Araştırma Makalesi
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Static deflection analysis of functionally graded beams using various beam theories

Yıl 2025, Cilt: 5 Sayı: 2, 396 - 420, 30.06.2025

Raghad Azeez Neamah , Ameen Ahmed Nassar , Luay S. Alansari , Emad Kadum Njim , Lazreg Hadji , Royal Madan

https://doi.org/10.53391/mmnsa.1524642

Öz

In the current study, static deflection analysis of a functionally graded (FG) beam is carried out for various theories such as Euler, Timoshenko, and high-order shear deformation theory. The governing equation was solved using the minimum total potential energy principle. Further, for different types of loads, the static deflection analysis of the FG beam was performed using Navier’s solution using the Fortran programming language. Moreover, finite element analysis was also carried out using ANSYS software. In this method, each layer of the FG beam possesses different material properties as per a power law distribution. The different solution techniques are used to calculate the static deflection, and their results are compared. Effect of various parameters such as power index value, modulus ratio, aspect ratio (L/h), and type of loading on the dimensionless transverse deflection of this FG beam model. The results show that the aspect ratio has no significant effect on transverse dimensionless deflection in the case of the Euler beam theory. However, there is a noticeable effect for the Timoshenko and higher-order shear deformation theories, indicating that shear significantly impacts dimensionless transverse deflection for short beams. In addition, it is proven that the present model is reliable and can calculate the static deflection for any other required beam with different loads and dimensions.

Anahtar Kelimeler

FG beam Dimensionless transverse deflection Euler beam theory

Etik Beyan

The authors state that this research complies with ethical standards. This research does not involve either human participants or animals.

Destekleyen Kurum

No funding was received for this research

Proje Numarası

NA

Teşekkür

The authors are grateful to the University of Kufa, College of Engineering/ Iraq, for providing facilities to carry out this work

