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    Buckling analysis of functionally graded materials by dynamic approach
    (Elsevier Ltd, 2020) Swaminathan, K.; Hirannaiah, H.; Rajanna, T.
    Laminated composites exhibit difference in the mechanical properties at the interface between two materials resulting in stress concentration. This may lead to damages in the form of delamination, matrix cracking and adhesive bond separation. Functionally Graded Materials (FGM) are formed by gradual variation of two or more material over a particular volume, thereby overcomes these issues. Buckling problems of FGM plates are usually solved by static approach. In some cases, particularly non-uniform loading and geometric discontinuity, the stress concentration usually occurs. In such cases, the solution to the buckling problem by dynamic approach is most suitable. In the dynamic approach, the natural frequencies are calculated by applying in-plane loads. As the intensity of the in-plane load increases, the frequency of the material decreases and finally becomes zero at the onset of buckling. The load at which the natural frequency becomes zero that load is called a buckling load. In this investigation, the vibration and buckling characteristics of FGM panels subjected to uniaxial and biaxial loading conditions have been studied by using the finite element method (F.E.M). In the Finite element (FE) formulation, the effective material properties of FGM plates are assumed to vary in the thickness direction according to the power-law distribution of volume fraction of the constituents. The plate is modelled by using 8-noded serendipity element by incorporating the effect of transverse shear deformation and rotary inertia. The effect of different parameters such as volume fraction index (n), the thickness of the panel (h) and boundary condition of the plate are considered to study the buckling behaviour of the FGM plate under uniaxial loading conditions. © 2020 Elsevier Ltd. All rights reserved.
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    Buckling Response of Functionally Graded Material Plates with Cutouts Subjected to Linearly Varying Loads
    (Springer Science and Business Media Deutschland GmbH, 2022) Swaminathan, K.; Hirannaiah, H.; Rajanna, T.
    In most of the studies, the buckling problems are solved analytically based on the assumption that the plates are subjected to only uniform in-plane edge loads without any damages, in spite of the fact that, the real structural components are subjected to various kinds of non-uniform edge loads along with geometrical discontinuous. The current study provides numerical solutions for buckling problems of functionally graded material plates with and without circular cutouts subjected to linearly varying edge loads by using the finite element package (ABAQUS). The effective material properties are found along the thickness using the homogenization technique involving power law function. In the FE modelling, the plate is modelled by using eight noded elements (S8R5) with five degrees of freedom at each node. The influence of various parameters such as size of the cutout and its position, volume fraction index and type of loads are considered to investigate the effect of each parameter on the buckling phenomenon. © 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
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    Stress, vibration and buckling analyses of FGM plates-A state-of-the-art review
    (Elsevier Ltd, 2015) Swaminathan, K.; Naveenkumar, D.T.; Zenkour, A.M.; Carrera, E.
    This paper presents a comprehensive review of the various methods employed to study the static, dynamic and stability behavior of Functionally Graded Material (FGM) plates. Both analytical and numerical methods are considered. The review is carried out with an emphasis to present stress, vibration and buckling characteristics of FGM plates predicted using different theories proposed by several researchers without considering the detailed mathematical implication of various methodologies. The effect of variation of material properties through the thickness, type of load case, boundary conditions, edge ratio, side-to-thickness ratio and the effect of nonlinearity on the behavior of FGM plates are discussed. The main objective of this paper is to serve the interests of researchers and engineers already involved in the analysis and design of FGM structures. © 2014 Elsevier Ltd.
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    Linear thermal buckling and free vibration analysis are presented for functionally graded cylindrical shells with clamped-clamped boundary condition based on temperature-dependent material properties. The material properties of functionally graded materials (FGM) shell are assumed to vary smoothly and continuously across the thickness. With high-temperature specified on the inner surface of the FGM shell and outer surface at ambient temperature, 1D heat conduction equation along the thickness of the shell is applied to determine the temperature distribution; thereby, the material properties based on temperature distribution are made available for thermal buckling and free vibration analysis. First-order shear deformation theory along with Fourier series expansion of the displacement variables in the circumferential direction are used to model the FGM shell. Numerical studies involved the understanding of the influence of the power-law index, r/h and l/r ratios on the critical buckling temperature. Free vibration studies of FGM shells under elevated temperature show that the fall in natural frequency is very drastic for the mode corresponding to the lowest natural frequency when compared to the lowest buckling temperature mode. © 2005 Elsevier Ltd. All rights reserved.
    (Academic Press, Buckling and free vibration analysis of functionally graded cylindrical shells subjected to a temperature-specified boundary condition) Kadoli, R.; Ganesan, N.
    2006
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    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.
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    Comparative analysis of steady state heat transfer in a TBC and functionally graded air cooled gas turbine blade
    (2010) Coomar, N.; Kadoli, R.
