An effective analytical method for buckling solutions of a restrained FGM nonlocal beam

Ömer Cívalek1, Büşra Uzun2, Mustafa Özgür Yaylı2
1Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
2Department of Civil Engineering, Faculty of Engineering, Bursa Uludag University, Görükle Campüs, 16059, Bursa, Turkey

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Akbaş ŞD (2017) Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory. Int J Struct Stab Dyn 17(03):1750033

Akbaş ŞD, Ersoy H, Akgöz B, Civalek Ö (2021) Dynamic analysis of a fiber-reinforced composite beam under a moving load by the Ritz method. Mathematics 9(9):1048

Akgöz B, Civalek O (2015a) A microstructure-dependent sinusoidal plate model based on the strain gradient elasticity theory. Acta Mech 226(7):2277–2294

Akgöz B, Civalek O (2015b) A novel microstructure-dependent shear deformable beam model. Int J Mech Sci 99:10–20

Alijani F, Amabili M, Bakhtiari-Nejad F (2011) Thermal effects on nonlinear vibrations of functionally graded doubly curved shells using higher order shear deformation theory. Compos Struct 93(10):2541–2553

Alshorbagy AE, Eltaher MA, Mahmoud FF (2011) Free vibration characteristics of a functionally graded beam by finite element method. Appl Math Model 35(1):412–425

Arda M (2021) Axial dynamics of functionally graded Rayleigh-Bishop nanorods. Microsyst Technol 27(1):269–282

Arefi M (2021) Third-order electro-elastic analysis of sandwich doubly curved piezoelectric micro shells. Mech Based Des Struct Mach 49(6):781–810

Arefi M, Soltan Arani AH (2018) Higher order shear deformation bending results of a magnetoelectrothermoelastic functionally graded nanobeam in thermal, mechanical, electrical, and magnetic environments. Mech Based Des Struct Mach 46(6):669–692

Arefi M, Zenkour AM (2017a) Vibration and bending analyses of magneto–electro–thermo-elastic sandwich microplates resting on viscoelastic foundation. Appl Phys A 123(8):1–17

Arefi M, Zenkour AM (2017b) Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams. Appl Phys A 123(3):202

Arefi M, Kiani M, Zenkour AM (2020) Size-dependent free vibration analysis of a three-layered exponentially graded nano-/micro-plate with piezomagnetic face sheets resting on Pasternak’s foundation via MCST. J Sandwich Struct Mater 22(1):55–86

Arefi M, Firouzeh S, Bidgoli EMR, Civalek Ö (2020a) Analysis of porous micro-plates reinforced with FG-GNPs based on Reddy plate theory. Compos Struct 247:112391

Arefi M, Mohammad-Rezaei Bidgoli E, Civalek O (2020b) Bending response of FG composite doubly curved nanoshells with thickness stretching via higher-order sinusoidal shear theory. Mech Based Des Struct Mach 1–29

Arif H, Lellep J (2021) Buckling analysis of cantilever nanobeams with defects. Appl Nanosci. https://doi.org/10.1007/s13204-021-01827-2

Asoor AA, Valipour P, Ghasemi SE (2016) Investigation on vibration of single-walled carbon nanotubes by variational iteration method. Appl Nanosci 6(2):243–249

Asrari R, Ebrahimi F, Kheirikhah MM, Safari KH (2020) Buckling analysis of heterogeneous magneto-electro-thermo-elastic cylindrical nanoshells based on nonlocal strain gradient elasticity theory. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2020.1728545

Attia MA, Mohamed SA (2020) Nonlinear thermal buckling and postbuckling analysis of bidirectional functionally graded tapered microbeams based on Reddy beam theory. Eng Comput. https://doi.org/10.1007/s00366-020-01080-1

Avcar M, Mohammed WKM (2018) Free vibration of functionally graded beams resting on Winkler–Pasternak foundation. Arab J Geosci 11(10):232

Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5):1651–1656

Barati MR, Zenkour AM (2017) Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection. Compos Struct 181:194–202

Barati MR, Zenkour AM (2018) Post-buckling analysis of imperfect multi-phase nanocrystalline nanobeams considering nanograins and nanopores surface effects. Compos Struct 184:497–505

Barati MR, Zenkour AM (2019) Thermal post-buckling analysis of closed circuit flexoelectric nanobeams with surface effects and geometrical imperfection. Mech Adv Mater Struct 26(17):1482–1490

Behera L, Chakraverty S (2014) Free vibration of Euler and Timoshenko nanobeams using boundary characteristic orthogonal polynomials. Appl Nanosci 4(3):347–358

Besisa DH, Ewais EM (2016) Advances in functionally graded ceramics–processing, sintering properties and applications. In: Advances in functionally graded materials and structures, pp 1–32

