Comparative Investigation of Deflection in a Two-directional Functionally Graded Porous Curved and Straight Beams Adapting Unified Shear Deformation Theory
Document Type : Research Paper
Authors
1 Department of Mechanical Engineering, MLR Institute of Technology, Hyderabad, India
2 Department of Mechanical Engineering, VNRVJIET, Hyderabad, India
3 Department of Mechanical Engineering, Malla Reddy Engineering College, Hyderabad, India
4 Department of Chemical & Materials Engineering, College of Science, Engineering and Technology, University of South Africa (UNISA), c/o Christiaan de Wet & Pioneer Avenue, Florida Campus 1710, Johannesburg, South Africa
Abstract
Functionally graded (FG) materials exhibit spatial variations in composition and structure, which enhance their performance under mechanical loads by tailoring material properties such as modulus of elasticity and density along the beam's length or thickness. This study presents a comparative analysis of the deflection behaviors of two-directional functionally graded porous beam, specifically focusing on circular and straight beams. Curved and straight beams are modeled and assessed under simply supported (SS), clamped (CC) and clamped simply supported (CS) boundary conditions with a mechanical load. The analysis involves deriving deflection equations considering the graded material properties, which vary according to a power-law distribution, adapting unified shear deformation theory (USDT), potential energy, neutral surface concept for better accuracy.
Keywords
Main Subjects
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[21] X. Wang, Z. Yuan, C. Jin, 3D free vibration analysis of multi-directional FGM parallelepipeds using the quadrature element method, Applied mathematical modelling, Vol. 68, pp. 383-404, 2019.
[22] H. Yang, C. Dong, Y. Wu, Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM, Applied Mathematical Modelling, Vol. 84, pp. 466-500, 2020.
[23] S. Thai, V. X. Nguyen, Q. X. Lieu, Bending and free vibration analyses of multi-directional functionally graded plates in thermal environment: A three-dimensional Isogeometric Analysis approach, Composite Structures, Vol. 295, pp. 115797, 2022.
[24] G. M. B. Chami, A. Kahil, L. Hadji, R. Madan, A. Tounsi, Free vibration analysis of multi-directional porous functionally graded sandwich plates, Steel and Composite Structures, An International Journal, Vol. 46, No. 2, pp. 263-277, 2023.
[25] L. Hadji, F. Bernard, R. Madan, A. Alnujaie, M. H. Ghazwani, Bending and buckling of porous multidirectional functionality graded sandwich plate, Structural Engineering and Mechanics, An Int'l Journal, Vol. 85, No. 2, pp. 233-246, 2023.
[26] Q.-H. Pham, V. K. Tran, P.-C. Nguyen, Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method, Case Studies in Thermal Engineering, Vol. 40, pp. 102478, 2022.
[27] I. Ahmadi, J. Sladek, V. Sladek, Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method, Mechanics of Advanced Materials and Structures, pp. 1-22, 2023.
[28] A. Karamanli, T. P. Vo, Finite element model for free vibration analysis of curved zigzag nanobeams, Composite Structures, Vol. 282, pp. 115097, 2022.
[29] M. Motezaker, R. Kolahchi, D. K. Rajak, S. Mahmoud, Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load, Polymer Composites, Vol. 42, No. 8, pp. 4073-4081, 2021.
[30] M. Al-Furjan, M. H. Hajmohammad, X. Shen, D. K. Rajak, R. Kolahchi, Evaluation of tensile strength and elastic modulus of 7075-T6 aluminum alloy by adding SiC reinforcing particles using vortex casting method, Journal of Alloys and Compounds, Vol. 886, pp. 161261, 2021.
[31] R. Kolahchi, B. Keshtegar, N.-T. Trung, Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions, Journal of Sandwich Structures & Materials, Vol. 24, No. 1, pp. 643-662, 2022.
[32] P. Wan, M. Al-Furjan, R. Kolahchi, Nonlinear flutter response and reliability of supersonic smart hybrid nanocomposite rupture trapezoidal plates subjected to yawed flow using DQHFEM, Aerospace Science and Technology, Vol. 145, pp. 108862, 2024.
[33] C. Chu, M. Al-Furjan, R. Kolahchi, Energy harvesting and dynamic response of SMA nano conical panels with nanocomposite piezoelectric patch under moving load, Engineering Structures, Vol. 292, pp. 116538, 2023.
[34] M. Al-Furjan, S. Fan, L. Shan, A. Farrokhian, X. Shen, R. Kolahchi, Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers, Waves in Random and Complex Media, pp. 1-30, 2023.
[35] M. Al-Furjan, R. Kolahchi, L. Shan, M. Hajmohammad, A. Farrokhian, X. Shen, Slamming impact induced hydrodynamic response in wave-piercing catamaran beam elements with controller, Ocean Engineering, Vol. 266, pp. 112908, 2022.
[36] M. Al-Furjan, M. Xu, A. Farrokhian, G. S. Jafari, X. Shen, R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves in Random and Complex Media, pp. 1-25, 2022.
