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Three-dimensional lattice structures with high specific strength, specific stiffness and low apparent density, are widely employed across multiple engineering fields. Under uniaxial compressive loading, the lattice structure may experience local buckling or global buckling. This paper conducted a systematic parametric study of the various factors affecting the buckling behavior of multilayer pyramid lattice structures to investigate the mechanism of the two main instability modes, local and global buckling. It was found that the critical buckling load increases with the increase in the size of the unit cell and decreases with the increase in the total height of the structure for the same relative density. As the relative density increases, the buckling resistance of the lattice structure increases. It is possible to examine various buckling modes by varying the geometrical properties of the pyramid unit cell (slenderness ratio, rod inclination angle, cross-sectional size of strut connection parts). Finally, numerical simulations were performed to calculate the yield strength and buckling strength of the lattice structure under uniaxial compression load, in order to estimate the threshold relative density for structural buckling and yield failure. The results demonstrated that buckling failure should be considered for aluminum alloy pyramid lattice when the relative density is below 4.07%. This study provides design criteria for lattice structures dominated by buckling and offers ideas for improving the buckling capacity of truss-type lattice structures. HIGHLIGHTS: Global and local buckling failures of lattice structure were studied Structure height and unit cell size have significant effects on both buckling mode and critical buckling loads Analyzed the threshold relative density for two failure modes of buckling and yielding [ABSTRACT FROM AUTHOR]

In this paper, the thermomechanical buckling and vibration analysis are investigated for carbon nanotube‐reinforced composite sandwich doubly curved shells (CNCSDS) under the action of both thermal loads and in‐plane compressive loads. Based on the von‐Karman non‐linear kinematic relations, First Order Shear Theory, and Hamilton's principle, the vibration and stability equations for CNCSDS under thermomechanical loads are deduced. For obtaining the critical thermomechanical buckling load and vibration frequency, an exact method is adopted. Subsequently, the results are validated by comparing with the finding in published literature and simulation results. At last, the influence of system parameters on critical thermomechanical buckling load and vibration frequency is studied and displayed graphically. Meanwhile, some new results about thermomechanical buckling and vibration analysis of CNCSDS are proposed for the first time. Highlights: Thermomechanical buckling and vibration of carbon nanotube‐reinforced composite sandwich doubly curved shells was studied.Vibration and stability equations under thermomechanical loads was deduced.The change rules of thermomechanical buckling load and frequency were obtained. [ABSTRACT FROM AUTHOR]

Additive Manufacturing (AM) is rapidly evolving due to its unlimited design freedom to fabricate complex and intricate light-weight geometries with the use of lattice structure that have potential applications including construction, aerospace and biomedical applications, where mechanical properties are the prime focus. Buckling instability in lattice structures is one of the main failure mechanisms that can lead to major failure in structural applications that are subjected to compressive loads, but it has yet to be fully explored. This study aims to investigate the effect of surface-based lattice structure topologies and structured column height on the critical buckling load of lattice structured columns. Four different triply periodic minimal surface (TPMS) lattice topologies were selected and three design configurations (unit cells in x, y, z axis), i.e., 2 × 2 × 4, 2 × 2 × 8 and 2 × 2 × 16 column, for each structure were designed followed by printing using HP MultiJet fusion. Uni-axial compression testing was performed to study the variation in critical buckling load due to change in unit cell topology and column height. The results revealed that the structured column possessing Diamond structures shows the highest critical buckling load followed by Neovius and Gyroid structures, whereas the Schwarz-P unit cell showed least resistance to buckling among the unit cells analyzed in this study. In addition to that, the Diamond design showed a uniform decrease in critical buckling load with a column height maximum of 5193 N, which makes it better for applications in which the column's height is relatively higher while the Schwarz-P design showed advantages for low height column maximum of 2271 N. Overall, the variations of unit cell morphologies greatly affect the critical buckling load and permits the researchers to select different lattice structures for various applications as per load/stiffness requirement with different height and dimensions. Experimental results were validated by finite element analysis (FEA), which showed same patterns of buckling while the numerical values of critical buckling load show the variation to be up to 10%. [ABSTRACT FROM AUTHOR]

