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The development of microengineered hydrogels has opened up unlimited possibilities for designing complex structures at the microscale. In this study, we constructed an origami-inspired tubular structure with controlled mechanical buckling based on optically induced electrokinetics (OEK). By inducing a stress gradient in the thickness, a tubular structure can be formed from a poly(ethylene glycol) diacrylate (PEGDA) hydrogel film of various shapes that have been custom fabricated. To achieve an ideal three-dimensional (3D) structure, the amplitude of the tubular structure can be controlled by adjusting the aspect ratios or polymerization time. Furthermore, the tubular structure can be manipulated for the collection and transportation of microspheres. In summary, we provide an effective method for designing 3D structures at the micro-nano scale. This forming method holds great potential for achieving various functions in tissue engineering, drug packaging, and transportation in the future. [ABSTRACT FROM AUTHOR]

Steel-coped beams are used in industrial structures to accommodate a cluster of water mains, fire hydrants, power cables and telecommunication wires. The coped regions restrict the ultimate capacity and cause unfavorable failure modes. The current study investigates the structural assessment of the coped section in offshore topsides while their use enhances operational safety for drilling and production. The structural evaluation is done through 2D digital image correlation (DIC) experiments to quantify the influence of various cope geometries. The DIC technique illustrated the strain and deformation measurements under different loading conditions for different coped geometry. The primary failure mode observed in local web buckling is characterized by noticeable lateral displacement and the development of buckling lines over the coped web. Studies showed the influence of the cope depth on the load-carrying capacity and buckling processes for different cope geometries. The results of the DIC analysis are strongly aligned with experimental data and finite element numerical results, suggesting this technique to the structural assessment of coped section. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) offers new possibilities to fabricate and design lightweight lattice materials. Due to the superior mechanical properties of these lattice structures, they have the potential to replace honeycombs as cores in sandwich panels. In addition to the advantage of the integral fabrication thanks to AM, additively manufactured lattice core sandwich panels may be also used as heat exchangers, enabling a multifunctional use of the core. To ensure a reliable and safe structure, the mechanical response of lattice core sandwich panels under given load conditions must be predictable. In conventional sandwich panels subjected to compressive loads, the sandwich's global buckling and the face sheets' local buckling are the dominant failure modes. In constrast, core strut buckling may be the critical failure mode in lattice core sandwich panels. Therefore, an analytical 2D model to predict the local buckling of lattice core struts is considered in this study. Furthermore, the critical load for global buckling is obtained based on the first-order shear deformation theory. Thus, the transition from local buckling to global buckling depending on the length-to-thickness ratio is captured by the presented model. The comparison with finite element modeling of the sandwich model with truss cores has proved the accuracy of the derived model. [ABSTRACT FROM AUTHOR]

Buckling of axially loaded beams is discussed in the context of Λ-fractional analysis and mechanics. An axially compressed cantilever beam is considered in the Λ-fractional space, and the critical load is defined. The variational buckling problem of the simply supported beam is considered in the Λ-fractional space. It is pointed out that the Euler–Lagrange equation corresponding to the minimization of the total energy function with the Weierstrass–Erdmann conditions is only acceptable. The Λ-fractional buckling elastic curve of a simply supported beam is presented. That elastic curve is transferred into the initial space. The post-critical buckling deformations are defined in the context of globally stable equilibrium deformations. [ABSTRACT FROM AUTHOR]

Composite structures can achieve greater performance through variable stiffness design. In consideration of inevitable manufacturing defects introduced by the Automatic Fiber Placement machine, modified models are established to calculate equivalent properties for materials with gaps or overlaps. A modeling method for variable stiffness structures with defects is proposed based on the modified models. This approach significantly reduces the dependence on mesh size for analysis accuracy, thereby improving modeling and calculation efficiency. Upon validation of the proposed modeling method, a Hierarchical Kriging surrogate modeling is employed to optimize the buckling performance of a variable stiffness wing box with defects. The impact of different manufacturing strategies on optimization results is also investigated. The findings demonstrate that the variable stiffness design improves the wing box buckling performance under a combined torsion-bending condition. Finally, the potential of utilizing overlaps without cut-restart is analyzed for weight reduction in the design of variable stiffness wing boxes. [ABSTRACT FROM AUTHOR]

