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The mechanical behaviours of bio-inspired helicoidal symmetric laminated composite (BIHLC) beams are investigated via the Ritz method. By exploiting the variational formulation, equations of motion along with element stiffness, geometrical stiffness, and mass matrices are derived. The study conducts a thorough examination, covering bending, buckling stability, and free vibration analyses of BIHLC beams with various lamination schemes. The developed model is verified against existing literature on conventional composite laminated and BIHLC beams. The study also examines the mechanical response of BIHLCs, considering boundary conditions, lamination schemes, orthotropy ratios, and aspect ratios. Notably, deflections, critical buckling loads, and fundamental frequencies demonstrate variations dependent on the specific lamination scheme, boundary condition, and aspect ratio. Novel findings, presented for the first time, offer valuable insights for future studies in this area. [ABSTRACT FROM AUTHOR]

• Higher order FEMs are proposed for bio-inspired laminated composites plates using a quasi-3D theory for the first time. • Three different FEMs are derived based on non-conforming elements with different number of nodes and degree of freedom. • No shear locking phenomenon was observed in the analyses conducted using these FEMs. • Effects of lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. A comprehensive study is carried out by employing various finite element models (FEMs) for the bending, buckling stability and free vibration analyses of bio-inspired helicoidal composite plates with various lamination schemes. A higher order quasi-3D kinematic plate theory is developed to include a shear deformation effect. The variational formulation of the problem is exploited to derive the equations of motion, element stiffness, geometrical stiffness, and mass matrices based on a non-conforming rectangular element. Three different finite elements models are derived based on non-conforming elements with different number of nodes and degree of freedom. The developed finite element model has been validated with those found in the open literature. The effects of boundary condition, lamination scheme, orthotropy ratio and aspect ratio on the mechanical response of the bio-inspired helicoidal composite plates are examined. Notably, for the lamination schemes investigated in this study, no shear locking phenomenon was observed in the analyses conducted using these FEMs. Dimensionless centre deflections, critical buckling loads and fundamental frequencies of bio-inspired helicoidal composite plates vary depending on the type of lamination scheme, boundary condition and aspect ratio. The new orientation schemes can replace the traditional ones to overcome the shear singularity and overcome the delamination defects. [ABSTRACT FROM AUTHOR]

• Size-dependent responses of 2D FG porous microbeams are studied using the modified strain gradient theory. • Two different porosity distribution models for 2D FG microbeams are considered. • Material length scale parameter (MLSP) is varied in both the axial and thickness directions as well as porosity. • The effects of small size, MLSP, porosity, gradient indexes and boundary conditions are investigated. • The effect of variable MLSP is significant and should be considered for analysis of 2D FG porous microbeams. Finite elemen model for the structural behaviours of bi-directional (2D) FG porous microbeams based on a quasi-3D theory and the modified strain gradient theory (MSGT) is presented. As the main novelty of this study, in order to capture accurately the size effects, the MSGT is employed with three material length scale parameters (MLSPs) rather than the modifed couple stress theory (MCST) with only one MLSP. The material properties including three MLSPs are varied in both the axial and thickness directions as well as porosity. By using a quasi-3D theory, which inludes normal and shear deformations, the governing equations for static, vibration and buckling analysis are derived and solved by Hermite-cubic beam element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in two directions on the deflections, natural frequencies and buckling loads of 2D FG porous microbeams are examined. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on bending, vibration and buckling behaviours of the zigzag and armchair nanobeams. Based on a third order shear deformation beam theory and the doublet mechanics, a finite element model is proposed and employed to solve the problems of zigzag and armchair nanobeams with various boundary conditions for the first time. The verification is performed by comparing the numerical results with those from the previous studies with respect to various boundary conditions. A number of numerical examples on zigzag and armchair nanobeams with four boundary conditions have been carried out. The effects of material length scale parameters, aspect ratio, nanobeam model and boundary conditions on the displacements, natural frequencies and buckling loads of nanobeams are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. [Display omitted] • The structural behaviors of the zigzag and armchair nanobeams are presented. • Doublet mechanics and finite element formulation are used. • S–S, C–S, C–C and C–F boundary conditions are analyzed for the first time. [ABSTRACT FROM AUTHOR]

