Numerical analysis of flexural behavior of sandwich beams using the FGM approach
DOI:
https://doi.org/10.34115/basrv9n1-005Keywords:
finite element, deformation approach, analytical modeling, bending behavior, sandwich beamAbstract
Analytical modeling to predict the flexural behavior of sandwich beams using a triangular finite element model, the Triangular Plate Finite Element with Airy Function (TPAF). The originality of this model lies in the use of the deformation approach, which comprises three nodes and three degrees of freedom per node (one translation Wi and two rotations θxi and θyi). The main aim of this work is to validate the model by comparison with other solutions, in particular by means of an analytical prediction based on layer theory and the results obtained using CSB software. The originality of this study lies in the fact that the mechanical properties vary according to an exponential function along the height of the FGM section and remain constant in the other parts of the different composite sections. Tabular and graphical results are presented to illustrate the impact of deffrents, such as geometric factors (thickness configurations and length/thickness ratios), as well as boundary conditions and loads, on the static behavior of the beam.
References
BAGHERI H, KIANI Y, ESLAMI MR. Geometrically nonlinear response of FGM beams on elastic foundation subjected to ther mal shock. Iran J Sci Technol: Trans Mech Eng 47(1):187–201, 2023.
BASU D, PRAMANIK S, DAS S ET AL. Analyse des vibrations sans éléments finis des plaques pliées fonctionnellement graduées. Iran J Sci Technol Trans Mech Eng 47:697–716, 2023.
BELKHODJA Y, BELKHODJA MEA, FEKIRINI H ET AL. New quasi three and two dimensional trigonometric-cubic monomial HSDT for thermal buckling and thermo-mechanical bending analyses of FGM symmetrical/non-symmetrical sandwich plates with hard/ soft core. Compos Struct 304:116402, 2023.
CHEN CD, HUANG BF. A novel higher-order refined zigzag theory for static bending analysis in sandwich composite beam. Appl Math Model 119:586–604, 2023.
DELALE, F., ERDOGAN, F. The crack problem for a nonhomogeneous plane. J. Appl. Mech. 50 (3), 609–614, 1983.
DEMIRHAN P., TASKIN V. Static analysis of simply supported functionally graded sandwich plates by using four variable plate theory. Teknik Dergi, 8987–9007, 2018. https://doi. org/10.18400/tekderg.396672
ELFATMI R., ZENZRI H. On the structural behavior and the Saint Venant solution in the exact beam theory Application to laminated composite beams. Computers and Structures, vol. 80 (16-17), p. 1441-1456, (2002).https://doi.org/10.1016/S0045-7949(02)00090-1
GARG A, CHALAK HD, CHAKRABARTI A. Comparative study on the bending of sandwich FGM beams made up of different mate rial variation laws using refined layerwise theory. Mech Mater 151:103634, 2020.
GARG A, CHALAK HD. A review on analysis of laminated com posite and sandwich structures under hygrothermal conditions. Thin-Walled Struct 142:205–226, 2019.
GHOLAMZADEH BABAKI, M., AND M. SHAKOURI. Free and forced vibration of sandwich plates with electrorheological core and functionally graded face layers. Mechanics Based Design of Structures and Machines 49 (5):689– 706, 2021. doi: 10.1080/15397734.2019.1698436
HAZWANI F, TODO M. Deformation mechanism of porous com posite sandwich beam for orthopaedical application under three point bending. Compos Struct 281:114983, 2022.
