Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

This article investigates the influence of porosity distributions on the nonlinear behavior of two-directional functionally graded porous plates (TDFGPP) made from four distinct materials for the first time. A simple and effectual approach is established based on the improved generalized shear deformation plate theory (GSDPT) and von Karman’s assumptions. The GSDPT incorporates transverse shear strains with a higher order polynomial to avoid shear locking. The TDFGPP constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both transverse and longitudinal directions. The governing equations are obtained using a nonlinear finite element approach in conjunction with Hamilton’s principle. Then, the direct iterative and Newmark’s methods are incorporated to accomplish the numerical results. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, thickness ratio, and aspect ratio for different support conditions provides a thorough insight into the linear and nonlinear responses of the porous plate. In addition, this study emphasizes the influence of the volume fraction gradation profiles with four different materials on the linear frequency, nonlinear frequency, and deflections of the TDFGPP. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in specified directions with appropriate materials. Hence, two-directional functionally graded materials panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.