Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium - Publikacja - MOST Wiedzy

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Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium

Abstrakt

The present investigation is focused on the buckling behavior of strain gradient nonlocal beam embedded in Winkler elastic foundation. The first-order strain gradient model has been combined with the Euler–Bernoulli beam theory to formulate the proposed model using Hamilton’s principle. Three numerically efficient methods, namely Haar wavelet method (HWM), higher order Haar wavelet method (HOHWM), and differential quadrature method (DQM) are employed to analyze the buckling characteristics of the strain gradient nonlocal beam. The impacts of several parameters such as nonlocal parameter, strain gradient parameter, and Winkler modulus parameter on critical buckling loads are studied effectively. The basic ideas of the numerical methods, viz. HWM, HOHWM, and DQM are presented comprehensively. Also, a comparative study has been conducted to explore the effectiveness and applicability of all the three numerical methods in terms of convergence study. Finally, the results, obtained by this investigation, are validated properly with other works published earlier.

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Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach
Opublikowano w:
ENGINEERING WITH COMPUTERS nr 37, strony 1251 - 1264,
ISSN: 0177-0667
Język:
angielski
Rok wydania:
2021
Opis bibliograficzny:
Jena S. K., Chakraverty S., Malikan M.: Implementation of Haar wavelet, higher order Haar wavelet, and differential quadrature methods on buckling response of strain gradient nonlocal beam embedded in an elastic medium// ENGINEERING WITH COMPUTERS -Vol. 37, (2021), s.1251-1264
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/s00366-019-00883-1
Bibliografia: test
  1. Press WH, Tuekolsky SA, Wetterling WT (2002) Numerical Recipes in C++: The Art of Scientific Computing. Cambridge University Press
  2. Murmu T, Pradhan SC (2009) Buckling analysis of a single-walled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Physica E 41(7): 1232-1239 otwiera się w nowej karcie
  3. Ansari R, Arjangpay A (2014) Nanoscale vibration and buckling of single-walled carbon nanotubes using the meshless local Petrov-Galerkin method. Physica E 63:283-292 otwiera się w nowej karcie
  4. Chakraverty S, Behera L (2016) Static and Dynamic Problems of Nanobeams and Nanoplates. 1st Edn (Singapore: World Scientific Publishing Co). otwiera się w nowej karcie
  5. Malikan M, Jabbarzadeh M, Dastjerdi Sh (2017) Non-linear Static stability of bi-layer carbon nanosheets resting on an elastic matrix under various types of in-plane shearing loads in thermo- elasticity using nonlocal continuum. Microsyst Technol 23:2973-2991 24 otwiera się w nowej karcie
  6. Malikan M, Sadraee Far MN (2018) Differential quadrature method for dynamic buckling of graphene sheet coupled by a viscoelastic medium using neperian frequency based on nonlocal elasticity theory. Journal of Applied and Computational Mechanics 4:147-160
  7. Golmakani ME, Malikan M, Sadraee Far MN, Majidi HR (2018) Bending and buckling formulation of graphene sheets based on nonlocal simple first order shear deformation theory. otwiera się w nowej karcie
  8. Mater Res Express 5: 065010 otwiera się w nowej karcie
  9. Ansari R, Sahmani S, Rouhi H (2011) Axial buckling analysis of single-walled carbon nanotubes in thermal environments via the Rayleigh-Ritz technique. Comput Mater Sci 50:3050- 3055 otwiera się w nowej karcie
  10. Jena SK, Chakraverty S (2018) Free vibration analysis of variable cross-section single layered graphene nano-ribbons (SLGNRs) using differential quadrature method. Front Built Environ 4:63 otwiera się w nowej karcie
  11. Behera L, Chakraverty S (2015) Application of Differential Quadrature method in free vibration analysis of nanobeams based on various nonlocal theories. Comput Math Appl 69:1444- 1462 otwiera się w nowej karcie
  12. Chakraverty S, Jena SK (2018) Free vibration of single walled carbon nanotube resting on exponentially varying elastic foundation. Curved and Layer Struct 5: 260-272 otwiera się w nowej karcie
