On the basis of the nonlocal strain gradient theory, a size-dependent Euler–Bernoulli beam model is formulated and devoted to investigating the scaling effect on the post-buckling behaviors of ...functionally graded (FG) nanobeams with the von Kármán geometric nonlinearity. The developed beam model can incorporate the scaling effect of both nonlocal long-range force and microstructure-dependent strain mechanism. To simplify the redundancy of the governing equation and derive the closed-form solutions, a physical neutral surface is applied for removing the bending-stretching coupling due to geometric nonlinearity and the coupling rigidity between the extensional and bending rigidities of the though-thickness FG material. The closed-form solutions for the post-buckled configuration and the critical buckling force (CBF) are deduced in the case of hinged-hinged boundary conditions. The effects of scaling parameters and material property variation on the post-buckled configuration and the CBF are investigated in detail. It is found that the stiffness-hardening or stiffness-softening effect is dependent of the values of scaling parameters.
•A model is derived to study the post-buckling of functionally graded nanobeams.•The model incorporates nonlocal stress and microstructure-dependent strain gradient effects.•Closed-form solutions for post-buckled configuration and critical buckling force are derived.•Stiffness-hardening or stiffness-softening effects can be found and depend on the values of small-scaled parameters.
In this study, an energy absorption lattice, comprised of multiple tetra-beam-plate unit cells with negative stiffness, was designed, fabricated by selective laser sintering method, and analyzed both ...numerically and experimentally. Snap-through behavior of the unit cell developed due to negative stiffness caused by geometric nonlinearity from large deflection of the constituent elastic beams, resulting in energy absorption. A criterion for the unit cell to achieve the snap-through behavior was investigated numerically in terms of the beam slenderness ratio and the inclined angle. This approach was chosen to facilitate control of energy dissipation performance and further design space such as tuning force threshold. The unit cell with the selected geometric parameters was then created and used to construct the energy absorption lattice. Load-displacement relationships of the lattices obtained from cyclic loading tests disclosed an area enclosed by two distinct loading and unloading curves, which indicates energy dissipation. This was shown both numerically and experimentally. Drop tests were also performed to investigate energy loss of the lattices due to an impact. An energy absorption phenomenon was revealed by observing a reduced rebound height when the lattice exhibited the snap-through behavior.
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In this research, analysis of post-buckling behavior of porous metal foam nanobeams is performed based on a nonlocal nonlinear refined shear deformation beam model with geometric nonlinearity and ...imperfection. In the metal foam nanobeam, porosities are dispersed by uniform, symmetric and asymmetric models. The present nanobeam model satisfies the shear deformation effect needless of any shear correction factor. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin’s method needless of any iteration process. New results show the importance of porosity coefficient, porosity distribution, geometrical imperfection, nonlocal parameter, foundation parameters and slenderness ratio on nonlinear buckling behavior of porous nanoscale beams. Specially, porosities have a great impact on post-buckling configuration of both ideal and imperfect nanobeams.
The Carrera Unified Formulation (CUF) was recently extended to deal with the geometric nonlinear analysis of solid cross-section and thin-walled metallic beams (Pagani and Carrera, 2017). The ...promising results provided enough confidence for exploring the capabilities of that methodology when dealing with large displacements and post-buckling response of composite laminated beams, which is the subject of the present work. Accordingly, by employing CUF, governing nonlinear equations of low- to higher-order beam theories for laminated beams are expressed in this paper as degenerated cases of the three-dimensional elasticity equilibrium via an appropriate index notation. In detail, although the provided equations are valid for any one-dimensional structural theory in a unified sense, layer-wise kinematics are employed in this paper through the use of Lagrange polynomial expansions of the primary mechanical variables. The principle of virtual work and a finite element approximation are used to formulate the governing equations in a total Lagrangian manner, whereas a Newton–Raphson linearization scheme along with a path-following method based on the arc-length constraint is employed to solve the geometrically nonlinear problem. Several numerical assessments are proposed, including post-buckling of symmetric cross-ply beams and large displacement analysis of asymmetric laminates under flexural and compression loadings.
•Post-buckling, free/forced vibration and energy absorption of rhombic plate are studied.•CNTs’ Waviness and Agglomeration are assumed.•Differential Quadrature Hierarchical Finite Element Method is ...applied for solution.•The rhombic plate is located on a viscoelastic torsional fractional substrate.•The results are shown for excitation frequency lower, equal and higher than natural frequency.
