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With the advancements of numerical upstream and central difference methods in modeling the subsonic and supersonic flows in different paths including the flow inside turbine blades, employing the numerical CUSP technique in the Jameson’s finite volume method can simultaneously benefit from the positive features of both mentioned methods. The novelty of this paper is first, improving Jameson’s finite volume method in modeling a 2D supersonic flow between the blades of a steam turbine using the CUSP method, and second, defining the most optimum control function mode using the Marquardt-Levenberg inverse method and by accounting for the mass conservation equation. By considering the importance of the shock regions in the blade’s surface suction side, the focus of the mentioned method is on this part which results in the significant improvement of the pressure ratio in Jameson’s finite volume method. The results of the first combined method (Jameson and CUSP) at the shock region of the blade’s suction surface desirably agree with the experimental data, and a decrease of numerical errors at this region is resulted. Furthermore, the results of the second combined method (Jameson, CUSP and inverse method) shows that in comparison with original Jameson’s method and the first combined method, by average, the conservation of mass condition is improved 15% at the shock region of the blade’s suction surface.

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In the present paper, a new combined technique consist of experimental results and numerical solution for determination of elastic constants of thin and thick orthotropic plates with various stacking sequences; and also isotropic plates under different boundary conditions is proposed. This new proposed technique makes use of vibrational test data, corresponding numerical solution and optimization methods. The vibration test data consists of a set of eigen frequencies that are obtained from transverse vibration test of the plate. The numerical solution is based on a finite element method using a commercial program. Material constants of the plate are determined by using of the inverse method and a particle swarm optimization algorithm in MATLAB software. The error function is based on the sum of square difference between experimental data and numerical data of eigen frequencies solution. The validation, performance and ability of the proposed technique in this paper are discussed using experimental and numerical data available in the literature. The higher accuracy of results that obtained by the present method in comparison with other methods proved the validity and capability f the new proposed method.

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Identification of elastic constants of three-dimensional anisotropic materials is much more complicated than the corresponding one in two-dimensional materials. This is because of the increased number of the elastic constants in three-dimensional materials. In this paper, an inverse method for determination of elastic constants of three-dimensional orthotropic, monoclinic and anisotropic materials using elastostatic measurements is presented. Strain measurements at some sampling points obtained from several elastostatic experiments are considered as the elastic response of the material. The solution is based on minimization of the difference between measured strains and the corresponding calculated ones at sampling points. The finite element method is used for sensitivity analysis, while the Tikhonov regularization method is used for stablizing the solution. Designing a single elastostatic experiment in which all of the material parameters affect the response distinctively is very difficult and seems impossible. By using the data obtained from a few different experiments, we are able to collect enough information to reach a stable and accurate solution. In the present research, 9 constants of orthotropic materials, 13 constants of monoclinic materials and 21 constants of anisotropic materials have been successfully identified. Effects of different parameters on accuracy and efficiency of the proposed method are studied by presenting several numerical examples.

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In this paper, a new inverse method has been presented for identifying the distribution of material properties and volume fraction index of rectangular functionally graded (FG) material plates. This method benefits from vibration analysis of FG plates accompanied by a novel and efficient meta-heuristic optimization algorithm called Drops Contact Optimization (DCO) algorithm, being proposed for the first time in this article. The presented algorithm relies on the initial population and mimics the behavior of water drops in different level of contacting successively with a fluid surface. Through using the second shear deformation theory and applying the Hamilton principle, the motion equations are derived and, subsequently, the natural frequencies of the considered FG plates are obtained. The outcomes relevant to considered different material phases and various length to thickness ratios are achieved and compared with those available in the literature. Making a comparative study of the obtained results with five well-known optimization algorithms confirms that the proposed DCO algorithm produces better performance in convergent speed and accurate characterization of FG materials.