• Structural behaviours of CNTRC and GPLRC beams are studied. • Normal and shear effects are included in the governing equations of motion. • Distribution pattern, volume fraction of CNTs, GPL weight fraction, etc. are investigated. • A finite element model is developed to analyze beams for various boundary conditions. This paper investigates bending, vibration and buckling analysis of carbon nanotube-reinforced composite (CNTRC) and graphene nanoplatelet-reinforced composite (GPLRC) beams. Both normal and shear effects are included in the formulation of the governing equations of motion of the beams. Finite element model is employed to determine displacements, critical buckling loads and natural frequencies of the beams with different boundary conditions. Several important factors in parametric studies including distribution pattern, volume fraction of CNTs, GPL weight fraction, slenderness ratio, boundary condition, etc. are investigated. Some new results are given as benchmark for further validation. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on bending, vibration and buckling behaviours of the multi-directional FG microplates. The material properties vary continuously both in-plane and through-thickness directions. Based on a quasi-3D shear and normal deformation plate theory and the modified strain gradient theory, a finite element model is proposed and employed to solve the problems of the multi-directional FG microplates with various boundary conditions. The verification is performed by comparing the numerical results with those from the previous studies. A number of numerical examples on the multi-directional FG microplates with nine boundary conditions and power-law index have been carried out. The effects of three material length scale parameters, aspect ratio, gradient indexes in spatial directions and boundary conditions on the displacements, natural frequencies and buckling loads of 1D, 2D and 3D-FG microplates are investigated in details. Some new results, which are not available in open literature, are provided as references for the future studies. [ABSTRACT FROM AUTHOR]

In this paper, the size-dependent responses of functionally graded (FG) porous microbeams using a quasi-3D theory and the modified strain gradient theory are investigated. Three different porosity distribution models of the FG porous microbeams are considered. By using the rule of mixture, all material properties including the material length scale parameters (MLSPs) are functions of the thickness, porosity coefficient and gradient index. The size-dependent governing equations are derived, and beam element is used to solve the problems. The verification of the proposed model is carried out and the effects of variable MLSP, porosity coefficient, gradient index and boundary conditions on the structural responses of FG porous microbeams are investigated. It can be observed that the effect of variable MLSP is significant and should be included for an accuracy analysis of the FG porous microbeams. [ABSTRACT FROM AUTHOR]

This work is presented to investigate the structural responses of three directional functionally graded (3D-FG) microplates by using the formulations of the modified couple stress theory (MCST) and finite element method. Their material properties including material length scale parameter (MLSP) are varied in three spatial directions with inclusion of the porosity volume fraction varies through the thickness direction. The governing equations for static, vibration and buckling analysis are derived and solved by conforming element for various boundary conditions. Through numerical examples, effects of variable MLSP and porosity as well as gradient index in spatial directions on the deflections, natural frequencies and buckling loads of 3D-FG porous microplates are examined. [ABSTRACT FROM AUTHOR]

This study is dedicated to understand the possibility of bending before the bifurcation buckling of the functionally graded (FG) plate which has the unsymmetrical material property distribution according to the its midplane. Based on the midplane formulation, the dimensionless critical buckling loads (DCBLs) of FG plates are computed by using a finite element method and shear and normal deformable plate theory for nine different boundary conditions (CCCC, CCCS, SCSC, SSSC, SSSS, CSCF, SCSF, SSSF and SFSF). And then, the FG plate is subjected to in-plane loads which are less than the associated DCBLs to observe the possibility of bending before buckling. It is found that the bifurcation buckling can only be obtained for CCCC, SCSC and SSSC BCs. The bifurcation buckling is impossible for other boundary conditions. For the FG plates having unsymmetrical design, the DCBLs are numerically calculated based on the neutral surface approach as well. It is noteworthy that the true bifurcation buckling can only be observed by using the neutral surface formulation. The transverse deflection due to the bending is quite pronounced especially for the plates with free edge. Since in-plane load is applied to the free edge, the transverse deflection is inevitable for the FG plates. [ABSTRACT FROM AUTHOR]