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EN
This paper deals with solving interval system of linear equations. The problem is to find a nonnegative algebraic solution. Based on sign function approach and using interval center and radius arithmetic operations, we propose an algorithm for computation of an algebraic interval solution vector. We also discuss fundamental properties of this solution vector, such as existence and uniqueness. Further, the nonnegative solution algorithm has been extended to other signrestricted approach. Numerical examples of interval system of linear equations show efficiency of the algorithms presented.
EN
Present study deals with static analysis of functionally graded (FG) rectangular plates subjected to various possible boundary conditions within the framework of classical plate theory. Material properties of the FG plate are assumed to vary continuously in the thickness direction according to power-law form. The trial functions denoting the transverse deflection of the plate are expressed as simple algebraic polynomials. Uniformly distributed load (UDL) and hydrostatic pressure are considered to be the external mechanical loads. Rayleigh–Ritz method along with mechanical kinematic relations and non-dimensionalization technique are employed in the numerical modeling to obtain the system of linear equations for the pure bending. Here the main objective is to study the effect of aspect ratio and volume fraction of the constituents on numerical factors associated with centroidal deflection, bending moments and normal stresses. New results for these factors are presented after checking the convergence pattern and validation has been done with the available results in special cases.
EN
This paper investigates the numerical solution of uncertain fractional order diffusion equation subject to various external forces. Homotopy Perturbation Method (HPM) is used for the analysis. Uncertainties present in the system are modelled through triangular convex normalised fuzzy sets. A new computational technique has been proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy fractional diffusion equation is converted first to an interval fuzzy fractional differential equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same is solved by HPM symbolically to obtain the uncertain bounds of the solution. Obtained results are depicted in term of plots. Results obtained by the proposed method are compared with existing results in special cases.
EN
This paper uses artificial neural network (ANN) technique for the identification of structural parameters of multistorey shear buildings. First, the identification has been done using response of the structure subject to ambient vibration with interval initial condition. Then, forced vibration with horizontal displacement in interval form has been used to investigate the identification procedure. The neural network has been trained by a methodology so as to handle interval data. This is because, in general we may not get the corresponding input and output values exactly (in crisp form) but we may only have the uncertain information of the data. These uncertain data are assumed in term of interval and the corresponding problem of system identification is investigated. The model has been developed for multistorey shear structure and the procedure is tested for the identification of the stiffness parameters of simple example problem using the prior values of the design parameters.
EN
Gaussian mixture models (GMM) and support vector machines (SVM) are introduced to classify faults in a population of cylindrical shells. The proposed procedures are tested on a population of 20 cylindrical shells and their performance is compared to the procedure, which uses multi-layer perceptrons (MLP). The modal properties extracted from vibration data are reduced into low dimension using the principal component analysis and are then used to train the GMM, SVM and MLP. It is observed that the GMM gives 98% classification accuracy, SVM gives 94% classification accuracy while the MLP gives 88% classification accuracy. Furthermore, GMM is found to be more computationally efficient than MLP which is in turn more computationally efficient than SVM.
EN
The free vibration natural frequencies of specially orthotropic annular elliptic and circular plates are analyzed by the Rayleigh-Ritz method, using two-dimensional boundary characteristic orthogonal polynomials generated following a recurrence scheme as assumed shape functions. The first eight natural frequencies are reported here for various values of aspect ratios of the outer and inner ellipse. Results are given for various boundary conditions at the inner and outer edges of the annular plate. The influence of the material property as it changes from isotropic to orthotropic on the natural frequencies is presented graphically. When the inner hole of the annular plate becomes zero i.e. for rectangular orthotropic full circular and elliptic plates, the results are compared with those that are available in the existing literature, and are found to be in good agreement. Presented results may be used as bench marks for validating those obtained by approximate methods such as the finite element method.
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