Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities

다국어 초록 (Multilingual Abstract)

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved firstorder shear deformation shell theory (IFSDST) and von Karman’s type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton’s principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

참고문헌 (Reference)

1 Ebrahimi, F., "Wave dispersion characteristics of heterogeneous nanoscale beams via a novel porosity-based homogenization scheme" 134 (134): 1-8, 2019

2 Ebrahimi, F., "Wave Propagation Analysis of Smart Nanostructures" CRC Press 2019

3 Zhao, J., "Vibration behavior of the functionally graded porous(FGP)doubly-curved panels and shells of revolution by using a semi-analytical method" 157 : 219-238, 2019

4 Li, H., "Vibration analysis of functionally graded porous cylindrical shell with arbitrary boundary restraints by using a semi analytical method" 164 : 249-264, 2019

5 Reza Pilafkan, "Three dimensional frequency analysis of bidirectional functionally graded thick cylindrical shells using a radial point interpolation method (RPIM)" Elsevier BV 39 : 26-34, 2013

6 Thang, P. T., "Thermomechanical buckling and post-buckling of cylindrical shell with functionally graded coatings and reinforced by stringers" 66 : 392-401, 2017

7 Ebrahimi, F., "Thermal buckling analysis of embedded graphene-oxide powder-reinforced nanocomposite plates" 7 (7): 293-310, 2019

8 Sobhani Aragh, B., "Static response and free vibration of two-dimensional functionally graded metal/ceramic open cylindrical shells under various boundary conditions" 223 (223): 309-330, 2012

9 Nemat-Alla, M., "Reduction of thermal stresses by developing two-dimensional functionally graded materials" 40 (40): 7339-7356, 2003

10 Mahmoud Nemat-Alla, "Reduction of thermal stresses by composition optimization of two-dimensional functionally graded materials" Springer Science and Business Media LLC 208 (208): 147-161, 2009

11 Mohammad Amir, "Nonlinear vibration characteristics of shear deformable functionally graded curved panels with porosity including temperature effects" Elsevier BV 172 : 28-41, 2019

12 Keleshteri, M. M., "Nonlinear vibration behavior of functionally graded porous cylindrical panels" 239 : 112028-, 2020

13 Praveen, G. N., "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates" 35 (35): 4457-4476, 1998

14 Gao, K., "Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales" 125 : 281-293, 2018

15 Kar, V. R., "Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method" 22 (22): 1935-1949, 2016

16 Chan, D. Q., "Nonlinear buckling and post-buckling of imperfect FG porous sandwich cylindrical panels subjected to axial loading under various boundary conditions" 232 (232): 1163-1179, 2021

17 Asgari, M., "Natural frequency analysis of 2D-FGM thick hollow cylinder based on three-dimensional elasticity equations" 30 (30): 72-81, 2011

18 Farzad Ebrahimi ; Ali Dabbagh, "NSGT-based acoustical wave dispersion characteristics of thermo-magnetically actuated double-nanobeam systems" 국제구조공학회 68 (68): 701-711, 2018

19 Thang, P. T., "Modeling and analysis of bi-directional functionally graded nanobeams based on nonlocal strain gradient theory" 407 : 126303-, 2021

20 Ebrahimi, F., "Mechanics of Nanocomposites" CRC Press 2020

21 Ebrahimi, F., "Magnetic field effects on thermally affected propagation of acoustical waves in rotary double-nanobeam systems" 31 (31): 25-45, 2021

22 Chen, M., "Isogeometric three-dimensional vibration of variable thickness parallelogram plates with in-plane functionally graded porous materials" 169 : 105304-, 2020

23 Kumar, H. S,, "Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates" 17 (17): 1918-1935, 2021

24 Rezaiee-Pajand, M., "Hygro-thermo-elastic nonlinear analysis of functionally graded porous composite thin and moderately thick shallow panels" 0 (0): 1-19, 2020

25 Chu, F., "Hermite radial basis collocation method for vibration of functionally graded plates with in-plane material inhomogeneity" 142 : 79-89, 2014