    Internal cooling passages and thermal barrier coatings (TBCs) are presently used to control metal temperatures in gas turbine blades. Functionally graded materials (FGMs), which are typically mixtures of ceramic and metal, have been proposed for use in turbine blades because they possess smooth property gradients thereby rendering them more durable under thermal loads. In the present work, a functionally graded model of an air-cooled turbine blade with airfoil geometry conforming to the NACA0012 is developed which is then used in a finite element algorithm to obtain a non-linear steady state solution to the heat equation for the blade under convection and radiation boundary conditions. The effects of external gas temperature, coolant temperature, surface emissivity changes and different average ceramic/metal content of the blade on the temperature distributions are examined. Simulations are also carried out to compare cooling effectiveness of functionally graded blades with that of blades having TBC. The results highlight the effect of including radiation in the simulation and also indicate that external gas temperature influences the blade heat transfer more strongly. It is also seen that graded blades with about 70% ceramic content can deliver better cooling effectiveness than conventional blades with TBC. © 2010 Indian Academy of Sciences.
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    Studies on Uniaxial compressive strength of laterite masonry prisms
    (2011) Unnikrishnan, S.; Narasimhan, M.C.; Venkataramana, K.
    Laterite is a well known conventional building material in Asian countries. In spite of its large popularity in construction, a systematic characterization of this material, as a building block, has not been seriously attempted so far. The strength and elastic properties of laterite masonry are influenced by the individual properties of the laterite blocks and the mortar. In the present study, characterization of the laterite block and the mortar and compressive strength of laterite masonry prisms have been investigated using detailed laboratory experiments and numerical analysis. The experimental results, related to the compressive strength and stress-strain characteristics of laterite and mortar and compressive strength of laterite masonry prisms are presented. Finite element analysis of laterite masonry prism has also been carried out. The studies have shown that the modulus of elasticity of laterite blocks tested is less than that of mortar used in making the laterite masonry. Further, the laterite masonry prisms have been observed to have failed by bond failure and subsequent splitting of laterite blocks. Also, increase in thickness of mortar joint gives rise to a decrease in laterite tensile stresses in mortar joint leading to higher prism strengths, if bond remains intact. © 2011 CAFET-INNOVA technical society. All right reserved.
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    Response of fly ash-reinforced functionally graded rubber composites subjected to mechanical loading
    (2012) Doddamani, M.R.; Kulkarni, S.M.
    A novel approach to estimate the Young's modulus of a functionally graded rubber composite (FGRC) from the damping ratio is demonstrated with the examples of unreinforced and fly ash-reinforced materials. FGRC coupons were prepared using the conventional casting technique. The occurrence of gradation in the specimens was attributed to the variable density of particles present in the fly ash, settling at different depths. The technique of free vibrations was used for experimentation. The damping response of the FGRC specimens was studied. The results obtained from the experiments showed that, with growing filler weight fraction, the Young's modulus of the composite increased. The empirical model developed to predict the magnitude of the modulus turned out to be in good agreement with experimental data. © 2012 Springer Science+Business Media, Inc.
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    Computational model for the transverse stress analysis of FGM plates - An assessment
    (2013) Swaminathan, K.; Naveenkumar, D.T.
    This paper presents the complete theoretical formulation and the analytical solutions for stress analysis of functionally graded material (FGM) plates using First-order Shear Deformation Theory (FSDT). The material properties are assumed to be isotropic along the plane of the plate and vary through the thickness according to the power law function. The governing equations of equilibrium are derived using Principle of Minimum Potential Energy (PMPE) and the analytical solutions are obtained in closed-form using Navier's solution technique. The effect of variation of side-to-thickness ratio, modulus of elasticity ratio, edge ratio and the power law function on the behaviour of the plate is studied. Numerical results are presented for the transverse displacement, the in-plane and the transverse stresses. © 2013 CAFET-INNOVA TECHNICAL SOCIETY.
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    Higher order refined computational models for the stability analysis of FGM plates - Analytical solutions
    (Elsevier Ltd, 2014) Swaminathan, K.; Naveenkumar, D.T.
    Analytical formulations and solutions for the stability analysis of simply supported Functionally Graded Material (FGM) sandwich plates hitherto not reported in the literature based on two higher-order refined computational models available in the literature are presented. These computational models are based on Taylor's series expansion of the displacements in the thickness coordinate and incorporate the realistic parabolic distribution of transverse strains through the plate thickness. One of them with twelve degrees-of-freedom considers the effects of both transverse shear and normal strain/stress while the other with nine degrees-of-freedom includes only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also considered for the evaluation purpose. For mathematical modeling purposes, the Poisson's ratio of the material is considered as constant whereas Young's modulus is assumed to vary through the thickness according to the power law function. The governing equations of equilibrium for buckling analysis are obtained using the Principle of Minimum Potential Energy (PMPE). Solutions are obtained in closed form using Navier's technique by solving the eigenvalue problem. The comparison of the present results with the available elasticity solutions and the results computed independently using the first-order and another higher-order theory available in the literature shows that the higher-order refined theory with 12 degrees-of-freedom predicts the critical buckling load more accurately than all other theories considered in this paper. After establishing the accuracy of prediction, extensive numerical results for FGM sandwich plates using all the models are presented which will serve as a benchmark for future investigations. © 2014 Elsevier Masson SAS. All rights reserved.