Contribution to the study of the mechanical behavior of curved structures made of advanced materials

BENOUNAS, Soufiane (2025) Contribution to the study of the mechanical behavior of curved structures made of advanced materials. Doctoral thesis, Faculté des sciences et technologie.

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Abstract

Doubly curved shallow shells (DCSSs), frequently encountered in advanced engineering such as aerospace, civil, and mechanical engineering, present substantial challenges in predicting mechanical responses due to their complex geometry and material properties. Moreover, research on functionally graded doubly curved shallow shells (FG DCSs) is very limited, with most studies relying on analytical methods, highlighting the need for a novel and efficient approach to improve predictive analysis. Therefore, to address this gap, the aim of this research work is to develop an efficient and simple finite element model to investigate the bending deflection, stress distribution, and free vibration behavior of FG DCSSs. A new eight-node quadrilateral isoparametric element, named SQ8-IFSDT, with five degrees of freedom per node, is formulated based on improved first-order shear deformation theory (IFSDT). The present IFSDT simplifies the assumptions related to transverse shear stresses, replacing the conventional shear correction factor. As a result, it accurately predicts the parabolic shear stress distribution across the thickness of the shell while maintaining free traction conditions on both surfaces. In the present study, five types of DCSSs, namely flat plates, cylindrical shells, spherical shells, hyperbolic paraboloid shells, and elliptical paraboloid shells, are considered for the analysis. The material properties of FG DCSS change continuously across the thickness according to a power-law function. A variety of comparative studies is conducted to assess the accuracy and robustness of the developed finite element model. A comparison study shows that the proposed model is: (a) accurate and comparable with the literature; b) of fast rate of convergence to the reference solution; c) excellent in terms of numerical stability; and d) valid for both thin and thick FG DCSs. Moreover, comprehensive numerical results are presented and discussed in detail to examine the effects of material properties, power-law index, radius-to-thickness ratio, radius-to-side ratio, radii of curvature, loading, vibration modes, and boundary conditions on the bending and free vibration response of FG DCSSs. Finally, the outcomes of this research provide a robust benchmark for the design, testing, and manufacture of DCSSs and will inform future investigations into shell structures.

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