This study introduces new Ritz-shape functions for analysing the buckling, bending, and free vibration behaviours of bio-inspired helicoidal laminated composite (BIHLC) beams with various lamination configurations. The higher-order shear deformation theory is utilised to formulate the beam displacement. The governing equations of motion are established using the Lagrange equation, and the Ritz-shape functions are constructed based on Laguerre polynomials. Several numerical examples are conducted to assess the proposed method and the investigation covers seven different helicoidal arrangements. The study evaluates the influence of boundary conditions, lamination schemes, orthotropy ratio, and slenderness on the mechanical response of BIHLC beams. Overall, the findings provide valuable insights for future research in this field.
GhazlanANgoTTanP, et al.Inspiration from Nature's body armours–A review of biological and bioinspired composites. Compos B Eng2021; 205: 108513.
4.
PengXZhangBWangZ, et al.Bioinspired strategies for excellent mechanical properties of composites. J Bionic Eng2022; 19(5): 1203–1228.
5.
ZhangWXuJYuTX. Dynamic behaviors of bio-inspired structures: design, mechanisms, and models. Eng Struct2022; 265: 114490.
6.
DengYJiangHRenY. Edge-on impact behaviors of helicoidal fiber arrangement of composite laminates. J Reinforc Plast Compos2023; 44(3–4): 178–192.
7.
TarafdarARazmkhahOAhmadiH, et al.Effect of layering layout on the energy absorbance of bamboo-inspired tubular composites. J Reinforc Plast Compos2022; 41(15-16): 602–623.
8.
BudholiyaSBhatARajSA, et al.State of the art review about bio-inspired design and applications: an aerospace perspective. Appl Sci2021; 11(11): 5054.
9.
SharmaAShuklaNKBelarbiM-O, et al.Bio-inspired nacre and helicoidal composites: from structure to mechanical applications. Thin-Walled Struct2023; 192: 111146.
10.
ApichattrabrutTRavi-ChandarK. Helicoidal composites. Mech Adv Mater Struct2006; 13(1): 61–76.
11.
ChengLThomasAGlanceyJL, et al.Mechanical behavior of bio-inspired laminated composites. Compos Appl Sci Manuf2011; 42(2): 211–220.
12.
TanTRibbansB. A bioinspired study on the compressive resistance of helicoidal fibre structures. Proc Math Phys Eng Sci2017; 473(2206): 20170538.
YinSYangRHuangY, et al.Toughening mechanism of coelacanth-fish-inspired double-helicoidal composites. Compos Sci Technol2021; 205: 108650.
15.
JonesMEZavattieriPSuksangpanyaN, Bio-inspired helicoidal composites: 3D printing and experiments. 2014.
16.
RibbansBLiYTanT. A bioinspired study on the interlaminar shear resistance of helicoidal fiber structures. J Mech Behav Biomed Mater2016; 56: 57–67.
17.
LiuJLLimEWLSunZP, et al.Improving strength and impact resistance of 3D printed components with helicoidal printing direction. Int J Impact Eng2022; 169: 104320.
18.
DingZXiaoHDuanY, et al.Bio-inspired self-stitching for enhancing ductility and impact resistance of unidirectional laminated composites. Compos Sci Technol2023; 242: 110184.
19.
LerewDFlaterPGaskeyB, et al.Mechanical behavior of bio-inspired helicoidal thermoplastic composites. J Thermoplast Compos Mater2023; 37(3): 1094–1110.
20.
LiuJLPhamVNHTayTE, et al.Bio-inspired helicoidal thin-ply carbon fiber reinforced epoxy laminates with nylon microparticles for improved toughness and healing. Compos Appl Sci Manuf2023; 171: 107588.
21.
AbarcarRBCunniffPF. The vibration of cantilever beams of fiber reinforced material. J Compos Mater1972; 6(3): 504–517.
22.
