Pores have a crucial role in shaping the features of functionally graded materials. If the distribution of pores is permitted to gradually rise from the outside inwards towards the center, many more features can be incorporated. A shear shape function is used to analyze the bending response of a two-directional functionally graded porous beam (FGPB), which can be considered a multifunctional heterogeneous material while accounting for both even as well as uneven porosity distributions. The power law is adapted to modify the material properties of FGPB through out the length and thickness dimensions. The notion of virtual displacements is applied when establishing equilibrium equations in FGPB. The Navier method is applied to clamped-clamped, clamped-free boundary conditions and simply supported boundary conditions to offer solutions to FGPB. The proposed methodology is supported by the numerical results of functionally graded beams from earlier studies. The dimensionless deflections and stresses under study are affected by gradient exponents, porosities, and aspect ratios.
MiyamotoYKaysserWARabinBH,et al.Processing and fabrication. In Functionally graded materials. Boston, MA: Springer, 1999, pp. 161–245.
2.
MoghaddamJJBagheriA. Suppressing vibration in a functionally graded material plate using genetic algorithm particle swarm optimization and sliding mode control system. Proc Inst Mech Eng, Part E: J Process Mech Eng2016; 230: 120–133.
3.
BoggarapuVRuthikLGaraDK, et al.Study on mechanical and tribological characteristics of layered functionally graded polymer composite materials. Proc Inst Mech Eng, Part E: J Process Mech Eng2022; 236: 1857–1868.
4.
ChawlaNChawlaKK. Processing. In Metal matrix compositesNew York, NY: Springer.2013, pp. 55–97.
5.
KimJŻurKKReddyJN. Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates. Compos Struct2019; 209: 879–888.
6.
RajILPValanarasuSHariprasadK, et al.Enhancement of optoelectronic parameters of nd-doped ZnO nanowires for photodetector applications. Opt Mater2020; 109: 110396.
7.
KalpanaGKumarPVAljawarnehS,et al.Shifted adaption homomorphism encryption for mobile and cloud learning. Comput Electr Eng2018; 65: 178–195.
8.
AtchudanREdisonTNJIManiS, et al.Facile synthesis of a novel nitrogen-doped carbon dot adorned zinc oxide composite for photodegradation of methylene blue. Dalton Trans2020; 49: 17725–17736.
9.
KotaVRBhukyaMN. A novel global MPP tracking scheme based on shading pattern identification using artificial neural networks for photovoltaic power generation during partial shaded condition. IET Renew Power Gener2019; 13: 1647–1659.
10.
KumarPSSAllamrajuKV. A review of natural fiber composites [Jute, Sisal, Kenaf]. Mater Today Proc2019; 18: 2556–2562.
11.
BudarapuPRYBSSNatarajanR. Design concepts of an aircraft wing: composite and morphing airfoil with auxetic structures. Front Struct Civil Eng2016; 10: 394–408.
12.
BudarapuPRYbSSJavvajiB,et al.Vibration analysis of multi-walled carbon nanotubes embedded in elastic medium. Front Struct Civil Eng2014; 8: 151–159.
13.
BhukyaMNKotaVRDepuruSR. A simple, efficient, and novel standalone photovoltaic inverter configuration with reduced harmonic distortion. IEEE Access2019; 7: 43831–43845.
Van VinhPAvcarMBelarbiMO,et al.A new higher-order mixed four-node quadrilateral finite element for static bending analysis of functionally graded plates. Structures2023; 47: 1595–1612.
16.
RuoccoEReddyJN. A closed-form solution for accurate stress analysis of functionally graded Reddy beams. Compos Struct2023; 307: 1–11.
17.
SamaniegoEAnitescuCGoswamiS, et al.An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications. Comput Methods Appl Mech Eng2020; 362: 112790.
18.
KrishnamoorthyNPrasadLNKumarCP, et al.Rice leaf diseases prediction using deep neural networks with transfer learning. Environ Res2021; 198: 111275.
19.
PeddakrishnaSKhanT. Design of UWB monopole antenna with dual notched band characteristics by using π-shaped slot and EBG resonator. AEU-Int J Electron Commun2018; 96: 107–112.
20.
TuranMAdiyamanG. A new higher-order finite element for static analysis of two-directional functionally graded porous beams. Arab J Sci Eng2023; 48: 13303–13321.
21.
TruVNLongNVTuTM,et al.Static analysis of functionally graded saturated porous plate rested on pasternak elastic foundation by using a new quasi-3D higher-order shear deformation theory. Arch Appl Mech2023; 93: 2565–2583.
22.
SeyfiAMalekiMChenZ,et al.A new higher-order shear deformation theory for frequency analysis of functionally graded porous plates. Proc Inst Mech Eng, Part C: J Mech Eng Sci2022; 236: 11066–11080.
23.
BelkhodjaYOuinasDZaouiFZ,et al.An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates. Adv Compos Lett2020; 29: 1–19.
24.
RamtekePMPandaSK. Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation. Proc Inst Mech Eng, Part C: J Mech Eng Sci2023; 237(20): 4840–4857.
25.