• Equations of a hyperelastic beam under time-varying axial loading are derived. • It falls into a barreling state with an axial load lower than the critical load. • Its transverse vibration is analyzed by Galerkin and harmonic balance methods. • The material parameter can change the behavior of its transverse vibration. Equations of motion of a hyperelastic beam under time-varying axial loading are derived via the extended Hamilton's principle in this work, where the transverse vibration is coupled with the longitudinal vibration, and nonlinear vibrations of the beam in the subcritical buckling regime are investigated. Complex nonlinear boundary conditions of the beam are determined under some geometric constraints. The critical buckling load is first determined through linear bifurcation analysis. Effects of material and geometric parameters on the forced longitudinal vibration of the beam are numerically investigated. Steady harmonic shapes of the beam at different times under harmonic axial loading are determined. The beam is in the barreling deformation state even when the axial load is not in excess of the critical buckling load. The governing equation for the nonlinear transverse vibration of the beam is obtained by decoupling its equations of motion. Natural frequencies of the free linearized transverse vibration of the beam are studied. By applying the eigenfunction expansion method, the governing equation for the nonlinear transverse vibration of the beam transforms to a series of strongly nonlinear ordinary differential equations (ODEs). Two-to-one internal resonance of the beam is studied by the numerical integration method and its phase-plane portraits are obtained. The harmonic balance method and pseudo arc-length method are used to determine steady-state periodic solutions of the beam from the strongly nonlinear ODEs, and amplitude-frequency responses of the beam are determined. Effects of the external mean axial load, excitation amplitude, and damping coefficient on the amplitude-frequency response of the beam are numerically investigated. Combined effects of the external excitation amplitude and frequency on response amplitudes are also investigated. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the buckling behavior of circular hollow section (CHS) T-joints in retrofitted and non-retrofitted states under axial brace compressive loading. For this purpose, two types of analysis are carried out. The first one is evaluating the critical buckling load in various tubular joints, and the other one is investigating the post-buckling behavior after each buckling mode. More than 180 CHS T-joints with various normalized geometric properties were numerically modeled in non-retrofitted state to compute their governing buckling mode, i.e., chord ovalization, brace local, or global buckling. Then three joints with different buckling modes were selected to be retrofitted by fiber-reinforced polymer (FRP) patches to illustrate the improving effect of the FRP wrapping on the post-buckling performance of the retrofitted joints. In addition, FRP composite failures were investigated. The results indicate that the FRP retrofitting is able to prevent the brace local buckling, and that matrix failure is the most common composite failure in the retrofitted joints. [ABSTRACT FROM AUTHOR]

Based on the Donnell shell theory and smeared stiffeners technique, the governing equations of functionally graded annular spherical segments with functionally graded eccentrically stiffeners are derived to investigate the buckling of these structures under compression load and radial pressure. The segment is reinforced by parallel eccentrically functionally graded stiffener system. Approximate solutions are assumed to satisfy the simply supported boundary condition and Galerkin method is applied to obtain closed-form relations of linear buckling loads. Numerical results are given to evaluate effects of stiffeners, volume fraction index and dimensional parameters to the buckling of structure. [ABSTRACT FROM AUTHOR]