26 Wang, Y., "Free vibration of functionally graded porous cylindrical shell using a sinusoidal shear deformation theory" 66 : 83-91, 2017

27 Li, H., "Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory" 144 : 106331-, 2019

28 Ebrahimi, M. J., "Free vibration analysis of two-dimensional functionally graded cylindrical shells" 38 (38): 308-324, 2014

29 Wattanasakulpong, N., "Free vibration analysis of layered functionally graded beams with experimental validation" 36 : 182-190, 2012

30 Zare Jouneghani, F., "Free vibration analysis of functionally graded porous doubly-curved shells based on the first-order shear deformation theory" 7 (7): 1252-, 2017

31 X. Zhao, "Free vibration analysis of functionally graded plates using the element-free kp-Ritz method" Elsevier BV 319 (319): 918-939, 2009

32 Jingchuan Zhu, "Fabrication of ZrO2–NiCr functionally graded material by powder metallurgy" Elsevier BV 68 (68): 130-135, 2001

33 Mahmoud Nemat-Alla, "Elastic–plastic analysis of two-dimensional functionally graded materials under thermal loading" Elsevier BV 46 (46): 2774-2786, 2009

34 Kamran Asemi, "Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads" Springer Science and Business Media LLC 217 (217): 119-134, 2010

35 H.S. Naveen Kumar, "Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study" Elsevier BV 18 (18): 918-936, 2022

36 Allahkarami, F., "Dynamic stability of bi-directional functionally graded porous cylindrical shells embedded in an elastic foundation" 10 (10): 1345-, 2020

37 Allahkarami, F., "Dynamic buckling analysis of bi-directional functionally graded porous truncated conical shell with different boundary conditions" 252 : 112680-, 2020

38 Masoud Asgari, "Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading" Springer Science and Business Media LLC 208 (208): 163-180, 2009

39 Ebrahimi, F., "Dispersion of waves in FG porous nanoscale plates based on NSGT in thermal environment" 7 (7): 325-335, 2019

40 Shariyat, M., "Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations" 81 (81): 1289-1306, 2011

41 Farzad Ebrahimi ; Mostafa Nouraei ; Ali Dabbagh ; Ö mer Civalek, "Buckling analysis of graphene oxide powder-reinforced nanocomposite beams subjected to non-uniform magnetic field" 국제구조공학회 71 (71): 351-361, 2019

42 Satouri, S., "Application of third order shear deformation theory in buckling analysis of 2D-functionally graded cylindrical shell reinforced by axial stiffeners" 79 : 236-253, 2015

43 Ebrahimi, F., "Analysis of propagation characteristics of elastic waves in heterogeneous nanobeams employing a new two-step porosity-dependent homogenization scheme" 7 (7): 135-143, 2019

44 Aminipour, H., "Analysis of functionally graded doubly-curved shells with different materials via higher order shear deformation theory" 251 : 112645-, 2020

45 Van Do, T., "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory" 119 : 687-699, 2017

46 Rad, A. B., "A three-dimensional elasticity solution for two-directional FGM annular plates with non-uniform elastic foundations subjected to normal and shear tractions" 26 (26): 671-690, 2013

47 Tanov, R., "A simple correction to the first-order shear deformation shell finite element formulations" 35 (35): 189-197, 2000

48 Thai, H. T., "A review of theories for the modeling and analysis of functionally graded plates and shells" 128 : 70-86, 2015

49 Ebrahimi, F., "A novel porosity-dependent homogenization procedure for wave dispersion in nonlocal strain gradient inhomogeneous nanobeams" 134 (134): 1-11, 2019

50 Ebrahimi, F., "A novel porosity-based homogenization scheme for propagation of waves in axially-excited FG nanobeams" 7 (7): 379-390, 2019

51 Jha, D. K., "A critical review of recent research on functionally graded plates" 96 : 833-849, 2013

52 Saleh, B., "30 Years of functionally graded materials : An overview of manufacturing methods, applications and future challenges" 201 : 108376-, 2020