Abstract
This paper examines the analysis of Carbon Nanotubes Reinforced Thin-Walled Steel Beams with Open Cross Sections (CNT-RTWSBOCS). The CNTs are mixed into Thin-Walled Steel Beams with Open Cross Sections (TWSBOCS) to form effective reinforcement. We assume that the distribution of CNTs is uniform or Functionally Graded (FG) across the thickness of TWSBOCS. The nonlinear equilibrium equations of CNT-RTWSBOCS have been derived without any hypothesis on the twist angle. The proposed model is adopted using both rule of mixture theory and Finite Element Method (FEM). The rule of mixture theory is used to estimate the effective material properties for CNT-RTWSBOCS. The incremental iterative methods (such as Newton–Raphson) or Asymptotic Numerical Method (ANM) can be used for solving complicated stability phenomenon of nonlinear-reinforced TWSBOCS. ANM is used in this paper, it is very efficient and takes less computation time for solving nonlinear equations numerically; this is achieved by associating a Taylor series expansions technique and the FEM. To produce high quality and low cost CNT-based TWSBOCS, the design optimization of CNT distributions in TWSBOCS is studied. In this regard, the influence of partial reinforcement on the buckling response of CNT-RTWSBOCS is investigated. The effects of various parameters, such as the CNT volume fraction and distribution patterns of CNTs, are also investigated.
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References
Al-Furjan MSH, Habibi M, Ni J, Jung DW, Tounsi A (2020) Frequency simulation of viscoelastic multi-phase reinforced fully symmetric systems. Eng Comput 35:1542
Al-Furjan MSH, Habibi M, Ghabussie A, Safarpour H, Safarpour M, Tounsi A (2021a) Non-polynomial framework for stress and strain response of the FG-GPLRC disk using three-dimensional refined higher-order theory. Eng Struct 228:111496
Al-Furjan MSH, Habibi M, Rahimi A, Chen G, Safarpour H, Safarpour M, Tounsi A (2022b) Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM. Eng Comput 38:219–242
Al-Furjan MSH, Habibi M, Jung DW, Sadeghi S, Safarpour H, Tounsi A, Chen G (2022c) Eng Comput 38:1679–1696
Al-Furjan MSH, Hatami A, Habibi M, Shan L, Tounsi A (2021b) On the vibrations of the imperfect sandwich higher-order disk with a lactic core using generalize differential quadrature method. Compos Struct 257:113150
Al-Furjan MSH, Safarpour H, Habibi M, Safarpour M, Tounsi A (2022a) A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method. Eng Comput 38:801–818
Alimirzaei S, Mohammadimehr M, Tounsi A (2019) Nonlinear analysis of viscoelastic microcomposite beam with geometrical imperfection using FEM: MSGT electro-magneto elastic bending, buckling and vibration solutions. Struct Eng Mech 71(5):485–502
Arshid E, Khorasani M, Soleimani-Javid Z, Amir S, Tounsi A (2021) Porosity-dependent vibration analysis of FG microplates embedded by polymeric nanocomposite patches considering hygrothermal effect via an innovative plate theory. Eng Comput 21:1253
Attard MM (1986) Lateral buckling analysis of beams by the FEM. Comput Struct 23:217–231
Batoz JL, Dhatt G (1990) Modélisation des structures par éléments finis. Hermès, Paris
Bazoune A, Khulief YA, Stephen NG, Mohiuddin MA (2001) Dynamic response of spinning tapered timoshenko beams using modal reduction. Finite Elem Anal Des 37(3):199–219
Bendenia N, Zidour M, Bousahla AA, Bourada F, Tounsi AJ, Benrahou KH, Adda Bedia EA, Mahmoud SR, Tounsi A (2020) Deflections, stresses and free vibration studies of FG-CNT reinforced sandwich plates resting on Pasternak elastic foundation. Comput Concr 26(3):213–226
