Top

Arabian Journal for Science and Engineering

Published in:

16-02-2021 | Research Article-Civil Engineering

An Exact Elasticity Solution for Monoclinic Functionally Graded Beams

Authors: İsa Çömez, Umit N. Aribas, Akif Kutlu, Mehmet H. Omurtag

Published in: Arabian Journal for Science and Engineering | Issue 5/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

In this study, an elasticity solution is presented for monoclinic functionally graded beams subject to a transverse pressure distributed sinusoidally. Monoclinic material properties are assumed to vary exponentially throughout the thickness of the beam’s layers. An analytical formulation based on the classical Euler–Bernoulli beam theory is also derived for comparison purposes of simply supported monoclinic functionally graded beams. In benchmark examples, the numerical results of normal stresses, transverse shear stress, as well as axial and vertical displacements are presented. The effect of material grading, fiber angle, and beam length to thickness ratio on the stress and displacement distributions is comprehensively investigated. The proposed elasticity-based analytical solution and presented numerical results can be used for verification or comparison purposes of numerical procedures.

previous article Experimental and Theoretical Research on Low-Strength Concrete Beams Reinforced with Basalt Fibre-Reinforced Plastic Sheets in a Freeze–Thaw Environment

next article An Improved Creep Model for Granite Based on the Deviatoric Stress-to-Peak Strength Ratio

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Mahamood, R.M.; Akinlabi, E.T.: Functionally Graded Materials. Springer International Publishing, Cham (2017)

Dorduncu, M.: Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory. Thin-Walled Structures (2020). https://doi.org/10.1016/j.tws.2019.106468CrossRef

Hamdia, K.M.; Msekh, M.A.; Silani, M.; Vu-Bac, N.; Zhuang, X.; Nguyen-Thoi, T.; Rabczuk, T.: Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Compos. Struct. 133, 1177–1190 (2015). https://doi.org/10.1016/j.compstruct.2015.08.051CrossRef

Khudari Bek, Y.; Hamdia, K.M.; Rabczuk, T.; Könke, C.: Micromechanical model for polymeric nano-composites material based on SBFEM. Compos. Struct. 194, 516–526 (2018). https://doi.org/10.1016/j.compstruct.2018.03.064CrossRef

Kutlu, A.; Meschke, G.; Omurtag, M.H.: A new mixed finite-element approach for the elastoplastic analysis of Mindlin plates. J. Eng. Math. 99, 137–155 (2016). https://doi.org/10.1007/s10665-015-9825-7MathSciNetCrossRefMATH

Kutlu, A.; Omurtag, M.H.: Large deflection bending analysis of elliptic plates on orthotropic elastic foundation with mixed finite element method. Int. J. Mech. Sci. 65, 64–74 (2012). https://doi.org/10.1016/j.ijmecsci.2012.09.004CrossRef

Aribas, U.N.; Ermis, M.; Eratli, N.; Omurtag, M.H.: The static and dynamic analyses of warping included composite exact conical helix by mixed FEM. Compos. B Eng. 160, 285–297 (2019). https://doi.org/10.1016/j.compositesb.2018.10.018CrossRef

Kutlu, A.; Uğurlu, B.; Omurtag, M.H.: A combined boundary-finite element procedure for dynamic analysis of plates with fluid and foundation interaction considering free surface effect. Ocean Eng. 145, 34–43 (2017). https://doi.org/10.1016/j.oceaneng.2017.08.052CrossRef

Zenkour, A.M.: Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate. Arch. Appl. Mech. 77, 197–214 (2007)MATH

10.

Li, X.Y.; Ding, H.J.; Chen, W.Q.: Elasticity solutions for a transversely isotropic functionally graded circular plate subject to an axisymmetric transverse load qrk. Int. J. Solids Struct. 45, 191–210 (2008)MATH

11.

Huang, Z.Y.; Lü, C.F.; Chen, W.Q.: Benchmark solutions for functionally graded thick plates resting on Winkler–Pasternak elastic foundations. Compos. Struct. 85, 95–104 (2008)

12.

Lü, C.F.; Lim, C.W.; Chen, W.Q.: Semi-analytical analysis for multi-directional functionally graded plates: 3-D elasticity solutions. Int. J. Numer. Methods Eng. 79, 25–44 (2009)MathSciNetMATH

13.

Kashtalyan, M.; Menshykova, M.: Three-dimensional elasticity solution for sandwich panels with a functionally graded core. Compos. Struct. 87, 36–43 (2009)

14.

Xu, Y.; Zhou, D.: Three-dimensional elasticity solution of functionally graded rectangular plates with variable thickness. Compos. Struct. 91, 56–65 (2009)

15.

Asghari, M.; Ghafoori, E.: A three-dimensional elasticity solution for functionally graded rotating disks. Compos. Struct. 92, 1092–1099 (2010)

16.

Vel, S.S.: Exact elasticity solution for the vibration of functionally graded anisotropic cylindrical shells. Compos. Struct. 92, 2712–2727 (2010)

17.

