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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.