Civalek Ö, Uzun B, Yaylı MÖ (2020a) Stability analysis of nanobeams placed in electromagnetic field using a finite element method. Arab J Geosci 13(21):1–9

Civalek Ö, Uzun B, Yaylı MÖ, Akgöz B (2020b) Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method. Eur Phys J plus 135(4):381

Civalek O, Dastjerdi S, Akbaş SD, Akgöz B (2020c) Vibration analysis of carbon nanotube-reinforced composite microbeams. Math Methods Appl Sci. https://doi.org/10.1002/mma.7069

Daikh AA, Zenkour AM (2019) Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory. Mater Res Express 6(11):115707

Dastjerdi S, Akgöz B, Civalek Ö (2020) On the effect of viscoelasticity on behavior of gyroscopes. Int J Eng Sci 149:103236

Dehghan M, Ebrahimi F, Vinyas M (2020) Wave dispersion characteristics of fluid-conveying magneto-electro-elastic nanotubes. Eng Comput 36:1687–1703

Demir C, Civalek O (2017) On the analysis of microbeams. Int J Eng Sci 121:14–33

Ebrahimi F, Barati MR, Civalek Ö (2019b) Application of Chebyshev–Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures. Eng Comput 1–12

Eringen AC (1972) Nonlocal polar elastic continua. Int J Eng Sci 10(1):1–16

Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710

Farokhi H, Ghayesh MH, Amabili M (2013) Nonlinear resonant behavior of microbeams over the buckled state. Appl Phys A 113(2):297–307

Ghayesh MH (2019) Mechanics of viscoelastic functionally graded microcantilevers. Eur J Mech A/Solids 73:492–499

Ghayesh MH, Amabili M (2013) Nonlinear dynamics of an axially moving Timoshenko beam with an internal resonance. Nonlinear Dyn 73(1):39–52

Ghayesh MH, Farokhi H, Amabili M (2013) Coupled nonlinear size-dependent behaviour of microbeams. Appl Phys A 112(2):329–338

Guo H, Zhuang X, Rabczuk T (2021) A deep collocation method for the bending analysis of Kirchhoff plate. http://arxiv.org/abs/2102.02617

Hosseini M, Fazelzadeh SA (2011) Thermomechanical stability analysis of functionally graded thin-walled cantilever pipe with flowing fluid subjected to axial load. Int J Struct Stab Dyn 11(03):513–534

Jalaei MH, Civalek Ӧ (2019) On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam. Int J Eng Sci 143:14–32

Jalali SK, Naei MH, Poorsolhjouy A (2011) Buckling of circular sandwich plates of variable core thickness and FGM face sheets. Int J Struct Stab Dyn 11(02):273–295

Jena SK, Chakraverty S, Malikan M, Sedighi H (2020) Implementation of Hermite-Ritz method and Navier’s technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using bi-Helmholtz nonlocal elasticity. J Mech Mater Struct 15(3):405–434

Kadoli R, Akhtar K, Ganesan N (2008) Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model 32(12):2509–2525

Kazemirad S, Ghayesh MH, Amabili M (2013) Thermo-mechanical nonlinear dynamics of a buckled axially moving beam. Arch Appl Mech 83(1):25–42

Koiter WT (1964) Couple stresses in the theory of elasticity, I and II. Proc k Ned Akad Wet (b) 67:17–44

Lam DC, Yang F, Chong ACM, Wang J, Tong P (2003) Experiments and theory in strain gradient elasticity. J Mech Phys Solids 51(8):1477–1508

Li X, Li L, Hu Y, Ding Z, Deng W (2017) Bending, buckling and vibration of axially functionally graded beams based on nonlocal strain gradient theory. Compos Struct 165:250–265

Li W, Han B (2018) Research and application of functionally gradient materials. In: IOP conference series: materials science and engineering, vol 394, no 2. IOP Publishing, p 022065

Mahamood RM, Akinlabi ET, Shukla M, Pityana SL (2012) Functionally graded material: an overview

Mindlin RD (1965) Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct 1(4):417–438

Mindlin RD, Tiersten HF (1962) Effects of couple-stresses in linear elasticity. Arch Ration Mech Anal 11(1):415–448

Pradhan KK, Chakraverty S (2013) Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method. Compos B Eng 51:175–184

Pradhan SC, Phadikar JK (2011) Nonlocal theory for buckling of nanoplates. Int J Struct Stab Dyn 11(03):411–429

Praharaj RK, Datta N (2020) On the transient response of plates on fractionally damped viscoelastic foundation. Comput Appl Math 39(4):1–20

Rahmani O, Jandaghian AA (2015) Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory. Appl Phys A 119(3):1019–1032

Sabrine C, Makram H (2020) Discrete energy behavior of a damped Timoshenko system. Comput Appl Math 39(1):1–19