Woodward, B.; Kashtalyan, M.: Three-dimensional elasticity solution for bending of transversely isotropic functionally graded plates. Eur. J. Mech.-A/Solids. 30, 705–718 (2011)MathSciNetMATH

18.

Yang, B.; Ding, H.J.; Chen, W.Q.: Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported. Appl. Math. Model. 36, 488–503 (2012)MathSciNetMATH

19.

Hosseini-Hashemi, Sh.; Salehipour, H.; Atashipour, S.R.; Sburlati, R.: On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: Explicit 3-D elasticity solutions. Compos. Part B: Eng. 46, 108–115 (2013)

20.

Sankar, B.V.: An elasticity solution for functionally graded beams. Compos. Sci. Technol. 61, 689–696 (2001)

21.

Venkataraman, S.; Sankar, B.V.: Elasticity solution for stresses in a sandwich beam with functionally graded core. AIAA J. 41, 2501–2505 (2003)

22.

Ding, H.J.; Huang, D.J.; Chen, W.Q.: Elasticity solutions for plane anisotropic functionally graded beams. Int. J. Solids Struct. 44, 176–196 (2007)MathSciNetMATH

23.

Lü, C.F.; Chen, W.Q.; Xu, R.Q.; Lim, C.W.: Semi-analytical elasticity solutions for bi-directional functionally graded beams. Int. J. Solids Struct. 45, 258–275 (2008)MATH

24.

Ying, J.; Lü, C.F.; Chen, W.Q.: Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Compos. Struct. 84, 209–219 (2008)

25.

Wang, M.; Liu, Y.: Elasticity solutions for orthotropic functionally graded curved beams. Eur. J. Mech.-A/Solids. 37, 8–16 (2013)MathSciNetMATH

26.

Nie, G.J.; Zhong, Z.; Chen, S.: Analytical solution for a functionally graded beam with arbitrary graded material properties. Compos. Part B: Eng. 44, 274–282 (2013)

27.

Daouadji, T.H.; Henni, A.H.; Tounsi, A.; El Abbes, A.B.: Elasticity solution of a cantilever functionally graded beam. Appl. Compos. Mater. 20, 1–15 (2013)

28.

Xu, Y.; Yu, T.; Zhou, D.: Two-dimensional elasticity solution for bending of functionally graded beams with variable thickness. Meccanica 49, 2479–2489 (2014)MathSciNetMATH

29.

Alibeigloo, A.: Three-dimensional thermo-elasticity solution of sandwich cylindrical panel with functionally graded core. Compos. Struct. 107, 458–468 (2014)

30.

Alibeigloo, A.; Liew, K.M.: Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity. Compos. Struct. 113, 23–30 (2014)

31.

Arefi, M.: Elastic solution of a curved beam made of functionally graded materials with different cross sections. Steel Compos. Struct. 18, 659–672 (2015)

32.

Zafarmand, H.; Kadkhodayan, M.: Three dimensional elasticity solution for static and dynamic analysis of multi-directional functionally graded thick sector plates with general boundary conditions. Compos. Part B: Eng. 69, 592–602 (2015)

33.

Chu, P.; Li, X.-F.; Wu, J.-X.; Lee, K.Y.: Two-dimensional elasticity solution of elastic strips and beams made of functionally graded materials under tension and bending. Acta Mech. 226, 2235–2253 (2015)MathSciNetMATH

34.

Demirbas, M.D.: Thermal stress analysis of functionally graded plates with temperature-dependent material properties using theory of elasticity. Compos. Part B: Eng. 131, 100–124 (2017)

35.

Benguediab, S.; Tounsi, A.; Abdelaziz, H.H.; Meziane, M.A.A.: Elasticity solution for a cantilever beam with exponentially varying properties. J. Appl. Mech. Tech. Phys. 58, 354–361 (2017)MathSciNetMATH

36.

He, X.-T.; Li, W.-M.; Sun, J.-Y.; Wang, Z.-X.: An elasticity solution of functionally graded beams with different moduli in tension and compression. Mech. Adv. Mater. Struct. 25, 143–154 (2018)

37.

Bhaskar, K.; Ravindran, A.: Elasticity solution for orthotropic FGM plates with dissimilar stiffness coefficient variations. Acta Mech. 230, 979–992 (2019)MathSciNetMATH

38.

Yang, Z.; Wu, P.; Liu, W.: Time-dependent behavior of laminated functionally graded beams bonded by viscoelastic interlayer based on the elasticity theory. Arch Appl Mech. 90, 1457–1473 (2020)

39.

Wu, P.; Yang, Z.; Huang, X.; Liu, W.; Fang, H.: Exact solutions for multilayer functionally graded beams bonded by viscoelastic interlayer considering memory effect. Compos. Struct. 249, 112492 (2020)

40.

Li, Z.; Xu, Y.; Huang, D.; Zhao, Y.: Two-dimensional elasticity solution for free vibration of simple-supported beams with arbitrarily and continuously varying thickness. Arch. Appl. Mech. 90, 275–289 (2020)

41.

Ravindran, A.; Bhaskar, K.: Elasticity solution for a sandwich plate having composite facesheets with in-plane grading. J. Sandwich Struct. Mater. 1, 1099636220909810 (2020)

42.

