Faculty Publications
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Item Static analysis of functionally graded beams using higher order shear deformation theory(2008) Kadoli, R.; Akhtar, K.; Ganesan, N.Displacement field based on higher order shear deformation theory is implemented to study the static behavior of functionally graded metal-ceramic (FGM) beams under ambient temperature. FGM beams with variation of volume fraction of metal or ceramic based on power law exponent are considered. Using the principle of stationary potential energy, the finite element form of static equilibrium equation for FGM beam is presented. Two stiffness matrices are thus derived so that one among them will reflect the influence of rotation of the normal and the other shear rotation. Numerical results on the transverse deflection, axial and shear stresses in a moderately thick FGM beam under uniform distributed load for clamped-clamped and simply supported boundary conditions are discussed in depth. The effect of power law exponent for various combination of metal-ceramic FGM beam on the deflection and stresses are also commented. The studies reveal that, depending on whether the loading is on the ceramic rich face or metal rich face of the beam, the static deflection and the static stresses in the beam do not remain the same. © 2007 Elsevier Inc. All rights reserved.Item Stress analysis of SUS 304 - Ceramics functionally graded beams using third order shear deformation theory(2008) Akhtar, K.; Kadoli, R.Kinematics for moderately thick rectangular beams satisfying zero shear strain on the top and bottom . surfaces is utilized to define the strain displacement relations involving the membrane, bending and higher order of displacements. Strain energy containing shear rotation term is deduced. The principle of stationary potential energy is used to obtain the static finite element equilibrium equations for the FGM (functionally graded material) beam with a uniformly distributed transverse load. FGM beams with continuous and smooth grading of metal and ceramics based on po wer law index are considered for the study. Equivalent single layer approach is followed for the evaluation of the constitutive matrix of the FGM beam. Numerical results are presented on the axialstresses and shear stresses in SUS304-Al3O3, SUS 304-ZrO2 and SUS 304-Si3N4FGM beams with clamped-clamped and simply supported boundary conditions. The effect of volume fraction of ceramic and metal on the nature of stress distribution through the thickness are investigated. The studies reveal that, the magnitude and distribution profile of static stresses in the beam depends on the power law index and also on the nature of load bearing surface, ie, whether the loading is on the ceramic rich face of the beam or metal rich face.Item Thermo-elastic response of SUS316-Al2O3 functionally graded beams under various heat loads(Elsevier Ltd, 2017) Malik, P.; Kadoli, R.Geometric nonlinearity and temperature dependent material properties are accounted for in the theoretical analysis of time dependent thermo-elastic response of thin functionally graded material (FGM) SUS316-Al2O3 beam subjected to various heat loads. A two dimensional Lagrangian rectangular finite element is used to obtain the temperature distribution on the transverse plane of the beam. Nonlinear thermo-elastic deflection and thermal stresses are evaluated for various structural and thermal boundary conditions. Thermo-elastic oscillations are observed in case of beams subjected to step, concentrated line and shock heat load whereas thermo-elastic deflection is observed for beams subjected to moving heat load. As the thermal load increases, the nonlinear thermal deflection of FGM beam are higher compared to linear analysis. In general, temperature dependency of material properties influence the amplitude of thermal oscillations. High thermal stresses are induced in beams with pin-pin and clamp-pin boundary condition as compared to hinge-hinge beam. © 2017 Elsevier LtdItem Thermal induced motion of functionally graded beams subjected to surface heating(Ain Shams University, 2018) Malik, P.; Kadoli, R.Thin beam of the functionally graded (FG) type subjected to a step heat input on one surface and insulated or exposed to convective heat loss on the opposite surface is under consideration for the evaluation of thermal induced motion. The dynamic displacement and dynamic thermal moment of the beam are analysed when the temperature gradient is independent of the beam displacement. The power law index dictates the metal–ceramic distribution across thickness of the beam and its effect on the thermal vibration of the beam is examined. The article discusses, in depth, the influence of various factors such as length to thickness ratio of beam, heat transfer boundary conditions, physical boundary conditions, and metal–ceramic combination on the thermal oscillations of FG beam. It is found that attenuation of the amplitude of static thermal deflection and superimposed thermal oscillations is a strong function of the metal–ceramic combination for the FG beam. © 2015 Faculty of Engineering, Ain