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This paper aims at investigating the buckling load of fully deployed linear array deployable structure based on scissor-like element (SLE) under its own weight. The deployable structure has been widely researched both in geometric configurations and structural dynamic characteristics. However, when the number of elements or degree of deployment exceeds the predetermined range, even if there is no external load, deployable structure will automatically collapse under its own weight. To address this issue, this paper derives a new stability model based on linear elastic analysis and energy method to compute the buckling load caused by its own weight for avoiding the structural instability, which can be applied to a linear array deployable structure with n SLEs. In the process of calculation, the first SLE is taken for mechanical analysis and the results are extended to any unit. In the sequel of this process, the scissor deployable structure is equivalent to a uniform solid column and its buckling condition under self-weight is obtained based on the principle of potential energy. Also, the effect of various parameters that affect the instability of the structure, such as the number of elements, bar length and degree of deployment is investigated, and the results of the theoretical analysis are verified through a comparison with the simulation results in ANSYS, which show that the new stability model proposed here can predict the buckling load of scissor deployable structure. [ABSTRACT FROM AUTHOR]

In this study, effects of the presence of vacancy defects in a hexagonal nanosheet on Young's modulus, effective Poisson's ratio, buckling loads and buckling modes, regardless of its constituent atoms, have been studied. Explicit expressions are proposed in order to define these characteristics considering a defect distribution term as a modifying parameter. Molecular structural mechanics concepts and FEM simulation are utilized in order to obtain these expressions and results. Different sizes and shapes of defects as well as random distribution of vacancies have been considered. The results for perfect Boron Nitride, Silicon Carbide and graphene nanosheet as well as defected Boron Nitride nanosheets are in a good agreement with those available in literature. Linear degradation behavior of Young's modulus and linear increase of effective Poisson's ratio in terms of defects distribution are observed in obtained results. A second order behavior is also observed in decreasing buckling load in terms of increasing vacancy distribution. Moreover, buckling mode characteristics due to the percentage of defects distribution has been investigated. [ABSTRACT FROM AUTHOR]

The effect of size and placement of pinhole-type atom vacancies on Euler’s critical load on free-standing, monolayer graphene, is investigated. The graphene is modeled by a structural spring-based finite element approach, in which every interatomic interaction is approached as a linear spring. The geometry of graphene and the pinhole size lead to the assembly of the stiffness matrix of the nanostructure. Definition of the boundary conditions of the problem leads to the solution of the eigenvalue problem and consequently to the critical buckling load. Comparison to results found in the literature illustrates the validity and accuracy of the proposed method. Parametric analysis regarding the placement and size of the pinhole-type vacancy, as well as the graphene geometry, depicts the effects on critical buckling load. Non-linear regression analysis leads to empirical-analytical equations for predicting the buckling behavior of graphene, with engineered pinhole-type atom vacancies. [ABSTRACT FROM AUTHOR]

Abstract: Much of what is known about co-existing responses in nonlinear systems under both deterministic and random dynamic loading is limited to phenomenological investigations of discrete systems, most commonly, the Duffing equation. From these results alone, it is difficult to extrapolate the behavior of the distributed nonlinear systems more commonly seen in real structures such as buckled beams and curved panels. This is because, beyond the simple increase in dimension, real systems bring with them imperfections and more complex forms of energy dissipation. The possibility of co-existing responses, particularly in the case of simultaneous “safe” and “unsafe” solutions (e.g. snap-through and non-snap-through), poses potential problems for engineers as it multiplies the workload, since one must be very careful to ensure that a particular simulation or experiment has captured the most critical response. Even in the case where random forces dominate the overall loading of a system, a situation in which one might anticipate an equally random response, a very small harmonic component can have an influence beyond its proportion. This effect, known as stochastic resonance, is quite counterintuitive to the analyst more familiar with linear systems where the principles of superposition and scalar multiplication of solutions make this impossible. In this paper, the effect of the damping and noise level on the number of co-existing responses in nonlinear systems is investigated. Stochastic resonance is also demonstrated, first with a double-well Duffing oscillator, and then it is shown to exist experimentally, we believe for the first time, on a macroscopic structure, that being, an (imperfect) buckled beam. [Copyright &y& Elsevier]