This study investigates the buckling and free vibration behavior of functionally graded saturated porous (FGSP) using a refined quasi-3D theory that ensures zero transverse shear stress at the top and bottom surfaces of the plate. The material properties depend on the porosity coefficient according to three patterns. Hamilton's principle and Biot's poroelasticity theory are employed to derive the equations of motion, which are then solved using Navier's technique. After examining the accuracy of the suggested approach, the effect of fluid compressibility on natural frequency and critical buckling load is investigated in the undrained condition. Also, the effect of porosity, geometrical parameters, and elastic foundation on the vibration and buckling response of FGSP plates are examined. The study reveals that saturating the pores with fluid leads to increased plate stiffness. This translates to higher critical buckling loads and fundamental frequencies. [ABSTRACT FROM AUTHOR]

In complex cardiovascular surgical reconstructions, conduit materials that avoid possible large-scale structural deformations should be considered. A fundamental mode of mechanical complication is torsional buckling which occurs at the anastomosis site due to the mechanical instability, leading surgical conduit/patch surface deformation. The objective of this study is to investigate the torsional buckling behavior of commonly used materials and to develop a practical method for estimating the critical buckling rotation angle under physiological intramural vessel pressures. For this task, mechanical tests of four clinically approved materials, expanded polytetrafluoroethylene (ePTFE), Dacron, porcine and bovine pericardia, commonly used in pediatric cardiovascular surgeries, are conducted (n = 6). Torsional buckling initiation tests with n = 4 for the baseline case (L = 7.5 cm) and n = 3 for the validation of ePTFE (L = 15 cm) and Dacron (L = 15 cm and L = 25 cm) for each are also conducted at low venous pressures. A practical predictive formulation for the buckling potential is proposed using experimental observations and available theory. The relationship between the critical buckling rotation angle and the lumen pressure is determined by balancing the circumferential component of the compressive principal stress with the shear stress generated by the modified critical buckling torque, where the modified critical buckling torque depends linearly on the lumen pressure. While the proposed technique successfully predicted the critical rotation angle values lying within two standard deviations of the mean in the baseline case for all four materials at all lumen pressures, it could reliably predict the critical buckling rotation angles for ePTFE and Dacron samples of length 15 cm with maximum relative errors of 31% and 38%, respectively, in the validation phase. However, the validation of the performance of the technique demonstrated lower accuracy for Dacron samples of length 25 cm at higher pressure levels of 12 mmHg and 15 mmHg. Applicable to all surgical materials, this formulation enables surgeons to assess the torsional buckling potential of vascular conduits noninvasively. Bovine pericardium has been found to exhibit the highest stability, while Dacron (the lowest) and porcine pericardium have been identified as the least stable with the (unitless) torsional buckling resistance constants, 43,800, 12,300 and 14,000, respectively. There was no significant difference between ePTFE and Dacron, and between porcine and bovine pericardia. However, both porcine and bovine pericardia were found to be statistically different from ePTFE and Dacron individually (p < 0.0001). ePTFE exhibited highly nonlinear behavior across the entire strain range [0, 0.1] (or 10% elongation). The significant differences among the surgical materials reported here require special care in conduit construction and anastomosis design. [ABSTRACT FROM AUTHOR]

