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Abstract

In this paper, the accuracy and the efficiency of the 3d-shell model based on a double directors shell element for the functionally graded material (FGM) shell structures analysis is studied. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. Thus, the third-order shear deformation plate theory (TSDT) is a particular case of the discrete double directors shell model (DDDSM) used in the present work. The DDDSM is introduced to remove the shear correction factors, when using the first-order shear deformation theory (FSDT), and improve an excellent performance when compared with other works. This model can be used for static, free vibration and buckling analyses of FGM. The convergence of the proposed model is compared to other well-known formulations found in the literature.

7. Conclusions

The analysis and the efficiency of the 3d-shell model based on a double directors shell element for the FGM shell structures is presented in this paper. The transverse shear deformations are taken into account in the DDDSM model. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. Dimensionless stresses and displacements of the simply supported functionally graded plate under sinusoidal load are computed by the present DDDSM model. By numerical investigation, the proposed model presents a good performance and high accuracy to predict the static behavior of shell structures when comparing with available published results. The proposed (DDDSM) formulation presented in this paper can be used in the following aspects: (a) Linearized formulation. This case is treated in this paper. (b) Free vibration. A dynamic equation of the DDDSM model for FGM shells will be derived through Hamilton’s principle. (c) Buckling. Buckling stresses of shells made of FGMs will be analyzed by taking into account the effects of transverse shear deformations. (d) Fully nonlinear formulation. The formulation will be assessed through numerical simulations involving the finite rotation and the geometric non-linearity. The authors will study these aspects in future articles.