The buckling and post-buckling behaviors are analyzed for the multilayer functionally graded graphene platelets reinforced piezoelectric (FG-GRP) plates. The FG-GRP plates are subjected to the ...external electric potential and axial forces, including the uniaxial loading and biaxial loading. The graphene platelets (GPLs) disperse uniformly and parallelly in each graphene platelets reinforced piezoelectric composite (GRPC) layer, but they spread grading across the thickness of the FG-GRP plates. The effective Young’s modulus of each layer for the FG-GRP plates is calculated by the Halpin-Tsai parallel model. The rule of the mixture is employed to predict the Poisson’s ratio, effective mass density and piezoelectric properties of each layer of the FG-GRP plates. The governing equations of motion for the FG-GRP plates are obtained by the first-order shear deformation plate theory, von Karman nonlinear theory and principle of virtual displacements. To obtain the buckling and post-buckling behaviors of the FG-GRP plates with different boundary conditions, the differential quadrature (DQ) method and a direct iterative technique are combined to solve the governing equations of motion for the FG-GRP plates. The impacts of the external electric voltage, distribution pattern, volume fraction, piezoelectric properties, length-to-thickness of the GPLs and geometry of the plates on the critical buckling load and post-buckling equilibrium paths of the FG-GRP plates are discussed in detailed. It is clearly illustrated that the GPLs have a significantly enhancing influence on the buckling and post-buckling strength of the FG-GRP plates.
Substrate-free films (i.e., films with in-plane and out-of-plane constraints only on some or all edges) can be found everywhere in nature, daily life, and industrial applications. The theory of their ...buckling and wrinkling behavior has been mature and widely used in engineering. Significant progress has been made in numerical computation of film instability. However, on the one hand, the inherent drawback of numerical calculations is that they cannot provide explicit results, and the relevant mechanism and parametric analysis are limited; on the other hand, the widely used finite element simulation is difficult to compare the energy of different modes, because the mode is always constrained to a certain order in the simulation (they cannot perform the post-buckling of specified higher order modes as the calculation process is guided by the inherent energy minimization mechanism of the computational frameworks and the higher order modes were excluded). Such two aspects constrain the mechanism study of deep post-buckling related behaviors that dependent on accurate and explicit descriptions of high order modes, e.g., the deep post-buckling bifurcation/secondary buckling. As a result, an explicit analytical description for deep post-buckling behaviors of films is still of significant research value. Reviewing classical explicit analytical descriptions, in any case of the explicit descriptions by multiple trigonometric series method, Galerkin method and perturbation method, in essence, at most three terms of double trigonometric series are used to describe the post-buckling behaviors of thin films explicitly, which always introduces significant error when the film enters deep post-buckling stage. To overcome the stated problems, herein, considering a uniform rectangular film model with arbitrary in-plane loads, and based on the Galerkin method, we firstly develop a high-precision explicit analytical description for the deep post-buckling behaviors of films upon complex in-plane biaxial loads, which proposes a new insight on the buckling mode transition upon extremely deep post-buckling or complex biaxial loads, and suggests that the correct solution of the deep post-buckling bifurcation/secondary buckling requires a complete dynamic model. The research results have theoretical significance on improving the instability mechanical system of thin films, and can also provide theoretical basis for precise control of wrinkle morphology and design of film devices corresponding applications.
•Developed a high-precision analytical description for deep post-buckling of films.•Strain energy of the film under different buckling modes is expressed analytically.•Argued that a dynamical model is required for studying the post-buckling bifurcation.
This work presents and discusses numerical results concerning the elastic post-buckling behaviour and imperfection sensitivity of regular convex polygonal cross-section (RCPS) tubular beams buckling ...in local, distortional and mixed local–distortional modes, a topic currently lacking research. This study is carried out in the framework of Generalised Beam Theory (GBT) geometrically non-linear analyses, enriched with a branch switching technique, and takes advantage of the GBT intrinsic modal nature to shed new light on the mechanics underlying the post-buckling behaviour of these members. Due to the small half-wavelength of all the buckling phenomena addressed, only simply supported members under uniform bending are investigated. In particular, this work investigates the post-buckling behaviour and imperfection sensitivity of RCPS beams (i) exhibiting several wall numbers (6, 8, 10, 14, 20, 30) with distinct combinations of circumradius-to-thickness ratios (ii) having distinct lengths, and (iii) containing critical-mode initial geometrical imperfections with several amplitudes. Relevant displacement profiles and modal participation diagrams are provided along trivial and non-trivial equilibrium paths, in order to draw meaningful conclusions concerning the post-buckling behaviour of RCPS tubes under bending. For comparison and validation purposes, ABAQUS shell finite element results are also presented.
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•L, D and L-D post-buckling behaviours of regular polygonal tubular beams studied.•GBT non-linear analyses shed new insight on the beam post-buckling mechanics.•Beams buckling in L (D) modes exhibit plate (shell)-like post-buckling behaviours.•L-D post-buckling behaviour strongly depends on the corner displacement restraints.•Loss of uniqueness occurs along the beam D and L-D numerical equilibrium paths.
