Faculty Publications

Now showing 1 - 3 of 3

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates
(China Ordnance Industry Corporation, 2021) Kumar H S, N.; Kattimani, S.; Nguyen, T.
This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew (PFGS) plates. The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate. A nonlinear finite element (FE) formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory (FSDT) in conjunction with von Karman's nonlinear strain displacement relations. The governing equations of the PFGS plate are derived using the principle of virtual work. The direct iterative method and Newmark's integration technique are espoused to solve nonlinear mathematical relations. The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters. The effects of volume fraction grading index and skew angle on the plate's nonlinear dynamic responses for various porosity distributions are illustrated in detail. © 2021 The Authors
Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials
(SAGE Publications Ltd, 2022) Hosur Shivaramaiah, N.K.; Kattimani, S.; Shariati, M.; Nguyen, T.
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. © IMechE 2022.
Geometrically Nonlinear Study of Functionally Graded Saturated Porous Plates Based on Re¯ned Shear Deformation Plate Theory and Biot's Theory
(World Scientific, 2023) Kumar, H.S.N.; Kattimani, S.; Marques, F.D.; Nguyen, T.; Shariati, M.
This research presents the geometrically nonlinear investigation of functionally graded saturated porous material (FGSPM) plate under undrained conditions. In conjunction with von Karman's nonlinearity, the re¯ned shear deformation plate theory (RSDPT) is implemented to model the FGSPM plate. The e®ective material characteristics of the saturated porous plate change constantly in the thickness direction. The pores of the saturated porous plate are examined in °uid-¯lled conditions. Thus, the constitutive equations are established using Biot's linear poroelasticity theory. The governing equations are developed by combining a nonlinear ¯nite element technique with Hamilton's principle. Then, the direct iterative approach is utilized to extract the geometrically nonlinear numerical results. The emphasis is placed on exploring the e®ects of numerous parameters such as Skempton coe±cient, volume fraction grading index, porosity volume index, porosity distributions, and boundary conditions during the extensive numerical analyses on the linear frequency, large amplitude frequencies, and nonlinear central de°ections of the FGSPM plate. It is evident from the investigation that saturated °uid in the pores substantially impacts the nonlinear de°ection and vibration behavior of the FGSPM plate. © World Scientic Publishing Company.

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