Abstract
Sandwich beams made of advanced materials are used in many engineering areas. This paper presents a study on the nonlinear hygro-thermo-mechanical coupling loading (NL-HTMCL). Various symmetric and non-symmetric sandwich beams with FG material in the skins of functionally graded sandwich beams (FGSBs) have been considered. The physico-mechanical properties vary gradually and continuously according to a power-law distribution of the constituent materials’ volume fractions. A new quasi-3D high shear deformation theory is used here to study the behavior of multi-type sandwich beams. The present model adopts a new field of displacement, which includes indeterminate integral variables. The governing equations for this investigation are obtained through the principle of virtual displacement and solved via the Navier-type method. Further, the nonlinear hygro-thermo-mechanical coupling loading (NL-HTMCL) is involved in these equations. A series of parametric studies discussing the flexural behavior of composite sandwich beams under different sets of hygro-thermo-mechanical loading is carried out. Finally, the numerical results show that the NL-HTMCL significantly affects the flexural characteristics of tested beams.
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References
Afzali M, Farrokh M, Carrera E (2022) Thermal buckling loads of rectangular FG plates with temperature-dependent properties using Carrera Unified Formulation. Compos Struct. https://doi.org/10.1016/j.compstruct.2022.115787
Akbas SD (2022) Moving-load dynamic analysis of AFG beams under thermal effect. Steel Compos Struct 42(5):649–655. https://doi.org/10.12989/scs.2022.42.5.649
Al-Osta MA (2022) Wave propagation investigation of a porous sandwich FG plate under hygrothermal environments via a new first-order shear deformation theory. Steel Compos Struct 43(1):117–127. https://doi.org/10.12989/scs.2022.43.1.117
Arbind ARCHANA, Reddy JN, Srinivasa AR (2014) Modified couple stress-based third-order theory for nonlinear analysis of functionally graded beams. Latin Am J Solids Struct 11:459–487. https://doi.org/10.1590/S1679-78252014000300006
Azandariani MG, Gholami M, Nikzad A (2022) Eringen’s nonlocal theory for nonlinear bending analysis of BGF Timoshenko nanobeams. Adv Nano Res 12(1):37–47. https://doi.org/10.12989/anr.2022.12.1.037
Ching HK, Chen JK (2007) Thermal stress analysis of functionally graded composites with temperature-dependent material properties. J Mech Mater Struct 2(4):633–653. https://doi.org/10.2140/jomms.2007.2.633
Cuong-Le T, Nguyen KD, Hoang-Le M, Sang-To T, Phan-Vu P, Wahab MA (2022) Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate. Physica B 631:413726. https://doi.org/10.1016/j.physb.2022.413726
Daouadji TH, Benferhat R (2016) Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation. Adv Mater Res 5(1):035. https://doi.org/10.12989/amr.2016.5.1.035
Du M, Liu J, Ye W, Yang F, Lin G (2022) A new semi-analytical approach for bending, buckling and free vibration analyses of power law functionally graded beams. Struct Eng Mech 81(2):179–194. https://doi.org/10.12989/sem.2022.81.2.179
El-Megharbel A (2016) A theoretical analysis of functionally graded beam under thermal loading. World J Eng Technol 4(3):437–449. https://doi.org/10.4236/wjet.2016.43044
Eltaher MA, Akbaş ŞD (2020) Transient response of 2D functionally graded beam structure. Struct Eng Mech Int J 75(3):357–367. https://doi.org/10.12989/sem.2020.75.3.357
Esfahani SE, Kiani Y, Eslami MR (2013) Nonlinear thermal stability analysis of temperature dependent FGM beams supported on nonlinear hardening elastic foundations. Int J Mech Sci 69:10–20. https://doi.org/10.1016/j.ijmecsci.2013.01.007
Ghamkhar M, Harbaoui I, Hussain M, Ayed H, Khadimallah MA, Alshoaibi A (2022) Structural monitoring of layered FGM distribution ring support: analysis with and without internal pressure. Adv Nano Res 12(3):337–344. https://doi.org/10.12989/anr.2022.12.3.337
Ghumare SM, Sayyad AS (2020) Analytical solutions for the hygro-thermo-mechanical bending of FG beams using a new fifth order shear and normal deformation theory. Appl Comput Mech. https://doi.org/10.24132/acm.2020.580
