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On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory

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Abstract

This article presents the static analysis of FG sandwich beams curved in elevation. Navier-type semi-analytical solutions are obtained based on polynomial type fifth order shear and normal deformation theory. The beam has FG skins and isotropic core. Material properties of FG skins are graded in z-direction according to the power-law distribution. The present theory accounts for a fifth-order distribution of axial displacement and fourth-order distribution of transverse displacement. The present theory considers the effect of thickness stretching and gives a realistic variation of transverse shear stress through the thickness of the beam. The governing equations are obtained within the framework of the principle of virtual work. Semi-analytical static solutions for the simply supported FG sandwich beams curved in elevation are obtained using Navier’s technique. The beam is subjected to uniformly distributed load. The non-dimensional numerical values for displacements and stresses are obtained for various power-law index and thickness of the core. The present results are found in good agreement with previously published results.

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References

  1. Euler L 1744 Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes. Lausanne and Geneva, Apud Marcum-Michaelem Bousquet and socios

  2. Timoshenko S P 1921 On the correction for shear of the differential equation for transverse vibration of prismatic bars Philos. Mag. Ser. 6(46): 744–746

    Google Scholar 

  3. Sayyad A S and Ghugal Y M 2015 On the free vibration analysis of laminated composite and sandwich plates: a review of recent literature with some numerical results. Compos. Struct. 129: 177–201

    Google Scholar 

  4. Sayyad A S and Ghugal Y M 2017 Bending, buckling and free vibration of laminated composite and sandwich beams: a critical review of literature. Compos. Struct. 171: 486–504

    Google Scholar 

  5. Sayyad A S and Ghugal Y M 2019 Modelling and analysis of functionally graded sandwich beams: a review. Mech. Adv. Mater. Struct. 26(21): 1776–1795

    Google Scholar 

  6. Khdeir A A and Reddy J N 1997 An exact solution for the bending of thin and thickcross-ply laminated beams. Compos. Struct. 37: 195–203

    Google Scholar 

  7. Aitharaju V R and Averill R C 1999 C0 zig-zag finite element for analysis of laminated composite beams. ASCE J. Eng. Mech. 125: 323–330

    Google Scholar 

  8. Shimpi R P and Ghugal Y M 1999 A new layerwise trigonometric shear deformation theory for two-layered cross-ply beams. Compos. Sci. Technol. 61: 1271–1283

    Google Scholar 

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

    Google Scholar 

  10. Venkataraman S and Snakar B 2003 Elastic solution for stresses in sandwich beams with functionally graded core. Am. Inst. Aeronaut. Astronaut. 41(12): 2501–2505

    Google Scholar 

  11. Rastgo A, Shafie H and Allahverdizadeh A 2005 Instability of curved beams made of functionally graded material under termal loading. Int. J. Mech. Mater. Des. 2: 117–128

    Google Scholar 

  12. Piovan MT and Cortinez VH 2007 Mechanics of thin-walled curved beams made of composite materials, allowing for shear deormability. Thin Walled Struct. 45: 759–789

    Google Scholar 

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

    MATH  Google Scholar 

  14. Tessler A, Di Sciuva M and Gherlone M 2009 A refine zig-zag beam theory for composite and sandwich beam theory. J. Compos. Mater. 43: 1051–1081

    Google Scholar 

  15. Yaghoobi H and Fereidoon A 2010 Influence of neutral surface position on defloration of functionally graded beam under uniformly distributed load. World Appl. Sci. J. 10: 337–341

    Google Scholar 

  16. Yousefi A and Rastgo A 2011 Free vibration of functionally graded spatialcurved beams. Compos. Struct. 93: 3048–3056

    Google Scholar 

  17. Vo T P and Thai H 2012 Static behavior of composite beams using various refined shear deformation theories. Compos. Struct. 94: 2513–2522

    Google Scholar 

  18. Guinta G, Crisafulli D, Belouettar S and Carerra E 2013 A thermo-mechanical analysis of functionally graded beams via hierarchical modeling. Compos. Struct. 95:676–690

    Google Scholar 

  19. Wang M and Liu Y 2013 Elastic solution of orthotropic functionally graded curved beams. Eur. J. Mech. A/Solids 37: 8–13

  20. Qu Y, Long X, Li HG and Meng G 2013 A variational formulation for dynamic analysis of composite laminated beams based on a general higher-order shear deformation theory. Compos. Struct. 102: 175–192

    Google Scholar 

  21. Carrera E, Filippi M and Zappino E 2013 Laminated beam analysis by polynomial, trigonometric, exponential and zig-zag theories. Eur. J. Mech. A/Solids 42: 58–69

    MathSciNet  MATH  Google Scholar 

  22. Pradhan K and Chakraverty S 2013 Free vibration of Euler and Thimoshenko functionally graded beams by Rayleigh–Ritz method. Compos. Part B Eng. 51: 175–184

    Google Scholar 

  23. Li J, Wu Z, Shao KX and Li X 2014 Comparison of various shear deformation theories for free vibration of laminated composite beams with general lay-ups. Compos. Struct. 108: 767–778

    Google Scholar 

  24. Hadji L, Khelifa Z, Daouadji T H and Bedia E A 2015 Static bending and free vibration of functionally graded beam using an exponential shear deformation theory. Coupled Syst. Mech. 4: 99–114

    Google Scholar 

  25. Vo T P, Thai H, Nguyen T, Inam F and Lee J 2015 A quasi-3D theory for vibration and buckling of functionally graded sandwich beams. Compos. Struct. 119: 1–12

    Google Scholar 

  26. Vo T P, Thai H, Nguyen T, Inam F and Lee J 2015 Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Compos. Part B Eng. 68: 59–74