  13. Bakhshi Khaniki H, Hosseini-Hashemi Sh, Nezamabadi A (2018) Buckling analysis of nonuniform nonlocal strain gradient beams using generalized differential quadrature method. Alex Eng J 57: 1361-1368
  14. Chen C, Li S, Dai L, Qian C-Z (2014) Buckling and stability analysis of a piezoelectric viscoelastic nanobeam subjected to van der Waals forces. Commun Nonlinear Sci 19:1626-1637 otwiera się w nowej karcie
  15. Tuna M, Kirca M (2017) Bending, buckling and free vibration analysis of Euler-Bernoulli nanobeams using Eringen's nonlocal integral model via finite element method. Compos Struct 179:269-284 otwiera się w nowej karcie
  16. Jena SK, Chakraverty S (2018) Free vibration analysis of single walled carbon nanotube with exponentially varying stiffness. Curved and Layer Struct 5: 201-212 otwiera się w nowej karcie
  17. Ghavamian A, Öchsner A (2012) Numerical investigation on the influence of defects on the buckling behavior of single-and multi-walled carbon nanotubes. Physica E 46: 241-249 25 otwiera się w nowej karcie
  18. Jena SK, Chakraverty S, Tornabene F (2019) Vibration characteristics of nanobeam with exponentially varying flexural rigidity resting on linearly varying elastic foundation using differential quadrature method. Mater Res Express 6: 085051 otwiera się w nowej karcie
  19. Jena SK, Chakraverty S, Jena RM, Tornabene F (2019) A novel fractional nonlocal model and its application in buckling analysis of Euler-Bernoulli nanobeam. Mater Res Express 6: 055016 otwiera się w nowej karcie
  20. Jena SK, Chakraverty S, Tornabene F (2019) Dynamical behavior of nanobeam embedded in constant, linear, parabolic, and sinusoidal types of Winkler elastic foundation using First-Order nonlocal strain gradient model. Mater Res Express 6: 60850f2 otwiera się w nowej karcie
  21. Jena RM, Chakraverty S, Jena SK (2019) Dynamic response analysis of fractionally damped beams subjected to external loads using Homotopy Analysis Method. Journal of Applied and Computational Mechanics 5: 355-366
  22. Jena SK, Chakraverty S (2019) Differential Quadrature and Differential Transformation Methods in Buckling Analysis of Nanobeams. Curved and Layer Struct 6:68-76 otwiera się w nowej karcie
  23. Jena SK, Chakraverty S (2018) Free vibration analysis of Euler-Bernoulli Nano beam using differential transform method. Int J Comput Mater Sci Eng 7:1850020 otwiera się w nowej karcie
  24. Jena SK, Chakraverty S, Tornabene F (2019) Buckling Behavior of Nanobeams Placed in Electromagnetic Field Using Shifted Chebyshev Polynomials-Based Rayleigh-Ritz Method. Nanomaterials 9(9):1326 otwiera się w nowej karcie
  25. Jena SK, Chakraverty S, Jena RM (2019) Propagation of uncertainty in free vibration of Euler-Bernoulli nanobeam. J Braz Soc Mech Sci & Eng 41(10):436 otwiera się w nowej karcie
  26. Jena SK, Chakraverty S (2019) Dynamic Analysis of Single-Layered Graphene Nano- Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation. Curved and Layer Struct 6:132-145 otwiera się w nowej karcie
  27. Haar Alfred (1910) Zur Theorie der orthogonalen Funktionensysteme. (German)
  28. Mathematische Annalen 69: 331-371 otwiera się w nowej karcie
  29. Hariharan G, Kannan K (2013) An Overview of Haar Wavelet Method for Solving Differential and Integral Equations. World Appl Sci J 23:01-14 26
  30. Majak J, Shvartsman B, Karjust K, Mikola M, Haavajõe A (2015) On the Accuracy of the Haar Wavelet Discretization Method. Compos Part B-Eng 80: 321-327 otwiera się w nowej karcie
  31. Jena SK, Chakraverty S (2019) Dynamic behavior of an electromagnetic nanobeam using the Haar wavelet method and the higher-order Haar wavelet method. Eur Phys J Plus 134: 538 otwiera się w nowej karcie
  32. Majak J, Pohlak M, Karjust K, Eerme M, Kurnitski J, Shvartsman BS (2018) New Higher Order Haar Wavelet Method: Application to Fgm Structures. Compos Struct 201:72-78 otwiera się w nowej karcie
  33. Shu C (2000) Differential quadrature and its application in engineering. Springer, Berlin otwiera się w nowej karcie
