Faculty Publications
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Item Porosity influence on structural behaviour of skew functionally graded magneto-electro-elastic plate(Elsevier Ltd, 2018) Kiran, M.C.; Kattimani, S.; Mahesh, M.This article presents a finite element (FE) formulation to assess the influence of porosity on the static responses and free vibration of functionally graded skew magneto-electro-elastic (FGSMEE) plate. The porosity is accounted for local density using modified power law. The skew edges of the plate are achieved by implementing transformation matrix. The coupled constitutive relations establish the different couplings associated with MEE materials. The displacements, potentials, and stresses for the porous skew plate are established through static analysis. The influence of porosity on the natural frequency of the skew plate is investigated via free vibration analysis. The influence of different porosity distributions on various skew angles of the FGSMEE plate has been studied. The effect of porosity volume, skew angle, and geometrical parameters such as aspect ratio, thickness ratio, and boundary conditions on the porous FGSMEE plate is investigated. © 2018 Elsevier LtdItem 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 AuthorsItem Nonlinear free vibration and transient responses of porous functionally graded magneto-electro-elastic plates(Springer Science and Business Media Deutschland GmbH, 2022) Sh, E.L.; Kattimani, S.; Mahesh, M.The geometrically nonlinear free vibration and transient response of porous functionally graded magneto-electro-elastic (PFG-MEE) plates are studied based on the first-order shear deformation (FSDT) theory, von Karman's nonlinear strain–displacement relations along with modified power law. With Hamilton's theory, the coupled equations of motion are obtained and analyzed by adapting finite element methods (FEM). Moreover, using Newmark's, Picard's, and Newton–Raphson methods, a porous FG-MEE plate's nonlinear and transient response is analyzed using MATLAB software. After validating the present study, the influence of porosity distribution, porosity index, boundary conditions, aspect ratios, and thickness to length ratios on the nonlinear frequency ratio and nonlinear transient response of porous FG-MEE plate is investigated. It is revealed that geometric parameters, porosity index, boundary conditions, and form of porosity distribution significantly influence the nonlinear frequency ratio and nonlinear transient deflections of porous FG-MEE plates. © 2021, Wroclaw University of Science and Technology.Item 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.Item Effect of porosity on active damping of geometrically nonlinear vibrations of a functionally graded magneto-electro-elastic plate(China Ordnance Industry Corporation, 2022) Esayas, L.S.; Kattimani, S.This paper investigates the effect of porosity on active damping of geometrically nonlinear vibrations (GNLV) of the magneto-electro-elastic (MEE) functionally graded (FG) plates incorporated with active treatment constricted layer damping (ATCLD) patches. The perpendicularly/slanted reinforced 1–3 piezoelectric composite (1–3 PZC) constricting layer. The constricted viscoelastic layer of the ATCLD is modeled in the time-domain using Golla-Hughes-McTavish (GHM) technique. Different types of porosity distribution in the porous magneto-electro-elastic functionally graded PMEE-FG plate graded in the thickness direction. Considering the coupling effects among elasticity, electrical, and magnetic fields, a three-dimensional finite element (FE) model for the smart PMEE-FG plate is obtained by incorporating the theory of layer-wise shear deformation. The geometric nonlinearity adopts the von Kármán principle. The study presents the effects of a variant of a power-law index, porosity index, the material gradation, three types of porosity distribution, boundary conditions, and the piezoelectric fiber's orientation angle on the control of GNLV of the PMEE-FG plates. The results reveal that the FG substrate layers' porosity significantly impacts the nonlinear behavior and damping performance of the PMEE-FG plates. © 2021 China Ordnance SocietyItem 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 SocietyItem 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.Item Static, buckling, and free vibration characteristics of porous skew partially functionally graded magneto-electro-elastic plate(Taylor and Francis Ltd., 2023) Kiran, K.; Wang, W.; Fang, C.; Kattimani, S.In this article, a new mathematical model to develop porous skew partially functionally graded (SPFG) magneto-electro-elastic (MEE) plate from a stepped functionally grade (SFG) plate is proposed. The combination of Barium Titanate (BaTiO3) and Cobalt Ferrite (CoFe2O4) is graded stepwise to achieve SFG plates. Such, SFG plate is approximated using modified power law for functional variation through its thickness. Modified first-order shear deformation theory (FSDT) is deployed in the current study to develop mathematical models. The geometrical modification from rectangular to skew plate is achieved using transformation matrix. Porosity in the partial functionally graded MEE plate is taken as local density. Free vibration study is carried out to reflect the influence of partial gradation, porosity distribution, porosity volume, and skew angle on the natural frequency of porous SPFG MEE plate. The influence of various types of porosity distribution, partial gradation, and skew angle on the primary quantities such as displacements, potentials, and secondary quantities such as stresses, electric displacement, and magnetic induction on SPFG MEE plate is studied. The stability characteristics of the SPFG MEE plate are also investigated to study the buckling behavior under various porosity distributions, partial gradation, and skew angles. The effect of change in aspect ratio, and thickness ratio on the free vibration and static behavior is also investigated. © 2021 Taylor & Francis Group, LLC.Item Effect of temperature and porosity on free vibration characteristics of a doubly-curved skew laminated sandwich composite structures with 3D printed PLA core(Elsevier Ltd, 2023) Kallannavar, V.; Kattimani, S.This paper deals with the investigation of the influence of temperature and porosity on the vibration response of the doubly-curved skew laminated sandwich composite (DSLSC) shells. The temperature-reliant properties of the graphite–epoxy face sheet and the 3D printed polylactic acid (PLA) core are considered for the numerical analysis. The coupled thermo-elastic finite element (FE) model is developed using the first-order shear deformation theory (FSDT) to study the influence of uniform temperature rise on the modal behavior of the DSLSC shells. The stiffness generated due to thermal exposure is accounted to introduce the initial stress stiffness matrix. Further, the initial stress stiffness matrix is developed using nonlinear strain–displacement relations, while the mechanical stiffness matrices are characterized using linear strain–displacement relations. A comprehensive parametric study has been performed to appreciate the effect of temperature, geometric restraints, and material constraints of a laminated composite sandwich spherical, hyperbolic, ellipsoidal, cylindrical shells, and flat plates. Series of experiments are performed to understand the influence of temperature on the natural frequency of glass–epoxy laminated composite sandwich plates with 3D printed PLA core. Further exploration is dedicated to comprehending the experimental challenges involved in studying the vibration performance of sandwich structures with 3D printed PLA core in the thermal environment. © 2022 Elsevier LtdItem 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.