Abstract: The effects of a single-edge crack and its locations on the buckling loads, natural frequencies and dynamic stability of circular curved beams are investigated numerically using the finite element method, based on energy approach. This study consists of three stages, namely static stability (buckling) analysis, vibration analysis and dynamic stability analysis. The governing matrix equations are derived from the standard and cracked curved beam elements combined with the local flexibility concept. Approximation for the displacements using coupled interpolations based on the constant-strain, linear-curvature element (SC) has yielded results with reasonable accuracy. The numerical results obtained from the present finite element model are found to be in good agreement with those, both experimental and analytic, of other researchers in the existing literature. Results show that the reductions in buckling load and natural frequency depend not only on the crack depth and crack position, but also on the related mode shape. Analyses also show that the crack effect on the dynamic stability of the considered curved beam is quite limited. [Copyright &y& Elsevier]

Abstract: For conservative systems instability can occur only by divergence and the presence of damage can produce both a reduction of the buckling loads and modification of the corresponding mode shapes, depending on the positions and intensities of the damage distribution. For nonconservative systems instability is found to occur by divergence, flutter, or both, characterised by multiple stable and unstable ranges of the loads whose boundary can be altered by the damage distribution. This paper focuses on the stability behaviour of multi-cracked cantilever Euler beam-column subjected to conservative or nonconservative axial loads. The exact flutter and divergence critical loads are obtained by means of the exact closed form solution of the multi-cracked beam-column, derived by the authors in a previous paper. The extensive numerical applications, reported in the paper, aimed at evaluating the influence of several damage scenarios for different values of the degree of nonconservativeness. It is shown how the presence of damage can strongly modify the ranges of divergence and flutter critical loads of the corresponding undamaged cantilever column, which has been the subject of several papers starting from the Pflüger paradoxical results. [Copyright &y& Elsevier]

This paper focuses on the dynamic stability behaviors of the functionally graded (FG) orthotropic circular cylindrical shell surrounded by the two-parameter (Winkler-Pasternak) elastic foundation subjected to a linearly increasing load with the consideration of damping effect. The material properties are assumed to vary gradually in the thickness direction based on an exponential distribution function of the volume fraction of constituent materials. Equations of motion are derived from Hamilton's principle and the nonlinear compatibility equation is considered by the means of modified Donnell shell theory including large deflection. Then the nonlinear dynamic buckling equation is solved by a hybrid analytical-numerical method (combined Galerkin method and fourth-order Runge-Kutta method). The nonlinear dynamic stability of the FG orthotropic cylindrical shell is assessed based on Budiansky-Roth criterion. Additionally, effects of different parameters such as various inhomogeneous parameters, loading speeds, damping ratios and aspect ratios and thickness ratios of the structure on dynamic buckling are discussed in details. Finally, the proposed method is validated with published literature. [ABSTRACT FROM AUTHOR]

Abstract: A general procedure for the determination of the natural frequencies and buckling load for a set of beam system under compressive axial loading is investigated using Timoshenko and high-order shear deformation theory. It is assumed that the set beams of the system are simply supported and continuously joined by a Winkler elastic layer. The model of beam includes the effects of axial loading, shear deformation and rotary inertia. In the special case of identical beams, explicit expressions for the natural frequencies and the critical buckling load are determined using a trigonometric method. The influences of the compressive axial loading and the number of beams in the system on the natural frequencies and the critical buckling load are discussed. These results are of considerable practical interest and have wide application in engineering practice of frameworks. [Copyright &y& Elsevier]

Abstract: In this paper we study the dynamic response of a pinned shallow arch subjected to a pair of equal and opposite end moments suddenly. An experimental setup is designed to measure both the static deflection and dynamic response of the loaded arch. The dynamic buckling load as a function of the rise parameter is of particular interest. In order to theoretically identify the necessary and sufficient condition for dynamic snap-through, an accurate estimate of the system damping is required. This, however, proves to be a difficult task. A more practical approach is to adopt a sufficient condition which ensures that the arch will be safe from dynamic snapping. This condition leads to a lower bound of the dynamic critical load. As long as the end moments are smaller than this lower bound, it is guaranteed that the arch will not snap dynamically no matter what the system damping may be. For an arch with rise parameter greater than 6.55, it is shown that a closed-form expression of this lower bound of dynamic critical load can be derived. This simple formula should prove useful to design engineers. [Copyright &y& Elsevier]

Nonlinear vibration of a two layers (bi-material) beam under thermal and mechanical loadings is studied in the paper. The model of the beam is based on the extended Timoshenko beam theory taking into account geometric nonlinearities. The derived nonlinear partial differential equations are reduced to ordinary differential equations for the first three vibration modes. The reduced model is compared with results based on modal experimental analysis and the finite element method and a very good agreement was found. The complete bifurcation analysis is carried out for the reduced 3 DOF system for the clamped–clamped boundary conditions. The obtained resonance curves demonstrated the hardening phenomenon with instability zones in a case of large vibrations. The elevated temperature leaded to buckling, stronger modes interaction, an increase of instability zones occurring on the resonance curves and to chaotic oscillations coexisting with the periodic response. [ABSTRACT FROM AUTHOR]