Huang, Y.; Ouyang, Z.-Y.: Exact solution for bending analysis of two-directional functionally graded Timoshenko beams. Arch. Appl. Mech. 90, 1005–1023 (2020)

43.

Chang, S.-H.; Parinov, I.A.; Topolov, VYu. (eds.): Advanced Materials: Physics. Mechanics and Applications. Springer International Publishing, Cham (2014)

44.

Alam, M.; Mishra, S.K.: Thermo-mechanical post-critical analysis of nonlocal orthotropic plates. Appl. Math. Model. 79, 106–125 (2020). https://doi.org/10.1016/j.apm.2019.10.018MathSciNetCrossRefMATH

45.

Alam, M.; Mishra, S.K.: Nonlinear vibration of nonlocal strain gradient functionally graded beam on nonlinear compliant substrate. Compos. Struct. (2020). https://doi.org/10.1016/j.compstruct.2020.113447CrossRef

46.

Alam, M.; Mishra, S.K.; Kant, T.: Scale dependent critical external pressure for buckling of spherical shell based on nonlocal strain gradient theory. Int. J. Struct. Stabil. Dyn. (2020). https://doi.org/10.1142/S0219455421500036CrossRef

47.

Zhang, P.; Qing, H.; Gao, C.-F.: Exact solutions for bending of Timoshenko curved nanobeams made of functionally graded materials based on stress-driven nonlocal integral model. Compos. Struct. 245, 112362 (2020)

48.

Zhang, P.; Qing, H.; Gao, C.-F.: Analytical solutions of static bending of curved Timoshenko microbeams using Eringen’s two-phase local/nonlocal integral model. ZAMM-J. Appl. Math. Mech. 100, e201900207 (2020)MathSciNet

49.

Tovstik, P.E.; Tovstik, T.P.: Two-dimensional model of a plate made of an anisotropic inhomogeneous material. Mech. Solids 52, 144–154 (2017). https://doi.org/10.3103/S0025654417020042CrossRefMATH

50.

Morozov, N.F.; Belyaev, A.K.; Tovstik, P.E.; Tovstik, T.P.: Two-dimensional equations of second order accuracy for a multilayered plate with orthotropic layers. Dokl. Phys. 63, 471–475 (2018). https://doi.org/10.1134/S1028335818110034CrossRef

51.

Schneider, P.; Kienzler, R.: A Reissner-type plate theory for monoclinic material derived by extending the uniform-approximation technique by orthogonal tensor decompositions of nth-order gradients. Meccanica 52, 2143–2167 (2017). https://doi.org/10.1007/s11012-016-0573-1MathSciNetCrossRefMATH

52.

Belyaev, A.K.; Morozov, N.F.; Tovstik, P.E.; Tovstik, T.P.; Zelinskaya, A.V.: Two-Dimensional Model of a Plate, Made of Material with the General Anisotropy. In: Altenbach, H.; Chróścielewski, J.; Eremeyev, V.A.; Wiśniewski, K. (Eds.) Recent Developments in the Theory of Shells, pp. 91–108. Springer International Publishing, Cham (2019)MATH

53.

Çömez, İ; Yilmaz, K.B.: Mechanics of frictional contact for an arbitrary oriented orthotropic material. ZAMM-J. Appl. Math. Mech. 99, e201800084 (2019)MathSciNet

54.

Yilmaz, K.B.; Çömez, İ; Güler, M.A.; Yildirim, B.: Sliding frictional contact analysis of a monoclinic coating/isotropic substrate system. Mech. Mater. 137, 103132 (2019)

55.

Çömez, İ: Contact mechanics of the functionally graded monoclinic layer. Eur. J. Mech.-A/Solids. 83, 104018 (2020)MathSciNetMATH

56.

Binienda, W.K.; Pindera, M.-J.: Frictionless contact of layered metal-matrix and polymer-matrix composite half planes. Compos. Sci. Technol. 50, 119–128 (1994)

Title: An Exact Elasticity Solution for Monoclinic Functionally Graded Beams
Authors: İsa Çömez
Umit N. Aribas
Akif Kutlu
Mehmet H. Omurtag
Publication date: 16-02-2021
Publisher: Springer Berlin Heidelberg
Published in: Arabian Journal for Science and Engineering / Issue 5/2021
Print ISSN: 2193-567X
Electronic ISSN: 2191-4281
DOI: https://doi.org/10.1007/s13369-021-05434-9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Other articles of this Issue 5/2021

Studies on Biocementation of Mortar and Identification of Causative Bacteria

Limited Sensor-Based Probabilistic Damage Detection Using Combined Normal–Lognormal Distributions

Model Test of Interaction Between Load-Caused Landslide and Double-Row Anti-slide Piles by Transparent Soil Material

Deep Learning Modelling and Generalisation of Carbonation Depth in Fly Ash Blended Concrete

Modeling the Impact of Weather Conditions on Pedestrian Injury Counts Using LASSO-Based Poisson Model

The Most Effective Index for Pavement Management of Urban Major Roads at a Network Level

Premium Partners