Precise analysis of the static bending response of functionally graded doubly curved shallow shells via an improved finite element shear model

Doubly curved shallow shells, common in aerospace and civil engineering, pose significant challenges in predicting bending responses due to their complex geometry and material properties. Therefore, this research focused on the development of an efficient eight-node quadrilateral isoparametric element model based on a new improved first-order shear deformation theory (IFSDT) to analyze the bending deflection and stresses distribution of Functionally Graded (FG) doubly curved shallow shells. The present IFSDT obviates the necessity of a shear correction factor, which has challenges in determining for FG doubly curved shallow shells, by adopting a simpler assumption about transverse shear stresses. This assumption guarantees that the model precisely predicts the parabolic shear stresses distribution throughout the thickness of the FG shell while also meeting the requirements for free traction conditions on the top and lower surfaces of the shell. In the present analysis, five distinct types of FG doubly curved shallow shells are modeled: flat plates, spherical shells, hyperbolic parabolic shells, cylindrical shells, and elliptical paraboloid shells. A power law is employed to describe the gradual changes in material properties through the thickness direction. Numerical results for displacements and stresses are obtained for various shell types, materials, power-law factors, radii of curvature, and boundary conditions under uniform and sinusoidal loads. Comprehensive comparison and convergence studies are conducted to assess the robustness and accuracy of the proposed numerical model. This study also contributes new numerical results that are valuable for future research. Ultimately, the proposed numerical model offers a robust and straightforward tool for engineers and researchers engaged in the design and analysis of complex shell structures. © 2024 Elsevier Ltd