Giunta G, Crisafulli D, Belouettar S, Carrera E (2013) A thermo-mechanical analysis of functionally graded beams via hierarchical modelling. Compos Struct 95:676–690. https://doi.org/10.1016/j.compstruct.2012.08.013
Guptaa S, Chalak HD (2022) Bending and free vibration analysis of FG sandwich beams using higher-order zigzag theory. Steel Compos Struct 45(4):483–499. https://doi.org/10.12989/scs.2022.45.4.483
Huang XH, Yu NT, Azim I, Zhu J, Wu MJ (2022a) A comparative analysis of thermos-mechanical behavior of CNT-reinforced composite plates: capturing the effects of thermal shrinkage. Case Stud Therm Eng 38:102347. https://doi.org/10.1016/j.csite.2022.102347
Huang X, Shan H, Chu W, Chen Y (2022b) Computational and mathematical simulation for the size-dependent dynamic behavior of the high-order FG nanotubes, including the porosity under the thermal effects. Adv Nano Res 12(1):101–115. https://doi.org/10.12989/anr.2022.12.1.101
Karami B, Shahsavari D, Janghorban M, Li L (2020) Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment. Struct Eng Mech Int J 73(2):191–207. https://doi.org/10.1289/sem.2020.73.2.191
Khosravi S, Arvin H, Kiani Y (2019) Interactive thermal and inertial buckling of rotating temperature-dependent FG-CNT reinforced composite beams. Compos B Eng 175:107178. https://doi.org/10.1016/j.compositesb.2019.107178
Kumar HS, Kattimani S (2022) Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities. Struct Eng Mech 82(4):477–490. https://doi.org/10.12989/sem.2022.82.4.477
Ma LS, Wang TJ (2003) Nonlinear bending and post-buckling of a functionally graded circular plate under mechanical and thermal loadings. Int J Solids Struct 40(13-14):3311–3330. https://doi.org/10.1016/S0020-7683(03)00118-5
Ma LS, Lee DW (2011) A further discussion of nonlinear mechanical behavior for FGM beams under in-plane thermal loading. Compos Struct 93(2):831–842. https://doi.org/10.1016/j.compstruct.2010.07.011
Ma LS, Lee DW (2012) Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading. Eur J Mech A Solids 31(1):13–20. https://doi.org/10.1016/j.euromechsol.2011.06.016
Madenci E, Gülcü Ş (2020) Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM. Struct Eng Mech Int J 75(5):633–642. https://doi.org/10.1289/sem.2020.75.5.633
Man Y (2022) On the dynamic stability of a composite beam via modified high-order theory. Comput Concr 30(2):151–164. https://doi.org/10.12989/cac.2022.30.2.151
Moradi A, Poorveis D, Khajehdezfuly A (2022) Buckling of FGM elliptical cylindrical shell under follower lateral pressure. Steel Compos Struct 45(2):175–191. https://doi.org/10.12989/SCS.2022.45.2.175
Polat A, Kaya Y (2022) Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method. Comput Concr 29(4):247–253. https://doi.org/10.12989/cac.2022.29.4.247
Sankar BV, Tzeng JT (2002) Thermal stresses in functionally graded beams. AIAA J 40(6):1228–1232. https://doi.org/10.2514/2.1775
Sator L, Sladek V, Sladek J (2018) Bending of FGM plates under thermal load: classical thermoelasticity analysis by a meshless method. Compos B Eng 146:176–188. https://doi.org/10.1016/j.compositesb.2018.04.004
Sayyad AS, Ghugal YM (2019) Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory. J Therm Stress 42(2):213–232. https://doi.org/10.1080/01495739.2018.1469962
Shen HS (2002) Nonlinear bending response of functionally graded plates subjected to transverse loads and in thermal environments. Int J Mech Sci 44(3):561–584. https://doi.org/10.1016/S0020-7403(01)00103-5
Shen HS, Xiang Y (2021) Examination of thermal postbuckling of temperature dependent FG-GRMMC laminated beams with negative Poisson’s ratio on elastic foundations. Compos Struct 272:114066. https://doi.org/10.1016/j.compstruct.2021.114066
Şimşek M, Al-Shujairi M (2017) Static, free and forced vibration of functionally graded (FG) sandwich beams excited by two successive moving harmonic loads. Compos B Eng 108:18–34. https://doi.org/10.1016/j.compositesb.2016.09.098
Sobhy M (2021) Differential quadrature method for magneto-hygrothermal bending of functionally graded graphene/Al sandwich-curved beams with honeycomb core via a new higher-order theory. J Sandw Struct Mater 23(5):1662–1700. https://doi.org/10.1177/1099636219900668
