Finite element model for free vibration analysis of functionally graded doubly curved shallow shells by using an improved first-order shear deformation theory

A novel finite element model based on the improved first-order shear deformation theory (IFSDT) is proposed to investigate the vibration behavior of functionally graded doubly curved shallow shells in this study. The IFSDT adopted in the present model eliminates the need for a shear correction factor by making a simplified assumption about the transverse shear stress. This assumption ensures that the model accurately predicts both normal and shear stresses across the shell's thickness while satisfying the free traction conditions on the shell's upper and lower surfaces. Five types of doubly curved shells, named flat plates, spherical shells, hyperbolic parabolic shells, cylindrical shells, and elliptical paraboloid shells, are selected here for numerical analysis. The fundamental equations are derived from the Hamiltonian principle, and they are solved numerically by the finite element method. The accuracy and efficiency of the proposed finite element model are demonstrated via several comparison studies. A comprehensive parameter study is then presented to illustrate the influence of some parameters on the vibration behaviors of the functionally graded doubly curved shallow shells. The outcomes of this research provide a robust benchmark for the design, testing, and manufacture of doubly curved shallow shells and will inform future investigations into shell structures.