Naveen Kumar, H.S.Kattimani, S.2026-02-042022Structural Engineering and Mechanics, 2022, 82, 4, pp. 477-49012254568https://doi.org/10.12989/sem.2022.82.4.477https://idr.nitk.ac.in/handle/123456789/22574This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman’s type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton’s principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction. © © 2022 Techno-Press, Ltd.Aspect ratioFunctionally graded materialsGeometryGradingIterative methodsNonlinear analysisNonlinear equationsNumerical methodsShear deformationShear flowVolume fractionDoubly curved panelsDoubly curved shellsFirst-order shear deformation theoryFunctionally gradedFunctionally graded doubly curved shellImproved first-order shear deformation theoryTwo-directionalTwo-directional FGMVon KarmanVon karman’s nonlinearityPorosity