YangFXieWMengS. Impact and blast performance enhancement in bio-inspired helicoidal structures: a numerical study. J Mech Phys Solid2020; 142: 104025.
23.
AlmitaniKHMohamedNAlazwariMA, et al.Exact solution of nonlinear behaviors of imperfect bioinspired helicoidal composite beams resting on elastic foundations. Mathematics2022; 10(6): 887.
MohamedSAMohamedNEltaherMA. Snap-through instability of helicoidal composite imperfect beams surrounded by nonlinear elastic foundation. Ocean Eng2022; 263: 112171.
26.
FengXZhuP. Study of impact resistance of a novel bio-inspired ceramic-composite structure using finite element simulations. Mech Adv Mater Struct2023; 31: 7420–7433.
27.
MohamedNMohamedSAAbdelrhmaanAA, et al.Nonlinear stability of bio-inspired composite beams with higher order shear theory. Steel and Composite Structures. Int J2023; 46(6): 759–772.
28.
KaramanliAVoTPBelarbiM-O, et al.On the bending, buckling and free vibration analysis of bio-inspired helicoidal laminated composite shear and normal deformable beams. Compos Struct2025; 352: 118641.
29.
SaurabhSKiranRSinghD, et al.A comprehensive investigation on nonlinear vibration and bending characteristics of bio-inspired helicoidal laminated composite structures. Appl Math Mech2025; 46(1): 81–100.
30.
DoanTSTranTTThaoPH, et al.Free vibration and buckling analysis of bio-inspired helicoid laminated composite plates resting on Pasternak foundation using the first-order meshfree. Lat Am J Solid Struct2025; 22(1): e8346.
31.
KhotjantaPAimmaneeS. Optimal interply angle of bio-inspired composite curved panels with helicoidal fiber architecture. Compos Struct2024; 343: 118269.
32.
GargABelarbiM-OLiL, et al. Free vibration analysis of bio-inspired helicoid laminated composite plates. J Strain Anal Eng Des2023; 58(7): 538–548.
33.
SharmaABelarbiMOGargA, et al.Bending analysis of bio-inspired helicoidal/Bouligand laminated composite plates. Mech Adv Mater Struct2023; 31: 5326–5340.
34.
SharmaATonkAGargA, et al.First-ply failure analysis of helicoidal/Bouligand bio-inspired laminated composite plates. AIAA J2023: 1–11.
35.
SinghAGargASahuV. Stability and mode shape analysis of doubly-and cross-helicoidal laminated sandwich plates inspired from dactyl’s club. Mech Adv Mater Struct2023; 31: 8764–8780.
36.
LuTShenH-SWangH, et al.Linear and nonlinear free vibration and optimal design of bio-inspired helicoidal CFRPC laminated plates. Int J Struct Stabil Dynam2023; 24(09): 2450098.
37.
KaramanliAVoTPEltaherMA. Comprehensive analysis of bio-inspired laminated composites plates using a quasi-3D theory and higher order FE models. Thin-Walled Struct2024; 198: 111735.
38.
KaramanliAVoTPEltaherMA. Transient analysis of bio-inspired shear and normal deformable laminated composite plates using a higher-order finite element model. Mech Base Des Struct Mach2024; 52: 9281–9305.
39.
KiranRSinghDSinghSK, et al.On the isogeometric analysis of vibration and buckling of bioinspired composite plates using inverse hyperbolic shear deformation theory. Mech Base Des Struct Mach2025; 53(2): 1067–1104.
40.
MalekinejadHCarbasRJCAkhavan-SafarA, et al.Bio-inspired helicoidal composite structure featuring graded variable ply pitch under transverse tensile loading. J Compos Sci2024; 8(6): 228.
41.
SharmaAShuklaNKGargA, et al.An insight into the buckling behavior of double- and cross-helicoidal laminated composite plates inspired by dactyl’s club. Mech Adv Mater Struct2024; 31(28): 10974–10988.
42.
