entropy coefficients for biased and unbiased beta distributions, recommendations for their application are given. By using the example of beta distributions mapping in the space of asymmetry and the entropy coefficient, it is shown that the synergistic combination of probabilistic and informational measures of the shape allows expanding the possibilities of estimating the shape parameters beta distributions. Two methods to display the positions of realizations of beta distributions is proposed. There are trajectories on a constant ratio of shape and realizations position curve on equal values of one parameter. In particular, the features of the choice of beta distributions with negative skewness are discussed.

Abstract: The article shows the process of analyzing and constructing the stiffness matrices for four-node elements in parallelogram and rhombus shapes using the method of potential deformation energy.

Abstract: The process of tube bending involves using mechanical force to push stock material pipe or tubing against a die, forcing the pipe or tube to conform to the shape of the die. For some tube bending processing, a mandrel is placed inside the tube to prevent collapsing. In this study, the elbow bending process using mandrel has been investigated to fabricate precise elbow-shaped tubes. To fabricate tube having target shape within the dimensional tolerance, the process analysis has been performed at various processing parameters such as tube dimensions, tilting angles, curved cutting surface and the radius of curvature. To estimate the dimensional accuracies of formed tubes, the standard deviations of dimensional errors between target and formed tubes have been used as a quantitative index. Results show that the elbow tube having larger radius of curvature shows higher dimensional accuracy due to the relatively uniform strain distribution. And the convex cutting surface is desirable to increase contacts between the punch and the tube ends during the bending process.

Abstract: Meta-modeling is a frequently used tool for analysis of systems' behavior. An original model of the system is often complex and its evaluation is expensive and time-consuming. Therefore it is desirable to execute the original model as few times as possible. A special case is when many evaluation of the model with different input parameters are necessary. Proposed solution is a use of the meta-model, in our case Radial Basis Function Network (RBFN) tool is presented. Here, the output of the meta-model is constructed as a linear combination of the radial basis functions. For good approximation a shape parameter of the radial basis functions has to be set properly. This paper describes a tuning of the shape parameters for several benchmark examples.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: 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.

Abstract: In this paper, a research is performed on the tuning strategy for the shape parameter of the RBF to improve accuracy. The shape parameter is an influential factor for the accuracy but the configuration is commonly based on experience. An algorithm is designed to optimize the shape parameter. Three high-order mathematical benchmarks are used to compare the common RBF and the optimized RBF. This paper shows that the optimized RBF is more accurate for various test functions.