Sahmani S, Aghdam MM, Rabczuk T (2018) Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory. Compos Struct 186:68–78

Shariati A, Mohammad-Sedighi H, Żur KK, Habibi M, Safa M (2020) On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams. Materials 13(7):1707

Shen HS (2009) Functionally graded materials: nonlinear analysis of plates and shells. CRC Press, Boca Raton

Talha M, Singh BN (2010) Static response and free vibration analysis of FGM plates using higher order shear deformation theory. Appl Math Model 34(12):3991–4011

Toupin RA (1962) Elastic materials with couple-stresses. Arch Ration Mech Anal 11(1):385–414

Tran TT, Tran VK, Pham QH, Zenkour AM (2021) Extended four-unknown higher-order shear deformation nonlocal theory for bending, buckling and free vibration of functionally graded porous nanoshell resting on elastic foundation. Compos Struct 264:113737

Uzun B, Yaylı MÖ (2020a) Nonlocal vibration analysis of Ti-6Al-4V/ZrO 2 functionally graded nanobeam on elastic matrix. Arab J Geosci 13(4):1–10

Uzun B, Yaylı MÖ (2020b) A solution method for longitudinal vibrations of functionally graded nanorods. Int J Eng Appl Sci 12(2):78–87

Uzun B, Kafkas U, Yaylı MÖ (2020) Stability analysis of restrained nanotubes placed in electromagnetic field. Microsyst Technol 26(12):3725–3736

Uzun B, Kafkas U, Yaylı MÖ (2020c) Axial dynamic analysis of a Bishop nanorod with arbitrary boundary conditions. ZAMM J Appl Math Mech 100(12):e202000039

Uzun B, Civalek Ö, Yaylı MÖ (2020b) Vibration of FG nano-sized beams embedded in Winkler elastic foundation and with various boundary conditions. Mech Based Des Struct Mach. https://doi.org/10.1080/15397734.2020.1846560

Viet NV, Zaki W, Wang Q (2020) Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis. Appl Math Mech 41(12):1787–1804

Vu-Bac N, Nguyen-Xuan HB, Chen L, Bordas S, Kerfriden P, Simpson RN, Rabczuk T et al (2011) A node-based smoothed extended finite element method (NS-XFEM) for fracture analysis. Comput Model Eng Sci 73(4):331

Wang CM, Zhang YY, Ramesh SS, Kitipornchai S (2006) Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory. J Phys D Appl Phys 39(17):3904

Wu H, Liu H (2021) Nonlinear thermo-mechanical response of temperature-dependent FG sandwich nanobeams with geometric imperfection. Eng Comput 37:3375–3395

Xie B, Sahmani S, Safaei B, Xu B (2021) Nonlinear secondary resonance of FG porous silicon nanobeams under periodic hard excitations based on surface elasticity theory. Eng Comput 37:1611–1634

Yahia SA, Atmane HA, Houari MSA, Tounsi A (2015) Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories. Struct Eng Mech 53(6):1143–1165

Yang FACM, Chong ACM, Lam DCC, Tong P (2002) Couple stress based strain gradient theory for elasticity. Int J Solids Struct 39(10):2731–2743

Yayli MÖ (2015) Buckling analysis of a rotationally restrained single walled carbon nanotube. Acta Phys Pol A 127(3):678–683

Yayli MÖ (2018) Torsional vibrations of restrained nanotubes using modified couple stress theory. Microsyst Technol 24(8):3425–3435

Yaylı MÖ, Uzun B, Deliktaş B (2021) Buckling analysis of restrained nanobeams using strain gradient elasticity. Waves Random Complex Media. https://doi.org/10.1080/17455030.2020.1871112

Youssef HM (2013) Vibration of gold nanobeam with variable thermal conductivity: state-space approach. Appl Nanosci 3(5):397–407

Zarezadeh E, Hosseini V, Hadi A (2020) Torsional vibration of functionally graded nano-rod under magnetic field supported by a generalized torsional foundation based on nonlocal elasticity theory. Mech Based Des Struct Mach 48(4):480–495

Zenkour AM (2020) A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods. J Braz Soc Mech Sci Eng 42:1–10

Zenkour A, Ebrahimi F, Barati MR (2019) Buckling analysis of a size-dependent functionally graded nanobeam resting on Pasternak’s foundations. Int J Nano Dimens 10(2):141–153

Zhang J, Liu S, Ullah S, Gao Y (2020) Analytical bending solutions of thin plates with two adjacent edges free and the others clamped or simply supported using finite integral transform method. Comput Appl Math 39(4):1–23

Żur KK, Arefi M, Kim J, Reddy JN (2020) Free vibration and buckling analyses of magneto-electro-elastic FGM nanoplates based on nonlocal modified higher-order sinusoidal shear deformation theory. Compos Part B Eng 182:107601