This article deals with experimental and finite element studies on the buckling of isotropic and laminated composite skew plates with circular holes subjected to uniaxial compression. The influence of skew angle, fiber orientation angle, laminate stacking sequence, and aspect ratio on critical buckling load are evaluated using the experimental method (using Methods I through V) and finite element method using MSC/NASTRAN. Method I yields the highest experimental value and Method IV the lowest experimental value for critical buckling load in the case of isotropic skew plates with circular holes. For all laminate stacking sequences considered, Method V yields the highest experimental value for critical buckling load for skew angle = 0° and Method IV yields the highest experimental value for critical buckling load for skew angles = 15° and 30°. For all laminate stacking sequences and skew angles considered, Method II yields the lowest experimental value for critical buckling load. The maximum discrepancy between the experimental values given by Method IV and the finite element solution is about 10% in the case of isotropic skew plates. The maximum discrepancy between the experimental values given by Method II and the finite element solution is about 21% in the case of laminated composite skew plates considered. The percentage of discrepancy between the numerical or finite element solution and experimental value increases as the skew angle increases. The critical buckling load decreases as the aspect ratio increases. [ABSTRACT FROM PUBLISHER]

Twenty-four specimens are tested to study the static performance of axially compressed square concrete filled CFRP-steel tubular (S-CF-CFRP-ST) columns. The tested results indicate that, for columns with relatively small slenderness, failure is dominated by the strength lose of the cross-section. However, for columns with relatively large slenderness, failure is controlled by instability. The load versus deflection curves at the mid-height of the composite columns can be divided into three stages, i.e., elastic, elasto-plastic and softening stages. The tested results also show that the longitudinal strain distribution along the depth on the cross-section is approximately linear, and the steel tube and its outer CFRP material can cooperate well both longitudinally and transversely. The longitudinal strain and the transverse strain at a point have opposite actions, and the steel tube under longitudinal tension has no transverse confinement effect on its concrete. Subsequently, axial load verses deflection curves at the mid-height and the deformed modes of the columns are simulated by using finite element (FE) method. The calculated results agree well with the experimental data to indicate that the accuracy of the FE model used is guaranteed. Then, stresses in the concrete, the steel tube and the CFRPs are then investigated by using FE method. The numerical results show that the transverse CFRP in tension provides effective confinement on the specimens and the longitudinal CFRP in tension provides effective enhancement on the flexural stiffness. The interaction force between the steel tube and the concrete reaches its maximum value on the mid-height cross-section, and it decreases when the distance to the end plates becomes smaller. On the cross-section, the interaction force has its maximum value at the corner and it decreases when the position moves to the mid-point of the tube side. The adhesive strength between the concrete and the steel tube has little effect on the critical buckling load and on the elastic stiffness of the columns. Equation for calculating the critical buckling load of the composite columns is proposed, and the estimated results agree well with the experimental data. [ABSTRACT FROM AUTHOR]

Highlights: [•] Elastically connected parallel beams under compressive axial loading. [•] Kerr type elastic layer. [•] Explicit expressions of natural frequencies and the associated amplitude ratio. [•] Effects of compressive axial load on the responses of the double beam system. [ABSTRACT FROM AUTHOR]

Abstract: An analytical approach is presented to investigate the nonlinear static and dynamic buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression. Based on the classical thin shell theory with the geometrical nonlinearity in von Karman–Donnell sense, initial geometrical imperfection and the smeared stiffeners technique, the governing equations of motion of eccentrically stiffened functionally graded circular cylindrical shells are derived. The functionally graded cylindrical shells with simply supported edges are reinforced by ring and stringer stiffeners system on internal and (or) external surface. The resulting equations are solved by the Galerkin procedure to obtain the explicit expression of static critical buckling load, post-buckling load–deflection curve and nonlinear dynamic motion equation. The nonlinear dynamic responses are found by using fourth-order Runge–Kutta method. The dynamic critical buckling loads of shells under step loading of infinite duration are found corresponding to the load value of sudden jump in the average deflection and those of shells under linear-time compression are investigated according to Budiansky–Roth criterion. The obtained results show the effects of stiffeners and input factors on the static and dynamic buckling behavior of these structures. [Copyright &y& Elsevier]