Abstract: The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual” energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather. [Copyright &y& Elsevier]

Abstract: The axial loading of a space frame may need to be quantified, perhaps for improvement of a finite element model (FEM) to better represent the structural dynamics or to ascertain how close the structure is to buckling. The coexistence of compressive and tensile forces in a space frame causes certain frequencies to increase with respect to load while others decrease. This intricate behaviour has been modelled in the FEM of a bi-tetrahedral space frame through consideration of the geometric stiffness, which accounts for stiffness changes in the loaded members. Updating the load pattern in the FEM using Newton''s method (traditional sensitivity-based model updating) brings the model frequencies closer to those physically measured from the real bi-tetrahedral frame and thus provides identification of the axial loads. This load pattern is a predetermined set of frame axial forces in equilibrium. Such a constraint means that the extent of loading can be described by just one scalar updating parameter, an improvement upon former methods that updated member forces as independent parameters. When compared to the loads measured using strain gauges, the loads identified by model updating are seen to offer approximations of the actual loading. Difficulties such as modelling joint behaviour are discussed. The present work extends a series of numerical studies on load updating published by the authors by offering a demonstration of load pattern identification using physically measured vibration data from a real space frame. [Copyright &y& Elsevier]

Loss of stability of beams in a linear static context due to the action of tensile loads has been disclosed only recently in the scientific literature. However, tensile instability in the dynamic regime has been only marginally covered. Several aspects concerning the role of shear deformation on the tensile dynamic instability on continuous and discontinuous beams are still to be addressed. It may appear as a paradox, but also for the case of the universally studied Timoshenko beam model, despite its old origin, frequency-axial load diagrams in the range of negative values of the load (i.e. tensile load) has never been brought to light. In this paper, for the first time, the influence of a conservative tensile axial loads on the dynamic behaviour of the Timoshenko model, according to the Haringx theory, is assessed. It is shown that, under increasing tensile loads, regions of positive/negative fundamental frequency variations can be distinguished. In addition, the beam undergoes eigen-mode changes, from symmetric to anti-symmetric shapes, until tensile instability of divergence type is reached. As a further original contribution on the subject, taking advantage of a new closed form solution, it is shown that the same peculiarities are recovered for an axially loaded Euler–Bernoulli vibrating beam with multiple elastic sliders. This latter model can be considered as the discrete counterpart of the Timoshenko beam-column in which the internal sliders concentrate the shear deformation that in the Timoshenko model is continuously distributed. Original aspects regarding the evolution of the vibration frequencies and the relevant mode shapes with the tensile load value are highlighted. [ABSTRACT FROM AUTHOR]

Abstract: The analysis, and ultimately the design, of air-breathing hypersonic cruise-type vehicles is hampered by the inability to accurately capture the coupled fluid–thermal–structure interactions. There are few laboratory experiments that have investigated the interactions of compliant surface panels and hypersonic flow. The vast majority of experimental studies are limited to replicating only parts of the physical mechanisms and couplings because of the difficulty in imposing the complete transient, hypersonic environment. Studies of hot-structures, thermal protection systems, or exotic material and structural configurations, typically neglect vibration induced fluctuating pressures, shock-boundary layer interaction, the effect of transition, and separated flow. Conversely, hypersonic wind-tunnel experiments purposely neglect the influence of non-rigid structure on the aforementioned high-speed flow effects in an effort to better understand the nature of the high-speed effects. The goal of this study is to implement a simple computational model that seeks to incorporate many of the fluid–thermal–structure interactions inherent in hypersonic flow. This is accomplished using simplified aerothermal and aerodynamic theories in conjunction with a simply supported von Kármán panel in cylindrical bending. Comparisons are made between the inclusion and exclusion of self-induced and forced fluctuating pressures, as well as the fidelity required in computing the temperature distributions. Results indicate that self-induced pressure fluctuations, which arise from interactions of a vibrating structure with an ambient mean flow, significantly impact the response of panels to random acoustic loadings. Additionally, the inclusion of forced fluctuating pressure loadings can significantly reduce the onset time of panel flutter. It is surmised that experimental investigations must combine thermal loads, as well as both forced and self-induced fluctuating pressures. [Copyright &y& Elsevier]