[37] M. Al‐Furjan, Y. Yang, A. Farrokhian, X. Shen, R. Kolahchi, D. K. Rajak, Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories, Polymer Composites, Vol. 43, No. 1, pp. 282-298, 2022.
[38] M. Al-Furjan, C. Yin, X. Shen, R. Kolahchi, M. S. Zarei, M. Hajmohammad, Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate, Mechanical Systems and Signal Processing, Vol. 178, pp. 109269, 2022.
[39] P. Wan, M. Al-Furjan, R. Kolahchi, L. Shan, Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration, Mechanical Systems and Signal Processing, Vol. 189, pp. 110064, 2023.
[2] A. RAZOUKI, B. Lhoucine, E. B. Khalid, The Exact Analytical Solution of the Bending Analysis of Thick Functionally Graded Beams with Higher Order Shear Deformation Theory Using Differential Transform Method, International Journal of Advanced Research in Engineering and Technology (IJARET), Vol. 11, No. 5, 2020.
[3] S. Coskun, J. Kim, H. Toutanji, Bending, free vibration, and buckling analysis of functionally graded porous micro-plates using a general third-order plate theory, Journal of Composites Science, Vol. 3, No. 1, pp. 15, 2019.
[4] R. Sayyad, V. Rathi, P. Kolase, Bending Analysis of Functionally Graded Beam Curved in Elevation Using Higher Order Theory, International Research Journal of Engineering and Technology (IRJET), Vol. 6, No. 8, pp. 361-367, 2019.
[5] J. Kim, K. K. Żur, J. N. Reddy, Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates, Composite Structures, Vol. 209, pp. 879-888, 2019.
[6] M. Lezgy-Nazargah, A four-variable global–local shear deformation theory for the analysis of deep curved laminated composite beams, Acta Mechanica, Vol. 231, No. 4, pp. 1403-1434, 2020.
[7] H. Hu, T. Yu, T. Q. Bui, Dynamic and static isogeometric analysis for laminated Timoshenko curved microbeams, Engineering Analysis with Boundary Elements, Vol. 128, pp. 90-104, 2021.
[8] M. S. Beg, M. Y. Yasin, Bending, free and forced vibration of functionally graded deep curved beams in thermal environment using an efficient layerwise theory, Mechanics of Materials, Vol. 159, pp. 103919, 2021.
[9] M.-O. Belarbi, M. S. A. Houari, H. Hirane, A. A. Daikh, S. P. A. Bordas, On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory, Composite Structures, Vol. 279, pp. 114715, 2022.
[10] A. S. Sayyad, Y. M. Ghugal, A sinusoidal beam theory for functionally graded sandwich curved beams, Composite Structures, Vol. 226, pp. 111246, 2019.
[11] A. Karamanlı, Bending analysis of two directional functionally graded beams using a four-unknown shear and normal deformation theory, Politeknik Dergisi, Vol. 21, No. 4, pp. 861-874, 2018.
[12] A. S. Sayyad, P. V. Avhad, A new higher order shear and normal deformation theory for the free vibration analysis of sandwich curved beams, Composite Structures, Vol. 280, pp. 114948, 2022.
[13] Y. Pei, L. Li, Comment on the Navier’s solution in “A sinusoidal beam theory for functionally graded sandwich curved beams”(Composite Structures 226 (2019) 111246), Composite Structures, Vol. 243, pp. 112248, 2020.
[14] L. Hadji, F. Bernard, N. Zouatnia, Bending and free vibration analysis of porous-functionally-graded (PFG) beams resting on elastic foundations, Fluid Dynamic and Material Process, Vol. 19, No. 4, pp. 1043-1054, 2023.
[15] M. Saad, L. Hadji, Thermal buckling analysis of porous FGM plates, Materials Today: Proceedings, Vol. 53, pp. 196-201, 2022.
[16] M. Avcar, L. Hadji, R. Akan, The influence of Winkler-Pasternak elastic foundations on the natural frequencies of imperfect functionally graded sandwich beams, Geomechanics and Engineering, Vol. 31, No. 1, pp. 99-112, 2022.
[17] L. Hadji, A. Fallah, M. M. Aghdam, Influence of the distribution pattern of porosity on the free vibration of functionally graded plates, Structural Engineering and Mechanics, Vol. 82, No. 2, pp. 151-161, 2022.
[18] R. Madan, S. Bhowmick, L. Hadji, A. Tounsi, Limit elastic speed analysis of rotating porous annulus functionally graded disks, Steel and Composite Structures, Vol. 42, No. 3, pp. 375-388, 2022.
[19] A. S. Sayyad, P. V. Avhad, L. Hadji, On the static deformation and frequency analysis of functionally graded porous circular beams, Forces in Mechanics, Vol. 7, pp. 100093, 2022.
[20] G. M. B. Chami, A. Kahil, L. Hadji, Influence of porosity on the fundamental natural frequencies of FG sandwich beams, Materials Today: Proceedings, Vol. 53, pp. 107-112, 2022.