MochidaYIlankoS. On the Rayleigh-Ritz method, Gorman's superposition method and the exact dynamic stiffness method for vibration and stability analysis of continuous systems. Thin-Walled Struct2021; 161: 107470.
43.
NguyenN-DNguyenT-NNguyenT-K, et al.A Legendre-Ritz solution for bending, buckling and free vibration behaviours of porous beams resting on the elastic foundation. Structures2023; 50: 1934–1950.
44.
AydogduM. Free vibration analysis of angle-ply laminated beams with general boundary conditions. J Reinforc Plast Compos2006; 25(15): 1571–1583.
45.
ŞimşekM. Static analysis of a functionally graded beam under a uniformly distributed load by Ritz method. Int J Eng Appl Sci2009; 1(3): 1–11.
46.
ReddyJ. A general non-linear third-order theory of plates with moderate thickness. Int J Non Lin Mech1990; 25(6): 677–686.
47.
KhdeirAReddyJ. Free vibration of cross-ply laminated beams with arbitrary boundary conditions. Int J Eng Sci1994; 32(12): 1971–1980.
48.
KhdeirAReddJ. Buckling of cross-ply laminated beams with arbitrary boundary conditions. Compos Struct1997; 37(1): 1–3.
49.
LiJHuoQLiX, et al.Vibration analyses of laminated composite beams using refined higher-order shear deformation theory. Int J Mech Mater Des2014; 10(1): 43–52.
50.
CookGMTesslerA. A {3, 2}-order bending theory for laminated composite and sandwich beams. Compos B Eng1998; 29(5): 565–576.
51.
NguyenT-KNguyenB-DVoTP, et al.A novel unified model for laminated composite beams. Compos Struct2020; 238: 111943.
52.
VoTPThaiH-TNguyenT-K, et al.Flexural analysis of laminated composite and sandwich beams using a four-unknown shear and normal deformation theory. Compos Struct2017.
53.
JonesRM. Mechanics of composite materials. Boca Raton: CRC Press, 2018.
54.
MantariJCanalesF. Free vibration and buckling of laminated beams via hybrid Ritz solution for various penalized boundary conditions. Compos Struct2016; 152: 306–315.
55.
RitzW. Theorie der Transversalschwingungen einer quadratischen Platte mit freien Rändern. Ann Phys1909; 333(4): 737–786.
56.
AttiaMAShanabRA. Dynamic analysis of 2DFGM porous nanobeams under moving load with surface stress and microstructure effects using Ritz method. Acta Mech2024; 235(1): 1–27.
57.
ChandrashekharaKKrishnamurthyKRoyS. Free vibration of composite beams including rotary inertia and shear deformation. Compos Struct1990; 14(4): 269–279.
58.
CookGM. A higher-order bending theory for laminated composite and sandwich beams. No. NAS 1.26: 201674. 1997.
59.
AydogduM. Buckling analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Compos Sci Technol2006; 66(10): 1248–1255.
60.
KumarY. The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: a literature review. J Vib Control2018; 24(7): 1205–1227.
61.
SmithSTBradfordMAOehlersDJ. Numerical convergence of simple and orthogonal polynomials for the unilateral plate buckling problem using the Rayleigh–Ritz method. Int J Numer Methods Eng1999; 44(11): 1685–1707.
62.
Moreno-GarcíaPdos SantosJVALopesH. A review and study on Ritz method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates. Arch Comput Methods Eng2018; 25(3): 785–815.
63.
OosterhoutGMVan Der HoogtPJMSpieringR. Accurate calculation methods for natural frequencies of plates with special attention to the higher modes. J Sound Vib1995; 183(1): 33–47.
64.
LiuJLLeeHPTanVBC. Effects of inter-ply angles on the failure mechanisms in bioinspired helicoidal laminates. Compos Sci Technol2018; 165: 282–289.
65.
ReddyJN. Mechanics of laminated composite plates and shells: theory and analysis. Boca Raton: CRC Press, 2003.