MohdFTalhaM. Influence of material uncertainties on thermo-elastic vibration characteristics of graphene reinforced functionally graded porous beams. Proc Inst Mech Eng, Part C: J Mech Eng Sci2023; 237(15): 3406–3429.
26.
BanerjeeJRPapkovSOVoTP,et al.Dynamic stiffness formulation for a micro beam using Timoshenko–Ehrenfest and modified couple stress theories with applications. J Vib Control2023; 29: 428–439.
27.
BarrageRPotapenkoSPolakMA. Finite element modelling of exponentially graded composites with microstructure. Math Mech Solids2023; 28(9): 1959–1977.
28.
SarkarPRRahmanAS. Finite-difference analysis of stresses of a non-uniform functionally graded material circular disk rotating in the magneto-thermal environment: an equal mass study. Proc Inst Mech Eng, Part L: J Mater: Des Appl2023; 237: 301–316.
29.
Faraji OskouieMAnsariRRouhiH. Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain-and stress-driven nonlocal model. J Strain Anal Eng Des2023; 58(6): 455–463.
30.
Guang-dingWAn-dongFChuan-liuX,et al.Vibration and stability analysis of a spinning shaft with arbitrary boundaries subjected to partial load. J Vib Control2023; 0(0). doi:10.1177/10775463231163613.
31.
SiamiANitzscheF. A harmonic balance solution for the intrinsic 1D nonlinear equations of the beams. J Vib Control0(0). doi:10.1177/10775463231162751.
32.
NguyenNDNguyenTNNguyenTK,et al.A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams. Compos Struct2022; 282: 115095.
33.
MelaibariAAbo-bakrRMMohamedSA,et al.Static stability of higher order functionally graded beam under variable axial load. Alexandria Eng J2020; 59: 1661–1675.
34.
NooriARAslanTATemelB. Dynamic analysis of functionally graded porous beams using complementary functions method in the laplace domain. Compos Struct2021; 256: 113094.
35.
ReddyJNLiuC. A higher-order shear deformation theory of laminated elastic shells. Int J Eng Sci1985; 23: 319–330.
36.
FilippiMPetroloMValvanoS,et al.Analysis of laminated composites and sandwich structures by trigonometric, exponential and miscellaneous polynomials and a MITC9 plate element. Compos Struct2016; 150: 103–114.
37.
LiXFWangBLHanJC. A higher-order theory for static and dynamic analyses of functionally graded beams. Arch Appl Mech2010; 80: 1197–1212.
38.
FazzolariFA. Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Compos B: Eng2018; 136: 254–271.
39.
PolitOAnantCAnirudhB,et al.Functionally graded graphene reinforced porous nanocomposite curved beams: bending and elastic stability using a higher-order model with thickness stretch effect. Compos B: Eng2019; 166: 310–327.
40.
ShimpiRPGuruprasadPJPakhareKS. Simple two variable refined theory for shear deformable isotropic rectangular beams. J Appl Comput Mech2020; 6: 394–415.
41.
AssieAAkbasSDKabeelAM, et al.Dynamic analysis of porous functionally graded layered deep beams with viscoelastic core. Steel and Composite Structures2022; 43: 79–90.
42.
AnirudhBGanapathiMAnantC,et al.A comprehensive analysis of porous graphene-reinforced curved beams by finite element approach using higher-order structural theory: bending, vibration and buckling. Compos Struct2019; 222: 110899.
43.
FangWYuTBuiTQ. Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis. Compos Struct2019; 221: 110890.
44.
EbrahimiFFarazmandniaN. Vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in thermal environment. Adv Aircraft And Spacecraft Sci2018; 5: 107.
45.
RjoubAYousefSHamadGA. Free vibration of axially loaded multi-cracked beams using the transfer matrix method. Int J Acoustics & Vib2019; 24: 119–138.
46.
ZhaoJWangQDengX, et al.Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions. Compos B: Eng2019; 168: 106–120.
47.
JamshidiMArghavaniJ. Optimal material tailoring of functionally graded porous beams for buckling and free vibration behaviors. Mech Res Commun2018; 88: 19–24.
48.
BridjeshPReddyGCMGeethaNK, et al.On numerical bending analysis of functionally graded porous beam–effect of porosity adapting higher order shear deformation theory. J Comput Appl Mech2023; 54: 49–67.
49.
NathiVK. Buckling analysis of 2D functionally graded porous beams using novel higher order theory. J Comput Appl Mech2022; 53: 393–413.
50.
KaramanlıA. Bending analysis of two directional functionally graded beams using a four-unknown shear and normal deformation theory. Politeknik Dergisi2018; 21: 861–874.
51.
KaramanlıA. Free vibration analysis of two directional functionally graded beams using a third order shear deformation theory. Compos Struct2018; 189: 127–136.
52.
ReddyGKumarNV. Bending analysis of 2-D functionally graded porous beams based on novel high order theory. J Eng Sci Technol Rev2022; 15: 189–203.
53.
VoTPThaiHTNguyenTK, et al.Static behaviour of functionally graded sandwich beams using a quasi-3D theory. Compos B: Eng2015; 68: 59–74.
54.
Van VinhPVan ChinhNTounsiA. Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM. Eur J Mech-A/Solids2022; 96: 104743.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