[21] X. Wang, Z. Yuan, C. Jin, 3D free vibration analysis of multi-directional FGM parallelepipeds using the quadrature element method, Applied mathematical modelling, Vol. 68, pp. 383-404, 2019.
[22] H. Yang, C. Dong, Y. Wu, Postbuckling analysis of multi-directional perforated FGM plates using NURBS-based IGA and FCM, Applied Mathematical Modelling, Vol. 84, pp. 466-500, 2020.
[23] S. Thai, V. X. Nguyen, Q. X. Lieu, Bending and free vibration analyses of multi-directional functionally graded plates in thermal environment: A three-dimensional Isogeometric Analysis approach, Composite Structures, Vol. 295, pp. 115797, 2022.
[24] G. M. B. Chami, A. Kahil, L. Hadji, R. Madan, A. Tounsi, Free vibration analysis of multi-directional porous functionally graded sandwich plates, Steel and Composite Structures, An International Journal, Vol. 46, No. 2, pp. 263-277, 2023.
[25] L. Hadji, F. Bernard, R. Madan, A. Alnujaie, M. H. Ghazwani, Bending and buckling of porous multidirectional functionality graded sandwich plate, Structural Engineering and Mechanics, An Int'l Journal, Vol. 85, No. 2, pp. 233-246, 2023.
[26] Q.-H. Pham, V. K. Tran, P.-C. Nguyen, Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method, Case Studies in Thermal Engineering, Vol. 40, pp. 102478, 2022.
[27] I. Ahmadi, J. Sladek, V. Sladek, Size dependent free vibration analysis of 2D-functionally graded curved nanobeam by meshless method, Mechanics of Advanced Materials and Structures, pp. 1-22, 2023.
[28] A. Karamanli, T. P. Vo, Finite element model for free vibration analysis of curved zigzag nanobeams, Composite Structures, Vol. 282, pp. 115097, 2022.
[29] M. Motezaker, R. Kolahchi, D. K. Rajak, S. Mahmoud, Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load, Polymer Composites, Vol. 42, No. 8, pp. 4073-4081, 2021.
[30] M. Al-Furjan, M. H. Hajmohammad, X. Shen, D. K. Rajak, R. Kolahchi, Evaluation of tensile strength and elastic modulus of 7075-T6 aluminum alloy by adding SiC reinforcing particles using vortex casting method, Journal of Alloys and Compounds, Vol. 886, pp. 161261, 2021.
[31] R. Kolahchi, B. Keshtegar, N.-T. Trung, Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions, Journal of Sandwich Structures & Materials, Vol. 24, No. 1, pp. 643-662, 2022.
[32] P. Wan, M. Al-Furjan, R. Kolahchi, Nonlinear flutter response and reliability of supersonic smart hybrid nanocomposite rupture trapezoidal plates subjected to yawed flow using DQHFEM, Aerospace Science and Technology, Vol. 145, pp. 108862, 2024.
[33] C. Chu, M. Al-Furjan, R. Kolahchi, Energy harvesting and dynamic response of SMA nano conical panels with nanocomposite piezoelectric patch under moving load, Engineering Structures, Vol. 292, pp. 116538, 2023.
[34] M. Al-Furjan, S. Fan, L. Shan, A. Farrokhian, X. Shen, R. Kolahchi, Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers, Waves in Random and Complex Media, pp. 1-30, 2023.
[35] M. Al-Furjan, R. Kolahchi, L. Shan, M. Hajmohammad, A. Farrokhian, X. Shen, Slamming impact induced hydrodynamic response in wave-piercing catamaran beam elements with controller, Ocean Engineering, Vol. 266, pp. 112908, 2022.
[36] M. Al-Furjan, M. Xu, A. Farrokhian, G. S. Jafari, X. Shen, R. Kolahchi, On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories, Waves in Random and Complex Media, pp. 1-25, 2022.
[37] M. Al‐Furjan, Y. Yang, A. Farrokhian, X. Shen, R. Kolahchi, D. K. Rajak, Dynamic instability of nanocomposite piezoelectric‐leptadenia pyrotechnica rheological elastomer‐porous functionally graded materials micro viscoelastic beams at various strain gradient higher‐order theories, Polymer Composites, Vol. 43, No. 1, pp. 282-298, 2022.
[38] M. Al-Furjan, C. Yin, X. Shen, R. Kolahchi, M. S. Zarei, M. Hajmohammad, Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate, Mechanical Systems and Signal Processing, Vol. 178, pp. 109269, 2022.
[39] P. Wan, M. Al-Furjan, R. Kolahchi, L. Shan, Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration, Mechanical Systems and Signal Processing, Vol. 189, pp. 110064, 2023.
)
Volume 56, Issue 1
January 2025Pages 145-161
- Receive Date: 30 May 2024
- Revise Date: 11 June 2024
- Accept Date: 12 June 2024