Sobhy M, Abazid MA, Al Mukahal FH (2022) Electro-thermal buckling of FG graphene platelets-strengthened piezoelectric beams under humid conditions. Adv Mech Eng 14(4):16878132221091004. https://doi.org/10.1177/1687813222109100
Thanh CL, Nguyen TN, Vu TH, Khatir S, Abdel Wahab M (2020) A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate. Eng Comput. https://doi.org/10.1007/s00366-020-01154-0
Vo TP, Thai HT, Nguyen TK, Inam F, Lee J (2015) Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Compos B Eng 68:59–74. https://doi.org/10.1016/j.compositesb.2014.08.030
Wu MJ, Zhao SY, Azim I, Zhu J, Huang XH (2022) Design and thermo-mechanical analysis of sandwich structures with negative thermal expansion. Int J Mech Mater Des 18(4):807–822. https://doi.org/10.1007/s10999-022-09609-6
Wu MJ, Zhu J, Azim I, Chen H, Huang XH (2023a) Auxetic effects in the large deflection bending characteristics of FG GRMMC shallow arches. Appl Math Model 119:534–548. https://doi.org/10.1016/j.apm.2023.02.034
Wu MJ, Huang XH, Azim I, Zhu J, Chen H (2023b) Nonlinear dynamic and vibration characteristics of metamaterial shallow arches. Eur J Mech A Solids 102:105084. https://doi.org/10.1016/j.euromechsol.2023.105084
Yang J, Huang XH, Shen HS (2020) Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson’s ratio resting on the Pasternak foundation. Eng Struct 207:110250. https://doi.org/10.1016/j.engstruct.2020.110250
Zenkour AM, Radwan AF (2019a) Bending response of FG plates resting on elastic foundations in hygrothermal environment with porosities. Compos Struct 213:133–143. https://doi.org/10.1016/j.compstruct.2019.01.065
Zenkour AM, Radwan AF (2019b) Hygrothermo-mechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model. Int J Comput Methods Eng Sci Mech 20(2):85–98. https://doi.org/10.1080/15502287.2019.1568618
Zenkour AM, Radwan AF (2020) Bending and buckling analysis of FGM plates resting on elastic foundations in hygrothermal environment. Arch Civ Mech Eng 20(4):1–23. https://doi.org/10.1007/s43452-020-00116-z
Zenkour AM, Allam MNM, Radwan AF (2014) Effects of transverse shear and normal strains on FG plates resting on elastic foundations under hygro-thermo-mechanical loading. Int J Appl Mech 6(05):1450063. https://doi.org/10.1142/S175882511450063X
Zhang L, Ko TH (2022) Bending and buckling of spinning FG nanotubes based on NSGT. Comput Concr 30(4):243. https://doi.org/10.12989/cac.2022.30.4.243
Zhang J, Qin Q, Chen S, Yang Y, Ye Y, Xiang C, Wang TJ (2020) Low-velocity impact of multilayer sandwich beams with metal foam cores: analytical, experimental, and numerical investigations. J Sandw Struct Mater 22(3):626–657. https://doi.org/10.1177/1099636218759
Zhang Z, Yang Q, Jin C (2022) Axisymmetric vibration analysis of a sandwich porous plate in thermal environment rested on Kerr foundation. Steel Compos Struct 43(5):581–601. https://doi.org/10.12989/SCS.2022.43.5.581
Zenkour AM, Radwan AF (2019) Hygrothermo-mechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model. International Journal for Computational Methods in Engineering Science and Mechanics 20(2):85–98. https://doi.org/10.1080/15502287.2019.1568618
Zhou HM, Zhang XM, Wang ZY (2019) Thermal analysis of 2D FGM beam subjected to thermal loading using meshless weighted least-square method. Math Probl Eng. https://doi.org/10.1155/2019/2541707
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Khaled MESKI: Conceptualization, Methodology, Investigation, Solution Approach, Writing-Original draft preparation. Abdelaziz BOUTRID: Reviewing and Editing. Abdelhakim Bouhadra: Software, Writing-Original, draft preparation, Reviewing and Editing. Belgacem Mamen: Software, Solution Approach, Validation, Reviewing and Editing. Abderahmane MENASRIA: Software,Validation and Editing. Abdelouahed Tounsi: Conceptualization, Reviewing and Editing, Supervision. Thanh Cuong-Le: Writing-Original, draft preparation, Reviewing and Editing, Supervision.
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Meski, K., Boutrid, A., Menasria, A. et al. Analytical modeling of flexural behavior of advanced composite sandwich beams under nonlinear hygro-thermo-mechanical loads. Multiscale and Multidiscip. Model. Exp. and Des. (2024). https://doi.org/10.1007/s41939-024-00414-6
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DOI: https://doi.org/10.1007/s41939-024-00414-6