HIMEUR M, GUENFOUD H, GUENFOUD M. A higher order triangular plate finite element using Airy functions. Advances in Mechanical Engineering, 2020. doi:10.1177/1687814020971906
HIRANE, H., BELARBI, MO., HOUARI, M.S.A. ET AL. On the layerwise finite element formulation for static and free vibration analysis of functionally graded sandwich plates. Engineering with Computers 38 (Suppl 5), 3871–3899, 2022. https://doi.org/10.1007/s00366-020-01250-1
JOSHI KK, KAR VR. Elastoplastic behaviour of multidirectional porous functionally graded panels: a nonlinear FEM approach. Iran J Sci Technol: Trans Mech Eng, 2023. https:// doi. org/ 10. 1007/ s40997-023-00653
K. P, A., SWAMINATHAN, K., INDU, N., & H, S. A novel EFG meshless-ANN approach for static analysis of FGM plates based on the higher-order theory. Mechanics of Advanced Materials and Structures, 31(25), 6501–6517, 2023. https://doi.org/10.1080/15376494.2023.2231459
KUMAR, R., A. LAL, AND B. M. SUTARIA. Static and dynamic response analysis of corrugated core sandwich plates under patch loading. Mechanics Based Design of Structures and Machines :1–19, 2022. doi: 10.1080/15397734. 2022.2061510
MEDJMADJ, S., AIT TALEB, S. & SI SALEM, A. Analytical Modeling of the Bending Behavior of Plaster/Cork Functionally Graded Core Sandwich Beams: Analysis and Experimental Validation. Iran J Sci Technol Trans Mech Eng 48, 1489–1507, 2024. https://doi.org/10.1007/s40997-023-00732-z
MOUTHANNA A, BAKHY SH, AL-WAILY M. Analytical investiga tion of nonlinear free vibration of porous eccentrically stiffened functionally graded sandwich cylindrical shell panels. Iran J Sci Technol: Trans Mech Eng 47(3):1035–1053, 2023.
NGUYEN VC, TRAN TT, NGUYEN-THOI T ET AL. A novel finite ele ment formulation for static bending analysis of functionally graded porous sandwich plates. Front Struct Civ Eng 16(12):1599–1620, 2022.
NGUYEN VD, PHUNG VB. Static bending, free vibration, and buckling analyses of two-layer FGM plates with shear connectors resting on elastic foundations. Alex Eng J 62:369–390, 2022.
SAYYAD AS, GHUGAL YM. Modeling and analysis of function ally graded sandwich beams: a review. Mech Adv Mater Struct 26:1776–1795, 2019.
SURESH, S., MORTENSEN, A. Fundamentals of Functionally Graded Materials. The Institut of Materials, London,1998.
SWAMINATHAN K, SANGEETHA DM. Thermal analysis of FGM plates: a critical review of various modeling techniques and solu tion methods. Compos Struct 160:43–60, 2017.
TEMEL, B., AND A. R. NOORI. Transient analysis of laminated composite parabolic arches of uniform thickness. Mechanics Based Design of Structures and Machines 47 (5):546–54, 2019. doi: 10.1080/15397734.2019.1572518
VAN VINH P. Static bending analysis of functionally graded sandwich beams using a novel mixed beam element based on first order shear deformation theory. Forces in Mech 4:100039, 2021.
VUONG PM, DINH DUC N. Nonlinear buckling and post-buckling behavior of shear deformable sandwich toroidal shell segments with functionally graded core subjected to axial compression and thermal loads. Aerosp Sci Technol 106:106084, 2020.
WU Y, ZHU X, LIU C ET AL. Assessment of interfacial fracture of asphalt mortar-aggregate system at low temperature: a study based on four-point bending test of sandwich beams. Constr Build Mater 352:129057, 2022.
ZHANG J, QIN Q, AI W, LI H, WANG TJ. The failure behavior of geometrically asymmetric metal foam core sandwich beams under three-point bending. J Appl Mech Trans ASME 81(7):1–12, 2014.
ZHANG J, HUANG W, MIAO F, DU J, SUN H. Plastic behavior of sandwich beams with fiber metal laminate face-sheets and metal foam core: combined local denting and overall deformation. Thin Walled Struct 173:108973, 2022 a.
ZHANG J, ZHU Y, YUAN H ET AL. Failure behavior of sandwich beams with glass fiber-reinforced epoxy/aluminum laminates face sheets and aluminum honeycomb core under three-point bending. Thin-Walled Struct 177:109476, 2022 b.
ZIOU, H., & GUENFOUD, M. Simple incremental approach for analyzing optimal non-prismatic functionally graded beams. Advances in Civil and Architectural Engineering, 14(26), 118–137, 2023. https://doi.org/10.13167/2023.26.8