  34. Bert CW, Malik M (1996) Differential quadrature method in computational mechanics: a review. Appl Mech Rev 49:1-28 otwiera się w nowej karcie
  35. Tornabene F, Fantuzzi N, Ubertini F, Viola E (2015) Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey. Appl Mech Rev 67:020801(1-55) otwiera się w nowej karcie
  36. Hein H, Feklistova L (2011) Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets. Eng Struct 33:3696-3701 otwiera się w nowej karcie
  37. Lepik Ü (2011) Buckling of elastic beams by the Haar wavelet method. Estonian Journal of Engineering 17:271-284 otwiera się w nowej karcie
  38. Kirs M, Mikola M, Haavajoe A, Ounapuu E, Shvartsman B, Majak J (2016) Haar wavelet method for vibration analysis of nanobeams. Waves Wavelets Fractals Advanced Analysis 2: 20- 28 otwiera się w nowej karcie
  39. Reddy JN (2007) Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 45:288-307 otwiera się w nowej karcie
  40. Malikan M, Tornabene F, Dimitri R (2018) Nonlocal three-dimensional theory of elasticity for buckling behavior of functionally graded porous nanoplates using volume integrals. Mater Res Express 5:095006 otwiera się w nowej karcie
  41. Thai S, Thai HT, Vo TP, Patel VI (2018) A simple shear deformation theory for nonlocal beams. Compos Struct 183:262-270 otwiera się w nowej karcie
  42. Zhu X, Wang Y, Dai H-H (2017) Buckling analysis of Euler-Bernoulli beams using Eringen's two-phase nonlocal model. Int J Eng Sci 116:130-140 27 otwiera się w nowej karcie
  43. Tuna M, Kirca M (2016) Exact solution of Eringen's nonlocal integral model for vibration and buckling of Euler-Bernoulli beam. Int J Eng Sci 107:54-67 otwiera się w nowej karcie
  44. Thai H-T (2012) A nonlocal beam theory for bending, buckling, and vibration of nanobeams. otwiera się w nowej karcie
  45. Int J Eng Sci 52: 56-64 otwiera się w nowej karcie
  46. Malikan M (2017) Electro-mechanical shear buckling of piezoelectric nanoplate using modified couple stress theory based on simplified first order shear deformation theory. Appl Math Model 48:196-207 otwiera się w nowej karcie
  47. Akgöz B, Civalek Ö (2012) Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory. Mater Design 42:164-171 otwiera się w nowej karcie
  48. Nematollahi MS, Mohammadi H (2019) Geometrically nonlinear vibration analysis of sandwich nanoplates based on higher-order nonlocal strain gradient theory. Int J Eng Sci 156:31- 45 otwiera się w nowej karcie
  49. Malikan M, Nguyen VB, Tornabene F (2018) Damped forced vibration analysis of single- walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory. Engineering Science and Technology, an International Journal 21:778-786 otwiera się w nowej karcie
  50. Malikan M, Dimitri R, Tornabene F (2019) Transient response of oscillated carbon nanotubes with an internal and external damping. Compos Part B-Eng 158:198-205 otwiera się w nowej karcie
  51. Wang J, Shen H, Zhang B, Liu J, Zhang Y (2018) Complex modal analysis of transverse free vibrations for axially moving nanobeams based on the nonlocal strain gradient theory. Physica E 101: 85-93 otwiera się w nowej karcie
  52. She GL, Yan KM, Zhang YL, Liu HB, Ren YR (2018) Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory. Eur Phys J Plus 133: 368 otwiera się w nowej karcie
  53. Mehralian F, Tadi Beni Y, Karimi Zeverdejani M (2017) Nonlocal strain gradient theory calibration using molecular dynamics simulation based on small scale vibration of nanotubes. Physica B 514:61-69 otwiera się w nowej karcie
  54. Malikan M, Nguyen VB, Dimitri R, Tornabene F (2019) Dynamic modeling of non- cylindrical curved viscoelastic single-walled carbon nanotubes based on the second gradient theory. Mater Res Express 6:075041 28 otwiera się w nowej karcie
  55. Zhu X, Li L (2017) Closed form solution for a nonlocal strain gradient rod in tension. Int J Eng Sci 119:16-28 otwiera się w nowej karcie
  56. Zhu X, Li L (2017) On longitudinal dynamics of nanorods, Int J Eng Sci 120:129-145 otwiera się w nowej karcie
  57. Tang H, Li L, Hu Y, Meng W, Duan K (2019) Vibration of nonlocal strain gradient beams incorporating Poisson's ratio and thickness effects. Thin-Walled Struct 137:377-391 otwiera się w nowej karcie