Vibrations and stability responses are two mechanical characteristics of engineering materials that are highly important for designing new engineering structures. This numerical research deals with investigating the effects of reinforcing a hybrid nanocomposite viscoelastic rhombic plate with Carbon Nano-Tubes (CNTs) and Carbon Fibers (CFs) on the post-buckling behavior, free and forced vibration as well as energy absorption characteristics. The structure is located on a viscoelastic torsional fractional substrate. In addition, the influence of random distribution, waviness, and agglomeration of CNTs is analyzed using the Halpin-Tsai theory. The structural damping is based on the Kelvin-Voigt method and the structure model is created according to the first-order shear deformation theory. Four types of boundary conditions such as fixed, simply, and free-supported are considered for the structure model. To solve the governing equations, a novel approach known as the Differential Quadrature Hierarchical Finite Element Method (DQHFEM) is applied. The numerical achievements revealed that by reducing the skewness angle to 30°, decreasing the aspect ratio to 1, and increasing the CNTs weight percentage up to 0.4, dimensionless frequency improved by 101%. Application of FFFF boundary conditions has dramatically effect since the amplitudes of the dynamic deflection sharply raised (about 91.78% higher than CCCC rhombic plate) and led to deteriorated energy absorption. The dynamic deflection of the structure is increased by nearly 29.36% when both waviness and random distribution (agglomeration) parameters are considered for CNTs. Besides, the random distribution factor is more effective than waviness on post-buckling behavior, energy absorption, and stability of the rhombic plate. It is also worth mentioning that the weight percent of the CNTs affects the number of oscillations and changes the vibration pattern so that with increasing the CNTs content, the number of oscillations is enhanced.
This article aims to investigate the post-buckling behavior of plates and cylindrical panels made of functionally graded materials (FGM) and carbon-nanotubes reinforced composites (FG-CNTRC) under ...mechanical loads. Unlike the other high order shear deformation theories, the proposed formulation is elaborated within a double directors finite shell element which allows a parabolic distribution of the transverse shear strains, guarantee the zero condition of the transverse shear stresses on the extreme surfaces of the shell and introduces large deformations and finite rotations through a non-linear framework. Newton-Raphson with arc length control solution strategy is used to resolve the equilibrium paths. A power-law distribution and the extended rule of mixture are used to determine the effective material properties of functionally graded materials and carbon-nanotubes reinforced composites. The effectiveness and the accuracy of the formulation is checked via several comparisons with published results in the literature. Especially, some complex post-buckling curves of FGM and FG-CNTRC curved panels and plates with different mechanical loadings are provided that could be useful for future references. The effects of various parameters are also reported.
In this paper, we investigate the post-buckling development of instability-induced patterns in soft particulate composites. Upon reaching the critical strain level, the composite experiences ...microstructural buckling. Interestingly, in the post-buckling regime, the initial buckling mode may evolve into different new patterns. These transformations are governed by the initial microstructure parameters. In particular, depending on the initial distance between the columns of inclusions, the initial instabilities may develop into (i) inclusion chains with a zigzag or wavy shapes, (ii) a combination of inclusion sets in different length scales, (iii) seemingly disordered inclusion sets, (iv) and structures with strictly doubled periodicity. The different post-buckling patterns are further characterized via the discrete Fourier transform (DFT) analysis. Our results also show that the initially formed post-buckling patterns can further evolve into rather complex new shapes beyond a simple amplification in deformation.
•Integrate the soft hyperelastic material into the main structure of Helmholtz resonator (HR) to design a star-shaped soft Helmholtz absorber, whose acoustic characteristics can be tuned by ...harnessing its post-buckling deformation.•Combine two star-shaped HRs with different wall-thickness to design a ventilated and mechanically tunable absorber to achieve asymmetric sound absorption and perfect sound absorption by applying specific and respective compression loads.•The sound absorption of the proposed pair of HRs can be real-time tuned effectively and repeatedly by mechanical loading and unloading.
Helmholtz resonator (HR) has always been an important part of artificial sound-absorbing materials, most of which however cannot be tuned in real time and hence have a limited scope of applications. In this work, we integrate for the first time the soft hyperelastic material into the main structure of HR to design a star-shaped soft Helmholtz absorber. The soft HR exhibits different post-buckling deformation behavior when its wall-thickness varies, which further yields different acoustic characteristics. By combining two star-shaped HRs with different wall-thickness, we are able to achieve asymmetric sound absorption when specific and respective compression loads are applied to the two HRs. In addition, high sound absorption at various frequencies can be obtained via different combinations of the applied loads. Due to the perfect capability of reversible large deformation of soft hyperelastic materials, the sound absorption of the proposed pair of HRs can be real-time tuned effectively by mechanical loading and unloading. In other words, the acoustic switch controlled by mechanical load can be realized. The proposed soft absorber has an obvious practical application value, and also provides an important illustration for the design of soft and tunable acoustic devices.
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In this paper we will investigate the impact of in-plane negative Poisson’s ratio (NPR) on the post-buckling responses of graphene-reinforced metal matrix composite (GRMMC) laminated plates under ...uni- and bi-axial in-plane compressive loads. The effects of temperature variation and foundation support on the post-buckling responses of GRMMC laminated plates are also taken into consideration. The graphene volume fractions in each layer of a GRMMC plate may vary along the plate thickness direction to achieve a functionally graded (FG) arrangement. The GRMMC layers have temperature-dependent material properties that can be modeled by the extended Halpin–Tsai model. Employing the Reddy’s third order shear deformation plate theory, the governing equations containing both thermal and foundation effects for the post-buckling problem of FG-GRMMC plates are formulated. The von Kármán geometrical nonlinearity is also considered. The post-buckling responses of the FG-GRMMC laminated plates are obtained by solving the governing equations using a two-step perturbation approach. The results have revealed that in-plane NPR has a substantial impact on the post-buckling responses of GRMMC laminated plates.
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