This work investigated buckling resistance of an X80 steel pipe containing a corrosion defect under axial compressive loading by finite element analysis. A 3-dimensional numerical model was developed to determine parametric effects on buckling behavior of the corroded pipeline. These included dimension of the corrosion defect (i.e., length, depth and width), pipeline geometry (i.e., outer diameter and wall thickness), internal pressure and mechanical properties of the steel (i.e., yielding strength, tensile strength and strain hardening exponent). The critical buckling load of the corroded pipeline is primarily affected by the depth and width of the corrosion defect, while the defect length is the least important. As the defect depth and width increase, the critical buckling load decreases, but the effect of corrosion width is not apparent when the dimensionless corrosion width w π D (w is width of corrosion defect and D is the pipe outer diameter) is greater than 0.5. The threshold defect length affecting the critical axial load of the pipeline is L D t = 4.86 (t is pipe wall thickness). When L D t > 4.86 , the influence of the defect length is ignorable. Pipeline containing a long corrosion defect feature of double buckling wave peaks, and a short corrosion defect contains a single buckling wave peak. The critical buckling load of the corroded pipeline subjected to the axial compression load increases with increased pipe outer diameter and wall thickness, but decreases with internal pressure. The increased yield and tensile strengths of the steel can improve the capacity to prevent local buckling of the corroded pipeline. The strain hardening exponent has a limited effect on the critical buckling load, which shows a significant decrease when the operating pressure is up to the critical internal pressure, resulting in yielding of the pipeline. • Developed a finite element model for buckling analysis of corroded X80 steel pipeline. • Determined the effects of corrosion dimension and pipeline geometry on buckling. • Determined the critical buckling load as a function of corrosion depth, width and length. • Determined the effects of pipe geometry and steel properties on critical buckling load. [ABSTRACT FROM AUTHOR]

This paper carries out the nonlinear stability of nanocomposite multilayer organic solar cell (NMOSC) subjected to axial compressive loads. The model of organic solar cell is assumed to consist five layers: Al, P3HT:PCBM, PEDOT:PSS, IOT and Glass. Based on the classical plate theory, the basic equations are established taking into account the effect of elastic foundations and initial imperfection. The approximation solutions are selected based on the boundary conditions of the four edges of NMOSC. The equation which indicates the relationship between axial compressive loads and deflection amplitude of NMOSC is obtained by using the Galerkin method. Bees Algorithm is applied to maximize the value of critical buckling load with nine variables including the thickness of five layers, the length and the width of NMOSC and two stiffness coefficients of elastic foundations. The numerical results show the effect of geometrical and material parameters, initial imperfection and elastic foundations on the nonlinear static stability and the critical buckling load of NMOSC. Optimal values of nine geometrical parameters of NMOSC are also determined. • The nonlinear stability of nanocomposite multilayer organic solar cell is investigated. • The classical plate theory is used to establish basic equations. • The effect of elastic foundations and initial imperfection are taken into account. • Effects of material and geometrical properties, elastic foundations and initial imperfection are discussed. • Bees Algorithm is used to determine the maximum value of critical buckling load depending on nine variables. [ABSTRACT FROM AUTHOR]

This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of positive-definite random elasticity matrices was first used, involving two stochastic parameters: the mean value and a dispersion parameter. In order to compute the nonlinear effects between load and lateral deflection for the buckling problem of the column, a finite element framework combining a Newton-Raphson solver was developed. The finite element tool was validated by comparing the as-obtained critical buckling loads with those from Euler's formula at zero-fluctuation of the elasticity matrix. Three levels of fluctuations of material uncertainties were then propagated through the validated finite element tool using the probabilistic method as a stochastic solver. Results showed that uncertain material properties considerably influenced the buckling behavior of columns under axial loading. The coefficient of variation of a critical buckling load over 500 realizations were 15.477%, 26.713% and 41.555% when applying dispersion parameters of 0.3, 0.5 and 0.7, respectively. The 95% confidence intervals of column buckling response were finally given. The methodology of modeling presented in this paper is a potential candidate for accounting material uncertainties with some instabilities of structural elements under compression. [ABSTRACT FROM AUTHOR]