In this paper, post-buckling behavior of geometrically imperfect porous beams reinforced with graphene platelets (GPLs) and resting on nonlinear hardening foundation is investigated. GPLs are ...uniformly and non-uniformly distributed thorough the thickness direction. Different porosity distributions called uniform, symmetric and asymmetric are considered. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The present refined beam 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, GPL distribution, GPL weight fraction, geometrical imperfection and foundation parameters on nonlinear buckling behavior of porous beams. Specially, porosities and GPL reinforcement have a great impact on post-buckling configuration of both ideal and imperfect nanocomposite beams.
In the current research, a comprehensive frequency analysis is performed for the circular sandwich plates in the pre-and post-buckling ranges occurred because of an in-plane thermal field. A sandwich ...system is fabricated with an open-cell foam (OCF) core and laminated composite face sheets reinforced with graphene platelets based on the functionally graded models (FG-GPLRC). The displacement field is counted using Reddy’s third-order shear deformation theory because the thick layers form the desired circular structure. Due to large deformations in the post-buckling situation, the geometrically nonlinear strain–displacement relations based on the von Kármán model are employed. The Chebyshev collocation solution is implemented to attain the discrete form of equilibrium and dynamic equations. A displacement control iterative procedure is also adopted to address the nonlinear equilibrium state of the system. Moreover, the adjacent-equilibrium criterion is considered to recognize the static paths from small-amplitude vibrations. After performing validation studies with available articles, novel results are displayed to verify the influence of geometrical and physical characteristics on the post-buckling path and fundamental natural frequency of circular sandwich plates.
•A comprehensive frequency analysis is performed for the circular sandwich plates.•The pre-and post-buckling ranges induced by in-plane thermal field are assumed.•The structure is fabricated with open-cell foam core and nanocomposite face sheets.•Due to large deformations in post-buckling, the nonlinear strain-relations are considered.•The Chebyshev collocation solution is implemented to solution.
In this article, we present for the first time a research analysis for the size-dependent effects on thermal buckling and post-buckling behaviors of functionally graded material micro-plates with ...porosities (imperfect FGM) using isogeometric analysis. A seventh-order shear deformation plate theory associated with the modified couple stress theory (MCST) is particularly imposed to capture the size-dependent phenomenon within imperfect FGM micro-plates. The material properties of imperfect FGM micro-plates with three different distributions of porosities including even, uneven and logarithmic-uneven varying across the plate thickness are derived from the modified rule-of-mixture assumption. The nonlinear governing equation for size-dependent imperfect FGM micro-plate under uniform, linear and nonlinear temperature rise is derived using the Von-Kármán assumption and Hamilton’s principle. Through numerical example, the effect of temperature rise, boundary conditions, power index, porosity volume fraction, porosity distribution pattern and material length scale parameter on thermal buckling and post-buckling behaviors of FGP micro-plates are investigated.
The post-buckling behavior and nonlinear vibration of a fluid-conveying pipe composed of a functionally graded material were analytically studied. The power-law material property was considered as ...continuously varying across the direction of the pipe wall thickness. A nonlinear governing equation for the pipe and relevant boundary conditions were derived based on Hamilton’s principle. The post-bucking configurations of the pipe were analytically predicted. The closed-form expression of the nonlinear free vibration of the pipe was determined using the homotopy analysis method. Numerical results are presented to display the dependence of the flow velocity, fluid density, and the initial stress on the post-buckling configurations. It was concluded that the statics and dynamics are significantly changed by the material properties, which suggests that the dynamic behavior of pipes may be tailored by use of man-made functionally graded materials.
Honeycomb structures display extraordinary stiffness-to-weight ratio when loaded in the out-of-plane direction. When realized using thermoplastic polyurethane (TPU), the structures offer the ...potential for repeatable and high specific energy absorption. Varying the cell size and wall thickness of TPU honeycombs facilitates changes in stiffness magnitude, though affords only modest capacity to alter the shape of the stress-strain curve. 3D printing facilitates advanced design exploration, beyond that of straight walls. Origami fold patterns have demonstrated the ability to influence the buckling behavior of tubular structures. Here we demonstrate the incorporation of origami folds into square honeycombs. The fold parameters facilitate significant tailoring of the stress-strain curve, allowing a range of profiles from quasi-rectangular to quasi-linear to be achieved; such structures can find applications in situation-specific energy absorption scenarios.
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•A method was developed to introduce origami fold patterns into square honeycombs.•The origami honeycombs were realized via 3D printing in thermoplastic polyurethane.•The crushing behavior of the origami honeycombs was studied via finite element analysis and experimental compression testing.•Varying the origami fold parameters allows significant tailoring of the honeycomb stress-strain response.•Absorption efficiencies as high as 0.49 were experimentally demonstrated, which rivals that of rigid polyurethane foams.
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.
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