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One of the most applicable methods to study the mechanical behavior of reinforced polymers with CNTs is modeling of representative volume element (RVE). It has been shown that the mechanical behavior of RVE depends on its ingredients mechanical properties and its geometrical parameters. In this research, a RVE which includes a CNT and its surrounding polymer is chosen as a rectangular cube. In this research, effects of the length and depth of the RVE, the length of the CNT and the CNT caps on the elastic behavior of the RVE have been studied. Furthermore, the effect of the volume fraction of CNTs is also considered. First, an analytical solution has been developed to predict the elastic modulus of the RVE. Then, using a finite element method, the elastic behavior of the RVE is modeled. The analytical and numerical results show that at a constant volume fraction of the CNT, variation of each material and geometrical parameters can affect the longitudinal elastic modulus of the RVE significantly. However, it has been shown that the transverse elastic modulus of RVE is not sensitive to the geometrical parameters variations. Finally, using a combination of the Halpin-Tsai micromechanical model and the present analytical solution, a proper aspect ratio of the RVE for each volume fraction of the CNT has been determined and suggested.

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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.