Kaynakça

  • [1] Tamrabet, A., Mourad, C., Ali Alselami, N., Menasria, A., Mamen, B. and Bouhadra, A. Efficient kinematic model for stability analysis of imperfect functionally graded sandwich plates with ceramic middle layer and varied boundary edges. Journal of Computational Applied Mechanics, 55(2), 184-200, (2024).
  • [2] Akba¸s, ¸S.D. Material nonlinear static analysis of axially functionally graded porous bar elements. Journal of Computational Applied Mechanics, 55(2), 223-234, (2024).
  • [3] Slimani, R., Menasria, A., Ali Rachedi, M., Mourad, C., Refrafi, S., Nimer, A.A. et al. A novel quasi-3D refined HSDT for static bending analysis of porous functionally graded Plates. Journal of Computational Applied Mechanics, 55(3), 519-537, (2024).
  • [4] Naebe, M. and Shirvanimoghaddam, K. Functionally graded materials: A review of fabrication and properties. Applied Materials Today, 5, 223-245, (2016).
  • [5] Kiarasi, F., Babaei, M., Sarvi, P., Asemi, K., Hosseini, M. and Omidi Bidgoli, M. A review on functionally graded porous structures reinforced by graphene platelets. Journal of Computational Applied Mechanics, 52(4), 731-750, (2021).
  • [6] Xu, F., Zhang, X. and Zhang, H. A review on functionally graded structures and materials for energy absorption. Engineering Structures, 171, 309-325, (2018).
  • [7] Çelik, T. and Ta¸s, Z.C. Biomechanical evaluation of a newly developed functional-grade composite material for pedicle screws. World Neurosurgery, 187, e525-e533, (2024).
  • [8] Boggarapu, V., Gujjala, R., Ojha, S., Acharya, S., Chowdary, S. and kumar Gara, D. State of the art in functionally graded materials. Composite Structures, 262, 113596, (2021).
  • [9] Wang, X., Guo, J., Hwang, K.S. and Fang, Z.Z. Review and recent progress on developments of functionally graded WC-Co via a carburizing process: principles, insights, and industrial implications. International Journal of Refractory Metals and Hard Materials, 118, 106443, (2024).
  • [10] Ghanavati, R. and Naffakh-Moosavy, H. Additive manufacturing of functionally graded metallic materials: A review of experimental and numerical studies. Journal of Materials Research and Technology, 13, 1628-1664, (2021).
  • [11] Ansari, M., Jabari, E. and Toyserkani, E. Opportunities and challenges in additive manufacturing of functionally graded metallic materials via powder-fed laser directed energy deposition: A review. Journal of Materials Processing Technology, 294, 117117, (2021).
  • [12] Bhandari, M. and Purohit, K. Dynamic fracture analysis of functionally graded material structures–a critical review. Composites Part C: Open Access, 7, 100227, (2022).
  • [13] Sam, M., Jojith, R. and Radhika, N. Progression in manufacturing of functionally graded materials and impact of thermal treatment—A critical review. Journal of Manufacturing Processes, 68, 1339-1377, (2021).
  • [14] Kiarasi, F., Asadi, A., Babaei, M., Asemi, K. and Hosseini, M. Dynamic analysis of functionally graded carbon nanotube (FGCNT) reinforced composite beam resting on viscoelastic foundation subjected to impulsive loading. Journal of Computational Applied Mechanics, 53(1) 1-23, (2022).
  • [15] Meksi, A., Bachir Bouiadjra, R., Benyoucef, S., Bouhadra, A., Bourada, M., Ghazwani, M. and Tounsi, A. Static stability analysis of FG thick plate supported by three parameters foundation under general boundary conditions. Journal of Computational Applied Mechanics, 55(3), 381-400, (2024).
  • [16] Jin, M., Dong, X., Zhu, D., Yang, J., Lu, C., Zheng, Q. et al. Structure and properties of particles/rubber composites applied on functionally graded lapping and polishing plate. Journal of Polymer Engineering, 40(4), 307-313, (2020).
  • [17] Mellal, F., Bennai, R., Avcar, M., Nebab, M. and Atmane, H.A. On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory. Acta Mechanica, 234, 3955-3977, (2023).
  • [18] Adiyaman, G. Free vibration analysis of a porous 2D functionally graded beam using a highorder shear deformation theory. Journal of Vibration Engineering & Technologies, 12, 2499-2516, (2024).
  • [19] Belkhodja, Y., Ouinas, D., Zaoui, F.Z. and Fekirini, H. An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates. Advanced Composites Letters, 29, 1-19, (2020).
  • [20] Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B. and Nguyen-Xuan, H. A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Composite Structures, 245, 112321, (2020).
