Faculty Publications

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Author: search.filters.author.Kattimani, S.Subject: search.filters.subject.Nonlinear equations

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Now showing 1 - 6 of 6
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    Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities
    (Techno-Press, 2022) Naveen Kumar, H.S.; Kattimani, S.
    This 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.
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    Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study
    (China Ordnance Industry Corporation, 2022) Kumar H S, H.S.; Kattimani, S.
    This article presents the investigation of nonlinear vibration analysis of tapered porous functionally graded skew (TPFGS) plate considering the effects of geometrical non-uniformities to optimize the thickness in the structural design. The TPFGS plate is analyzed considering linearly, bi-linearly, and exponentially varying thicknesses. The plate's effective material properties are tailor-made using a modified power-law distribution in which gradation varies along the thickness direction of the TPFGS plate. Incorporating the non-linear finite element formulation to develop the kinematic equation's displacement model for the TPFGS plate is based on the first-order shear deformation theory (FSDT) in conjunction with von Karman's nonlinearity. The nonlinear governing equations are established by Hamilton's principle. The direct iterative method is adopted to solve the nonlinear mathematical relations to obtain the nonlinear frequencies. The influence of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the TPFGS plate for different skew angles and variable thicknesses are studied for various geometrical parameters. The influence of taper ratio, variable thickness, skewness, porosity distributions, gradation, and boundary conditions on the plate's nonlinear vibration is demonstrated. The nonlinear frequency analysis reveals that the geometrical non-uniformities and porosities significantly influence the porous functionally graded plates with varying thickness than the uniform thickness. Besides, exponentially and linearly variable thicknesses can be considered for the thickness optimizations of TPFGS plates in the structural design. © 2021 China Ordnance Society
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    Frequency response analysis of edge-cracked magneto-electro-elastic functionally graded plates using extended finite element method
    (Elsevier B.V., 2022) Sh, E.L.; Kattimani, S.; Thoi Trung, N.
    This paper studies the frequency response of edge-cracked magneto-electro elastic functionally graded (ECMEE-FG) plates using the extended finite element method (XFEM). First-order shear deformation theory (FSDT), von Karman's nonlinear strain-displacement equations, and a modified power-law are used to develop the numerical model. The coupled equations are derived and analyzed using Hamilton's principle and extended finite element methods. The influence of B-rich bottom and F-rich bottom material gradation, crack orientation, crack length, and aspect ratio on the geometrically nonlinear frequency response was investigated after the current study was validated. Furthermore, crack propagation behavior in the ECMEE-FG plate was examined. The results could be helpful for the design of functionally graded magneto electro elastic structures and devices. © 2022 Elsevier Ltd
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    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.
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    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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    Influence of saturated porosity distributions on the geometrically nonlinear behavior of functionally graded porous plates in a thermal environment
    (Springer Science and Business Media Deutschland GmbH, 2025) Kumar, H.S.N.; Kattimani, S.; Lingaraju, S.V.; Dhuttargaon, M.S.; Gidaveer, S.M.
    The nonlinear vibration behavior of functionally graded saturated porous (FGSP) plates in thermal environments is a complex problem influenced by material gradients, pore saturation, and temperature effects. Accurately capturing the impact of saturated porosity distributions and geometric nonlinearity on the dynamic behavior of these plates presents a key challenge. This study investigates the linear and nonlinear vibration characteristics of FGSP plates under thermal gradients, focusing on the role of saturated porosities. A modified power-law defines the temperature-dependent effective material properties through the plate’s thickness, while Biot’s theory models the effects of saturated pores. The governing equations are developed using the refined shear deformation plate theory combined with von Karman’s nonlinear relations and Hamilton’s principle. Numerical simulations via the direct iterative model provide insights into the linear and large-amplitude frequencies and the nonlinear central deflection of FGSP plates. Results indicate that saturated fluids within the pores significantly affect both vibrational frequencies and deflections, emphasizing the importance of considering porosity and thermal effects in modeling. This study highlights the necessity of incorporating saturated porosities and temperature-dependent properties for precise performance prediction, offering valuable guidance for designing porous materials in thermomechanical applications. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.