Bourada F, Bousahla AA, Tounsi A, Adda Bedia A, Mahmoud SR, Benrahou KH, Tounsi A (2020) Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic foundation. Comput Concr 25(6):485–495
Bourihane O, Ed-dinari A, Braikat B, Jamal M, Mohri F, Damil N (2016) Stability analysis of thin-walled beams with open section subject to arbitrary loads. Thin-Walled Struct 105:156–171
Djilali N, Bousahla AA, Kaci A, Selim MM, Bourada F, Tounsi AJ, Tounsi A, Benrahou KH, Mahmoud SR (2022) Large cylindrical deflection analysis of FG carbon nanotube-reinforced plates in thermal environment using a simple integral HSDT. Steel Compos Struct 42:779–789
Ed-dinari A, Mottaqui H, Braikat B, Jamal M, Mohri F, Damil N (2014) Large torsion analysis of thin-walled open sections beams by the asymptotic numerical method. Eng Struct 81:240–255
El Kadmiri R, Belaasilia Y, Timesli A, Kadiri MS (2022) A hybrid algorithm using the FEM-MESHLESS method to solve nonlinear structural problems. Eng Anal Bound Elem 140:531–543
El Kaimbillah A, Bourihane O, Braikat B, Jamal M, Mohri F, Damil N (2019) Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings. Disc Contin Dyn Syst Ser S 12:1685–1708
Garg A, Belarbi MO, Tounsi A, Li L, Singh A, Mukhopadhyay T (2022a) Predicting elemental stiffness matrix of FG nanoplates using Gaussian Process Regression based surrogate model in framework of layerwise model. Eng Anal Bound Elem 143:779–795
Garg A, Aggarwal P, Aggarwal Y, Belarbi MO, Chalak HD, Tounsi A, Gulia R (2022b) Machine learning models for predicting the compressive strength of concrete containing nano silica. Comput Concr 30(1):33–42
Hajmohammad MH, Kolahchi R, Zarei MS, Nouri AH (2019) Dynamic response of auxetic honeycomb plates integrated with agglomerated CNT-reinforced face sheets subjected to blast load based on visco-sinusoidal theory. Int J Mech Sci 153–154:391–401
Heidari F, Taheri K, Sheybani M, Janghorban M, Tounsi A (2021) On the mechanics of nanocomposites reinforced by wavy/defected/aggregated nanotubes. Steel Compos Struct 38(5):533–545
Hsiao KM, Lin WY (2000) A co-rotational formulation for thin-walled beams with monosymmetric open section. Comput Methods Appl Mech Eng 190:1163–1185
Huang Y, Karami B, Shahsavari D, Tounsi A (2021) Static stability analysis of carbon nanotube reinforced polymeric composite doubly curved micro-shell panels. Arch Civil Mech Eng 21:139
Janane Allah M, Timesli A, Belaasilia Y (2022) Nonlinear dynamic analysis of porous functionally graded materials based on new third-order shear deformation theory. Steel Compos Struct 43(1):1–17
Kaci A, Tounsi A, Bakhti K, Adda Bedia EA (2012) Nonlinear cylindrical bending of functionally graded carbon nanotube-reinforced composite plates. Steel Compos Struct 12(6):491–504
Katsikadelis JT, Tsiatas GC (2004) Non-linear dynamic analysis of beams with variable stiffness. J Sound Vib 270(4–5):847–863
Kitipornchai S, Trahair NS (1975) Elastic behavior of tapered monosymmetric i-beams. J Struct Div ASCE 11479 Proc 101:1524
Kong F, Dong F, Duan M, Habibi M, Safarpour H, Tounsi A (2022) On the vibrations of the Electrorheological sandwich disk with composite face sheets considering pre and pos yield regions. Thin-Walled Struct 179:109631
Liao M, Zhong H (2008) Nonlinear vibration analysis of tapered Timoshenko beams. Chaos, Solitons Fract 36(5):1267–1272
Lin WY, Hsiao KM (2001) A co-rotational formulation for geometric nonlinear analysis of doubly symmetric thin-walled beams. Comput Methods Appl Mech Eng 190:6023–6052