  • [21] Zhang, J., Yang, Q.S. and Liu, X. Peridynamics methodology for elasto-viscoplastic ductile fracture. Engineering Fracture Mechanics, 277, 108939, (2023).
  • [22] Akba¸s, ¸S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load. Engineering with Computers, 38, 365-377, (2022).
  • [23] Pei, Y.L. and Li, L.X. A simplified theory of FG curved beams. European Journal of MechanicsA/Solids, 85, 104126, (2021).
  • [24] Noorı, A.R., Aslan, T.A. and Temel, B. Static analysis of FG beams via complementary functions method. European Mechanical Science, 4(1), 1-6, (2020).
  • [25] Boutahar, Y., Lebaal, N. and Bassir, D. A refined theory for bending vibratory analysis of thick functionally graded beams. Mathematics, 9(12), 1422, (2021).
  • [26] Reddy, J.N., Ruocco, E., Loya, J.A. and Neves, A.M. Theories and analysis of functionally graded beams. Applied Sciences, 11(15), 7159, (2021).
  • [27] ¸Sim¸sek, M. and Yurtcu, H.H. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures, 97, 378-386, (2013).
  • [28] Hadji, L., Khelifa, Z. and El Abbes, A.B. A new higher order shear deformation model for functionally graded beams. KSCE Journal of Civil Engineering, 20(5), 1835-1841, (2016).
  • [29] Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3), 519-539, (2003).
  • [30] Madan, R., Bhowmick, S., Hadji, L. and Alnujaie, A. Limit angular speed analysis of porous functionally graded rotating disk under thermo-mechanical loading. Multidiscipline Modeling in Materials and Structures, 19(2), 311-323, (2023).
  • [31] Raad, H., Najim, E.K., Jweeg, M.J., Al-Waily, M., Hadji, L. and Madan, R. Vibration analysis of sandwich plates with hybrid composite cores combining porous polymer and foam structures. Journal of Computational Applied Mechanics, 55(3), 485-499, (2024).
  • [32] Al-Furjan, M.S.H., Yin, C., Shen, X., Kolahchi, R., Zarei, M.S. and Hajmohammad, M.H. Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate. Mechanical Systems and Signal Processing, 178, 109269, (2022).
  • [33] Amara, K., Bouazza, M. and Fouad, B. Postbuckling analysis of functionally graded beams using nonlinear model. Periodica Polytechnica Mechanical Engineering, 60(2), 121-128, (2016).
  • [34] 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 Mechanics, 4, 100039, (2021).
  • [35] Zhang, L., Liao, W., Fan, J. and Feng, S. A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads. Smart Materials and Structures, 33(5), 055051, (2024).
  • [36] Thi, T.H.N., Tran, V.K., Phung, V.M., Trinh, V.H. and Pham, Q.H. Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions. Acta Mechanica Sinica, 40, 523257, (2024).
  • [37] Nam, V.H., Vinh, P.V., Chinh, N.V., Thom, D.V. and Hong, T.T. A new beam model for simulation of the mechanical behaviour of variable thickness functionally graded material beams based on modified first order shear deformation theory. Materials, 12(3), 404, (2019).
  • [38] Njim, E.K., Hasan, H.R., Jweeg, M.J., Al-Waily, M., Hameed, A.A., Youssef, A.M. and Elsayed, F.M. Mechanical properties of sandwiched construction with composite and hybrid core structure. Advances in Polymer Technology, 2024(1), 3803199, (2024).
  • [39] Madan, R. and Bhowmick, S. Fabrication, microstructural characterization and finite element analysis of functionally graded Al-Al2O3 disk using powder metallurgy technique. Materials Today Communications, 32, 103878, (2022).
  • [40] Rahmani, F., Kamgar, R. and Rahgozar, R. Finite element analysis of functionally graded beams using different beam theories. Civil Engineering Journal, 6(11), 2086-2102, (2020).
  • [41] Farhatnia, F. and Sarami, M. Finite element approach of bending and buckling analysis of FG beams based on refined zigzag theory. Universal Journal of Mechanical Engineering, 7(4), 147-158, (2019).
  • [42] Thai, H.T. and Vo, T.P. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57-66, (2012).
  • [43] Madan, R. and Bhowmick, S. Fabrication and microstructural characterization of Al-SiC based functionally graded disk. Aircraft Engineering and Aerospace Technology, 95(2), 292-301, (2023).
  • [44] Madan, R., Khobragade, P. and Bhowmick, S. Impact of porosity on free vibration and limit analysis of power-law-based functionally graded disks. Multidiscipline Modeling in Materials and Structures, 20(6), 1192-1212, (2024).