Shams UniversityItem Nonlinear bending and free vibration response of SUS316-Al2O3 functionally graded plasma sprayed beams: theoretical and experimental study(SAGE Publications Inc. claims@sagepub.com, 2018) Malik, P.; Kadoli, R.Functionally graded SUS316-Al2O3 beams with ceramic content varying from 0 to 40% were prepared by a plasma spraying technique. Nonlinear finite element analysis was used to obtain the static deflection and free vibration of a clamped-free functionally graded beam. Von Kármán geometric nonlinearity and power law variation in material gradation through the beam thickness are considered in the analysis. The maximum error between the experimental and nonlinear finite element results for deflection is 6.68% and 14.31% on the fundamental frequency. Numerical results have also been attempted using ANSYS 3D solid element and they compare more closely with the experimental results. © 2016, © The Author(s) 2016.Item Influence of Winkler and viscoelastic foundation on free vibration of functionally graded beam integrated with Terfenol-D layer(Springer Science and Business Media Deutschland GmbH info@springer-sbm.com, 2020) Patil, M.A.; Kadoli, R.Free vibration of functionally graded beam integrated with Terfenol-D layer on Winkler-two parameter and viscoelastic foundation are studied by means of differential quadrature method within the framework of classical beam theory. The material properties of functionally graded beam integrated Terfenol-D layer are estimated by using the rule of mixture. The applied kinematic boundary conditions are implemented using ?-point and modified weighting coefficient approach. The solution of simply supported functionally graded material beam with Terfenol-D layer (FGMT) resting on the Winkler elastic foundation is obtained by using the technique of Navier. The numerical results obtained using differential quadrature method (DQM) and modified differential quadrature method (MDQM) are compared with exact results obtained from analytical formulation where excellent agreement is observed. The parametric study is carried out to encapsulate the influence of Winkler-two parameter and the viscoelastic foundation on the vibration characteristics of functionally graded beams integrated with Terfenol-D layer. © 2020, The Brazilian Society of Mechanical Sciences and Engineering.Item Analytical solution for free vibration of symmetric Terfenol-D layered functionally graded beam with different boundary conditions(Springer Science and Business Media Deutschland GmbH, 2023) Patil, M.A.; Kadoli, R.A unified analytical approach is established to predict the frequency behaviour of symmetric functionally layer-wise graded beams with an integrated Terfenol-D layer under simply supported, clamped-clamped, and clamped-simply supported boundary conditions. In contrast to previous research, the analytical solution relies on transcendental equations. Terfenol-D layered functionally graded beam uses Reddy’s generalised beam theory as the basis for its governing equation. First-order shear deformation and rotating inertia were taken into consideration in the study. To ensure the accuracy of the analytical solution, comparisons are made with the current differential quadrature solution based on Euler–Bernoulli beam theory. The current analytical solution yields frequency results that are in good agreement with those obtained by the differential quadrature approach. The present analytical means is straightforward and easy to understand as compared to previous researcher’s work. © 2023, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.Item Investigation of moving load-induced vibrations in layered functionally graded Terfenol-D beams: a differential quadrature method and analytical approach(Taylor and Francis Ltd., 2024) Patil, M.A.; Saraf, S.; Kadoli, R.; Naskar, S.The paper investigates the potential of the full-sinusoidal Fourier series as a solution form for the deflection of layered functionally graded beams associated with smart actuators, drawing on the fundamental principles of classical Fourier series theory. The current method simplifies the difficult beam problem to a set of linear algebraic equations by using the Duhamel integration technique and the orthogonality of the trial function. The study takes into account generalized boundary conditions and moving forces, which are seldom discussed in previous research. Under the action of a moving load, the boundary value problem for a functionally graded beam integrated with Terfenol-D is efficiently addressed using the approach of combined differential and integral quadrature. The generalized boundary conditions may be easily achieved by adjusting the stiffness of the restraining springs. The significant agreement between the differential quadrature solution and the Fourier series solution underlines the efficiency and accuracy of both methods. Furthermore, the influences of various crucial physical characteristics on the natural frequencies and the essential flow velocities are explored, including boundary stiffness, foundation parameters, and geometric parameters. © 2024 Taylor & Francis Group, LLC.