Mohri F, Potier-Ferry M (2006) Effects of load height application and pre-buckling deflections on lateral buckling of thin-walled beams. Steel Compos Struct 6(5):401–415
Mohri F, Damil N, Potier-Ferry M (2008) Large torsion finite element model for thin-walled beams. Comput Struct 86:671–683
Moradi-Dastjerdi R, Payganeh G (2017) Transient heat transfer analysis of functionally graded CNT reinforced cylinders with various boundary conditions. Steel Compos Struct 24(3):359–367
Radhamani AV, Lau HC, Ramakrishna S (2018) CNT-reinforced metal and steel nanocomposites: a comprehensive assessment of progress and future directions. Compos A Appl Sci Manuf 114:170–187
Raju KK, Shastry BP, Rao GV (1976) A finite element formulation forthe large amplitude vibrations of tapered beams. J Sound Vib 47:595–598
Ronagh HR, Bradford MA, Attard MM (2000) Nonlinear analysis of thinwalled members of variable cross section (part i). Theoret Comput Sci 27:285–599
Ronagh HR, Bradford MA, Attard MM (2000) Nonlinear analysis of thin-walled members of variable cross-section part i: theory. Comput Struct 77(3):285–299
Russillo AF, Failla G, Alotta G, Sciarra FM, Barretta R (2021) On the dynamics of nano-frames. Int J Eng Sci 160:103433
Saffah Z, Timesli A, Lahmam H, Azouani A, Amdi M (2021) New collocation path-following approach for the optimal shape parameter using Kernel method. SN Appl Sci 3:249
Sapountzakis EJ, Mokos VG (2004) Non uniform torsion of composite bars of variable thickness by bem. Int J Solids Struct 41(7):1753–1771
Shafiei H, Setoodeh AR (2017a) Nonlinearfree vibration and post-buckling of FG-CNTRC beams on nonlinear foundation. Steel Compos Struct 24(1):65–77
Shafiei H, Setoodeh AR (2017b) Nonlinear free vibration and post-buckling of FG-CNTRC beams on nonlinear foundation. Steel Compos Struct 24(1):65–77
Shavezipur M, Hashemi SM (2009) Free vibration of triply coupled centrifugally stiffened nonuniform beams, using a refined dynamic finite element method. Aerosp Sci Technol 13(1):59–70
Shokravi M (2017) Buckling of sandwich plates with FG-CNT-reinforced layers resting on orthotropic elastic medium using Reddy plate theory. Steel Compos Struct 23(6):623–631
Tagrara SH, Benachour A, Bouiadjra MB, Tounsi A (2015) On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams. Steel Compos Struct 19:1259–1277
Timesli A (2020) Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation. Comput Concr 26(1):53–62
Timesli A (2021) A cylindrical shell model for nonlocal buckling behavior of CNTs embedded in an elastic foundation under the simultaneous effects of magnetic field, temperature change, and number of walls. Adv Nano Res 11(6):581–593
Tımesli A (2022) Analytical modeling of buckling behavior of porous FGM cylindrical shell embedded within an elastic foundation. Gazi Univ J Sci 35(1):148–165
Vinh PV, Chinh NV, Tounsi A (2022) Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM. Eur J Mech A Solids 96:104743
Vlasov VZ (1959) Thin-walled elastic beam, 2nd edn. Gosudarstvenoe Izdatelstvo Fiziko-Matematicheskoi Literaturi (in Russian), Moscow
Zerrouki R, Karas A, Zidour M, Bousahla AA, Tounsi A, Bourada F, Tounsi AJ, Benrahou KH, Mahmoud SR (2021) Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam. Struct Eng Mech 78(2):117–124
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El Haouzi, A., Belaasilia, Y. & Timesli, A. Analysis of CNT-Reinforced Thin-Walled Steel Beams with Open Cross Sections. Iran J Sci Technol Trans Mech Eng 47, 1747–1759 (2023). https://doi.org/10.1007/s40997-022-00582-1
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DOI: https://doi.org/10.1007/s40997-022-00582-1