Yıl 2025, Cilt: 5 Sayı: 2, 396 - 420, 30.06.2025

Raghad Azeez Neamah , Ameen Ahmed Nassar , Luay S. Alansari , Emad Kadum Njim , Lazreg Hadji , Royal Madan

https://doi.org/10.53391/mmnsa.1524642

Öz

Proje Numarası

NA

Kaynakça

  • [1] Tamrabet, A., Mourad, C., Ali Alselami, N., Menasria, A., Mamen, B. and Bouhadra, A. Efficient kinematic model for stability analysis of imperfect functionally graded sandwich plates with ceramic middle layer and varied boundary edges. Journal of Computational Applied Mechanics, 55(2), 184-200, (2024).
  • [2] Akba¸s, ¸S.D. Material nonlinear static analysis of axially functionally graded porous bar elements. Journal of Computational Applied Mechanics, 55(2), 223-234, (2024).
  • [3] Slimani, R., Menasria, A., Ali Rachedi, M., Mourad, C., Refrafi, S., Nimer, A.A. et al. A novel quasi-3D refined HSDT for static bending analysis of porous functionally graded Plates. Journal of Computational Applied Mechanics, 55(3), 519-537, (2024).
  • [4] Naebe, M. and Shirvanimoghaddam, K. Functionally graded materials: A review of fabrication and properties. Applied Materials Today, 5, 223-245, (2016).
  • [5] Kiarasi, F., Babaei, M., Sarvi, P., Asemi, K., Hosseini, M. and Omidi Bidgoli, M. A review on functionally graded porous structures reinforced by graphene platelets. Journal of Computational Applied Mechanics, 52(4), 731-750, (2021).
  • [6] Xu, F., Zhang, X. and Zhang, H. A review on functionally graded structures and materials for energy absorption. Engineering Structures, 171, 309-325, (2018).
  • [7] Çelik, T. and Ta¸s, Z.C. Biomechanical evaluation of a newly developed functional-grade composite material for pedicle screws. World Neurosurgery, 187, e525-e533, (2024).
  • [8] Boggarapu, V., Gujjala, R., Ojha, S., Acharya, S., Chowdary, S. and kumar Gara, D. State of the art in functionally graded materials. Composite Structures, 262, 113596, (2021).
  • [9] Wang, X., Guo, J., Hwang, K.S. and Fang, Z.Z. Review and recent progress on developments of functionally graded WC-Co via a carburizing process: principles, insights, and industrial implications. International Journal of Refractory Metals and Hard Materials, 118, 106443, (2024).
  • [10] Ghanavati, R. and Naffakh-Moosavy, H. Additive manufacturing of functionally graded metallic materials: A review of experimental and numerical studies. Journal of Materials Research and Technology, 13, 1628-1664, (2021).
  • [11] Ansari, M., Jabari, E. and Toyserkani, E. Opportunities and challenges in additive manufacturing of functionally graded metallic materials via powder-fed laser directed energy deposition: A review. Journal of Materials Processing Technology, 294, 117117, (2021).
  • [12] Bhandari, M. and Purohit, K. Dynamic fracture analysis of functionally graded material structures–a critical review. Composites Part C: Open Access, 7, 100227, (2022).
  • [13] Sam, M., Jojith, R. and Radhika, N. Progression in manufacturing of functionally graded materials and impact of thermal treatment—A critical review. Journal of Manufacturing Processes, 68, 1339-1377, (2021).
  • [14] Kiarasi, F., Asadi, A., Babaei, M., Asemi, K. and Hosseini, M. Dynamic analysis of functionally graded carbon nanotube (FGCNT) reinforced composite beam resting on viscoelastic foundation subjected to impulsive loading. Journal of Computational Applied Mechanics, 53(1) 1-23, (2022).
  • [15] Meksi, A., Bachir Bouiadjra, R., Benyoucef, S., Bouhadra, A., Bourada, M., Ghazwani, M. and Tounsi, A. Static stability analysis of FG thick plate supported by three parameters foundation under general boundary conditions. Journal of Computational Applied Mechanics, 55(3), 381-400, (2024).
  • [16] Jin, M., Dong, X., Zhu, D., Yang, J., Lu, C., Zheng, Q. et al. Structure and properties of particles/rubber composites applied on functionally graded lapping and polishing plate. Journal of Polymer Engineering, 40(4), 307-313, (2020).
  • [17] Mellal, F., Bennai, R., Avcar, M., Nebab, M. and Atmane, H.A. On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory. Acta Mechanica, 234, 3955-3977, (2023).
  • [18] Adiyaman, G. Free vibration analysis of a porous 2D functionally graded beam using a highorder shear deformation theory. Journal of Vibration Engineering & Technologies, 12, 2499-2516, (2024).
  • [19] Belkhodja, Y., Ouinas, D., Zaoui, F.Z. and Fekirini, H. An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates. Advanced Composites Letters, 29, 1-19, (2020).
  • [20] Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B. and Nguyen-Xuan, H. A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets. Composite Structures, 245, 112321, (2020).
  • [21] Zhang, J., Yang, Q.S. and Liu, X. Peridynamics methodology for elasto-viscoplastic ductile fracture. Engineering Fracture Mechanics, 277, 108939, (2023).
  • [22] Akba¸s, ¸S.D., Fageehi, Y.A., Assie, A.E. and Eltaher, M.A. Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load. Engineering with Computers, 38, 365-377, (2022).
  • [23] Pei, Y.L. and Li, L.X. A simplified theory of FG curved beams. European Journal of MechanicsA/Solids, 85, 104126, (2021).
