Improved first-order shear deformation-based finite element approach for predicting free vibration frequencies of functionally graded sandwich doubly curved shallow shells

Problems associated with sandwich laminates, such as delamination and stress concentrations, paved the way for functionally graded materials (FGM). The present work aims to predict the free vibration behavior of cylindrical, spherical, hyperbolic, and elliptical functionally graded sandwich shallow shells. This study presents an improved first-order shear deformation theory (IFSDT)-based finite element approach to predict the free vibration behavior of cylindrical, spherical, hyperbolic, and elliptical FG sandwich shallow shells. The novelty of this work lies in the enhanced shear stress field formulation, which ensures shear stress naturally vanishes on the free surfaces and follows a nonlinear distribution through the shell thickness. This improvement allows for accurate shear stress evaluation without increasing the number of degrees of freedom, thereby maintaining computational efficiency compared to higher-order theories. The study establishes a new eight-noded C⁰ isoparametric finite element with five degrees of freedom per node. Four different layup arrangements of functionally graded material and isotropic materials were adopted during the present study. Comparisons with reference solutions for various FG sandwich shell configurations and boundary conditions verified that the proposed finite element model is accurate, presents a fast rate of convergence to the reference results, and is valid for both thin and thick FGM sandwich doubly curved shallow shells. Moreover, the influences of the power-law index, radius of curvature, material distribution, side-to-thickness ratio, face-to-core-thickness ratio, and boundary condition on the natural frequencies of symmetric and nonsymmetric FGM sandwich shells were thoroughly discussed. Several new results were also presented, which will serve as benchmarks for future studies. The results demonstrate that the developed C0 finite element model exhibits excellent accuracy and computational efficiency in capturing the free vibration characteristics of FG sandwich doubly curved shallow shells, making it a suitable tool for practical design and analysis.