    Google Scholar 

  27. Osofero A, Vo T P, Nguyen T K and Jaehing L 2015 Analytical solution for vibration and buckling of functionally graded sandwich beams using various quasi-3D theories. J. Sandw. Struct. Mater. 18(1): 3–29

    Google Scholar 

  28. Fereidoona A, Andalb M and Hemmatian H 2015 Bending analysis of curved sandwich beams with functionally graded core. Mech. Adv. Mater. Struct. 22: 564–577

    Google Scholar 

  29. Nanda N and Kapuria S 2015 Spectral finite element for wave propagation analysis of laminated composite curved beams using classical and first order shear deformation theories. Compos. Struct. 132: 310–320

    Google Scholar 

  30. Luu AT, Kimm N and Lee J 2015 Bending and buckling of general laminated curved beams using NURBS-based isogeometric analysis. Eur. J. Mech. A/Solids 54: 218–231

    MathSciNet  MATH  Google Scholar 

  31. Chen D, Yang J and Kitipornchai S 2015 The elastic buckling and static bending of shear deformable functionally graded porous beam. Compos. Struct. 133: 54–61

    Google Scholar 

  32. Kurtaran H 2015 Large displacement static and transient analysis of functionally graded deep curved beams with generalized differential quadrature method. Compos. Struct. 131: 821–831

    Google Scholar 

  33. Nguyen T, Vo T P, Nguyen B and Lee, J 2016 An analytical solution for buckling and vibration analysis of functionally graded sandwich beams using a quasi-3D shear deformation theory. Compos. Struct. 156: 238–252

    Google Scholar 

  34. Ye T, Jin G and Su Z 2016 A spectral-sampling surface method for the vibration of 2-D laminated curved beams with variable curvatures and general restraints. Int. J. Mech. Sci. 110: 170–189

    Google Scholar 

  35. Khdeir A A and Aldraihem O J 2016 Free vibration of sandwich beam with soft core. Compos. Struct. 154: 179–189

    Google Scholar 

  36. Eroglu U 2016 Large deflection analysis of planar curved beams made of functionally graded materials using variational iterational method. Compos. Struct. 136:204–216

    Google Scholar 

  37. Liu B, Ferreira A J M, Xing X F and Neves A M A 2016 Analysis of functionally graded sandwich and laminated shell using a layer wise and a differential quadrature finite element method theory. Compos. Struct. 136: 5446–553

    Google Scholar 

  38. Huynh T A, Luu A T and Lee J 2017 Bending, buckling and free vibration analyses of functionally graded curved beams with variable curvatures using isogeometric approach. Meccanica 52: 2527–2546

    MathSciNet  Google Scholar 

  39. Guo J, Shi D, Wang Q, Pang F and Liang Q 2019 A domain decomposition approach for static and dynamic analysis of composite laminated curved beam with general elastic restrains. Mech. Adv. Mater. Struct. 26(21): 1390–1402

    Google Scholar 

  40. Mohamad N, Eltaher M A, Mohamed S A and Seddek L F 2018 Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations. Int. J. Non-Linear Mech. 101: 157–173

    Google Scholar 

  41. Li WX, Ma H and Gao W 2019 A higher order shear deformable mixed beam element model for accurate analysis of functionally graded sandwich beams. Compos. Struct. 221: 1–16

    Google Scholar 

  42. Chen Z, Li J, Sun L and Li L 2019 Flexural buckling of sándwich beam with termal induced non uniform sectional properties. J. Build. Eng. 25: 1–6

    Google Scholar 

  43. Sayyad A S and Avhad P V 2019 On static bending, elastic buckling and free vibration analysis of symmetric functionally graded sandwich beams. J. Solid Mech. 11: 166–180

    Google Scholar 

  44. Sayyad A S and Ghugal Y M 2019 A sinusoidal beam theory for functionally graded sandwich curved beams. Compos. Struct. 226: 1–13

    Google Scholar 

  45. Kiani Y, Taheri S and Eslami M R 2011 Thermal buckling of piezoelectric functionally graded material beams. J. Therm. Stress. 34(8): 835–850

    Google Scholar 

  46. Kiani Y, Sadighi M, Salami S J, Eslami M R 2013 Low velocity impact response of thick fgm beams with general boundary conditions in thermal field. Compos. Struct. 104: 293–303

    Google Scholar 

  47. Komijani M, Kiani Y and Eslami M R 2012 Non-linear thermoelectrical stability analysis of functionally graded piezoelectric material beams. J. Intell. Mater. Syst. Struct. 67(1): 74–84

    Google Scholar 

  48. Kargani A, Kiani Y and Eslami M R 2013 Exact solution for nonlinear stability of piezoelectric FGM Timoshenko beams under thermo-electrical loads. J. Therm. Stress. 36(10): 1056–1076

    Google Scholar 

  49. Ghiasian S E, Kiani Y and Eslami M R 2014 Non-linear rapid heating of FGM beams. Int. J. Non-Linear Mech. 67: 74–84

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Sanjivani College of Engineering, Savitribai Phule Pune University, Kopargaon, Pune, India

    Pravin V Avhad & Atteshamuddin S Sayyad

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  1. Pravin V Avhad
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  2. Atteshamuddin S Sayyad
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Correspondence to Atteshamuddin S Sayyad.

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Avhad, P.V., Sayyad, A.S. On the static deformation of FG sandwich beams curved in elevation using a new higher order beam theory. Sādhanā 45, 188 (2020). https://doi.org/10.1007/s12046-020-01425-y

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  • DOI: https://doi.org/10.1007/s12046-020-01425-y

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