  • [24] Noorı, A.R., Aslan, T.A. and Temel, B. Static analysis of FG beams via complementary functions method. European Mechanical Science, 4(1), 1-6, (2020).
  • [25] Boutahar, Y., Lebaal, N. and Bassir, D. A refined theory for bending vibratory analysis of thick functionally graded beams. Mathematics, 9(12), 1422, (2021).
  • [26] Reddy, J.N., Ruocco, E., Loya, J.A. and Neves, A.M. Theories and analysis of functionally graded beams. Applied Sciences, 11(15), 7159, (2021).
  • [27] ¸Sim¸sek, M. and Yurtcu, H.H. Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory. Composite Structures, 97, 378-386, (2013).
  • [28] Hadji, L., Khelifa, Z. and El Abbes, A.B. A new higher order shear deformation model for functionally graded beams. KSCE Journal of Civil Engineering, 20(5), 1835-1841, (2016).
  • [29] Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. A new beam finite element for the analysis of functionally graded materials. International Journal of Mechanical Sciences, 45(3), 519-539, (2003).
  • [30] Madan, R., Bhowmick, S., Hadji, L. and Alnujaie, A. Limit angular speed analysis of porous functionally graded rotating disk under thermo-mechanical loading. Multidiscipline Modeling in Materials and Structures, 19(2), 311-323, (2023).
  • [31] Raad, H., Najim, E.K., Jweeg, M.J., Al-Waily, M., Hadji, L. and Madan, R. Vibration analysis of sandwich plates with hybrid composite cores combining porous polymer and foam structures. Journal of Computational Applied Mechanics, 55(3), 485-499, (2024).
  • [32] Al-Furjan, M.S.H., Yin, C., Shen, X., Kolahchi, R., Zarei, M.S. and Hajmohammad, M.H. Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate. Mechanical Systems and Signal Processing, 178, 109269, (2022).
  • [33] Amara, K., Bouazza, M. and Fouad, B. Postbuckling analysis of functionally graded beams using nonlinear model. Periodica Polytechnica Mechanical Engineering, 60(2), 121-128, (2016).
  • [34] 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 Mechanics, 4, 100039, (2021).
  • [35] Zhang, L., Liao, W., Fan, J. and Feng, S. A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads. Smart Materials and Structures, 33(5), 055051, (2024).
  • [36] Thi, T.H.N., Tran, V.K., Phung, V.M., Trinh, V.H. and Pham, Q.H. Nonlocal isogeometric analysis for bidirectional functionally graded porous curved microbeams with arbitrary boundary conditions. Acta Mechanica Sinica, 40, 523257, (2024).
  • [37] Nam, V.H., Vinh, P.V., Chinh, N.V., Thom, D.V. and Hong, T.T. A new beam model for simulation of the mechanical behaviour of variable thickness functionally graded material beams based on modified first order shear deformation theory. Materials, 12(3), 404, (2019).
  • [38] Njim, E.K., Hasan, H.R., Jweeg, M.J., Al-Waily, M., Hameed, A.A., Youssef, A.M. and Elsayed, F.M. Mechanical properties of sandwiched construction with composite and hybrid core structure. Advances in Polymer Technology, 2024(1), 3803199, (2024).
  • [39] Madan, R. and Bhowmick, S. Fabrication, microstructural characterization and finite element analysis of functionally graded Al-Al2O3 disk using powder metallurgy technique. Materials Today Communications, 32, 103878, (2022).
  • [40] Rahmani, F., Kamgar, R. and Rahgozar, R. Finite element analysis of functionally graded beams using different beam theories. Civil Engineering Journal, 6(11), 2086-2102, (2020).
  • [41] Farhatnia, F. and Sarami, M. Finite element approach of bending and buckling analysis of FG beams based on refined zigzag theory. Universal Journal of Mechanical Engineering, 7(4), 147-158, (2019).
  • [42] Thai, H.T. and Vo, T.P. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. International Journal of Mechanical Sciences, 62(1), 57-66, (2012).
  • [43] Madan, R. and Bhowmick, S. Fabrication and microstructural characterization of Al-SiC based functionally graded disk. Aircraft Engineering and Aerospace Technology, 95(2), 292-301, (2023).
  • [44] Madan, R., Khobragade, P. and Bhowmick, S. Impact of porosity on free vibration and limit analysis of power-law-based functionally graded disks. Multidiscipline Modeling in Materials and Structures, 20(6), 1192-1212, (2024).
Toplam 44 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Diferansiyel ve İntegral Denklemlerin Sayısal Çözümü, Sonlu Elemanlar Analizi, Teorik ve Uygulamalı Mekanik Matematiği
Bölüm Araştırma Makalesi
Yazarlar

Raghad Azeez Neamah 0000-0003-1780-5035

Ameen Ahmed Nassar 0000-0001-7230-4394

Luay S. Alansari 0000-0002-2989-8614

Emad Kadum Njim 0000-0001-9694-971X

Lazreg Hadji 0000-0002-3333-5902

Royal Madan 0000-0002-3445-9210

Proje Numarası NA
Erken Görünüm Tarihi 15 Temmuz 2025
Yayımlanma Tarihi 30 Haziran 2025
Gönderilme Tarihi 31 Temmuz 2024
Kabul Tarihi 17 Haziran 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 5 Sayı: 2

Kaynak Göster

APA Azeez Neamah, R., Ahmed Nassar, A., Alansari, L. S., Kadum Njim, E., vd. (2025). Static deflection analysis of functionally graded beams using various beam theories. Mathematical Modelling and Numerical Simulation With Applications, 5(2), 396-420. https://doi.org/10.53391/mmnsa.1524642
 Kapak Resmi İndir


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