  58. Li L, Tang H, Hu Y (2018) The effect of thickness on the mechanics of nanobeams, Int J Eng Sci 123:81-91 otwiera się w nowej karcie
  59. Li L, Hu Y (2015) Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int J Eng Sci 97:84-94 otwiera się w nowej karcie
  60. Lim CW, Zhang G, Reddy JN (2015) A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids 78:298-313 otwiera się w nowej karcie
  61. Khaniki HB, Hosseini-Hashemi S (2017) Buckling analysis of tapered nanobeams using nonlocal strain gradient theory and a generalized differential quadrature method. Mater Res Express 4:065003
  62. Li L, Hu Y (2015) Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int J Eng Sci 97:84-94 otwiera się w nowej karcie
  63. Li L, Li X, Hu Y (2016) Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int J Eng Sci 102:77-92 otwiera się w nowej karcie
  64. Li L, Hu Y (2017) Post-buckling analysis of functionally graded nanobeams incorporating nonlocal stress and microstructure-dependent strain gradient effects. Int J Eng Sci 120:159-170 otwiera się w nowej karcie
  65. Karami B, Shahsavari D, Li L (2018) Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory. Physica E 97: 317-327 otwiera się w nowej karcie
  66. Sahmani S, Fattahi AM, Ahmed NA (2019) Analytical mathematical solution for vibrational response of postbuckled laminated FG-GPLRC nonlocal strain gradient micro-/nanobeams. Engineering with Computers 35:1173-1189 29 otwiera się w nowej karcie
  67. Ebrahimi F, Barati MR., Civalek Ö (2019) Application of Chebyshev-Ritz method for static stability and vibration analysis of nonlocal microstructure-dependent nanostructures, Engineering with Computers,https://doi.org/10.1007/s00366-019-00742-z otwiera się w nowej karcie
  68. Ebrahimi F, Karimiasl M, Mahesh V (2019) Chaotic dynamics and forced harmonic vibration analysis of magneto-electro-viscoelastic multiscale composite nanobeam. Engineering with Computers, https://doi.org/10.1007/s00366-019-00865-3 otwiera się w nowej karcie
  69. Malikan M, Nguyen VB (2018) Buckling analysis of piezo-magnetoelectric nanoplates in hygrothermal environment based on a novel one variable plate theory combining with higher-order nonlocal strain gradient theory. Physica E 102: 8-28 otwiera się w nowej karcie
  70. Malikan M, Nguyen VB, Tornabene F (2018) Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory. Mater Res Express 5:075031 otwiera się w nowej karcie
  71. Malikan M, Dimitri R, Tornabene F (2018) Effect of sinusoidal corrugated geometries on the vibrational response of viscoelastic nanoplates. Applied Sciences 8:1432 otwiera się w nowej karcie
  72. Chen CF, Hsiao CH (1997) Haar wavelet method for solving lumped and distributed- parameter systems. IEE Proceedings-Control Theory and Applications 144:87-94 otwiera się w nowej karcie
  73. Lepik U (2012) Exploring vibrations of cracked beams by the Haar wavelet method. Estonian J Eng 18:58 otwiera się w nowej karcie
  74. Quan JR, Chang CT (1989) New insights in solving distributed system equations by the quadrature method-I. Analysis. Computers & Chemical Engineering 13:779-788 otwiera się w nowej karcie
  75. Quan JR, Chang CT (1989) New insights in solving distributed system equations by the quadrature method-II. Numerical experiments. Computers & Chemical Engineering 13:1017- 1024 otwiera się w nowej karcie
  76. Majak J, Shvartsman BS, Kirs M, Pohlak M, Herranen H (2015) Convergence theorem for the Haar wavelet based discretization method. Compos Struct 126:227-232 otwiera się w nowej karcie
  77. Kirs M, Eerme M, Bassir D, Tungel E (2019) Application of HOHWM for Vibration Analysis of Nanobeams. In Key Engineering Materials 799:230-235 otwiera się w nowej karcie
  78. 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 39:3904 30 otwiera się w nowej karcie
  79. Shvartsman BS, Majak J (2016) Numerical method for stability analysis of functionally graded beams on elastic foundation. Appl Math Model 40:3713-3719 otwiera się w nowej karcie
Weryfikacja:
Politechnika Gdańska

wyświetlono 146 razy

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