Piezoelectric sensors whose sensing performances can be flexibly regulated hold significant promise for efficient signal-acquisition applications in the healthcare field. The existing methods for regulating the properties of polyvinylidene fluoride (PVDF) films mainly include material modification and structural design. Compared to material modification, which has a long test period and an unstable preparation process, structural design is a more efficient method. The irigami structure combined with compressive buckling can endow the flexible film with rich macrostructural features. Here, a method is fabricated to modulate the sensing performance by employing distinct 3D structures and encapsulation materials with varying Young's moduli. The relationship among the aspect ratio (α), pattern factor (η), elastic modulus of encapsulation materials, and equivalent stiffness is obtained by finite element simulation, which provides theoretical guidance for the design of the 2D precursor and the selection of encapsulation materials. In the demonstration applications, the sensor accurately captures pulse waveforms in multiple parts of the human body and is employed for the pressure monitoring of different parts of the sole under various posture states. This method of structure design is efficient, and the preparation process is convenient, providing a strategy for the performance control of piezoelectric pressure sensors. [ABSTRACT FROM AUTHOR]

In this paper, a new model for porous structures in functionally graded plates (FGPs) is introduced that under significant differences in constitutive material properties and high porosity ratios, the difference in elasticity modulus of the suggested pattern reaches twice as many as the previous model. This study is based on the finite strip method, incorporating Eringen nonlocal elasticity and third-order shear deformation theory, to create standard and geometric stiffness matrices for mechanical and thermal buckling analyses of functionally graded porous nanoplates (FGPNPs). The procedure is founded on Lagrangian and Hermitian shape functions to account for significant shear deformation effects in thick plates, and all in-plane displacements are applied in the geometric matrix based on the virtual work principle. Various factors like boundary conditions, porosity distributions, temperature variations, and nonlocal parameter are investigated for their impact on the mechanical and thermal buckling loads of FGPNPs. The findings reveal the substantial influence of size effects on thick porous nanoplate evaluations. Mechanical analysis shows that O-, V-, X-shaped and uniform patterns exhibit the best performance against mechanical loads, respectively. Despite the material properties deteriorating with increased porosity ratios, thermal resistance is improved. The new uniform pattern performs the best under uniform loading, and V-shaped porous structures excel at strength against nonlinear loading. However, the X-shaped model exhibits the lowest thermal resistance in both conditions. [ABSTRACT FROM AUTHOR]

In this manuscript, the long-term behaviour of piled-raft foundations (PRFs) due to the consolidation of clayey soils has been investigated by 3D finite element analysis. The validation of the numerical prototype has been carried out using the field test outcomes performed in the field laboratory and other reported results. The ultimate load capacity of the PRFs has been assessed by varying the number of piles, diameter of piles, width of raft and ground water level. Compressive loads are provided starting from an increment of 10% of the ultimate load till the ultimate load capacity of the PRFs. Settlements of PRFs have been observed till a time period of 1 month for each increment of loading and for a period of 1 year after the ultimate load capacity has been applied. The influence of load sharing behaviour, interaction effects and factor of safety on consolidation settlement of PRFs have been analysed, and predicted expressions are suggested. Average, differential and reference settlements are evaluated. Multiple linear regression analysis is implemented for estimating consolidation settlement. The proposed design equation has been validated using an example. It is inferred that load sharing ratio increased by about 34–48%, 6–19% and 11–20% with increase in the number of piles, pile diameter and width of raft in the PRF, respectively. The reduction rate of factor of safety of PRFs is insignificant and nearly minimizes to a constant value at higher settlement magnitude. The reference settlement increases from 49 to 54% as the value of load sharing ratio decreases. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a novel shear deformation theory to study the static bending and buckling of nanoplates subjected to flexomagnetic influence. This is done using the revolutionary shear strain theory and establishing finite element formulations based on the finite element technique. Methods: This study uses a finite element method to solve the nanoplate bending and buckling problem while taking into consideration the flexoelectromagnetic effect. Results: The investigation's novel aspects are summarized: since the flexomagnetic effect makes the plate stiffer, the maximum deflection is lowered when this effect is included. This effect also has varying influences on the plate under various boundary conditions, particularly the maximum position of the deflection, stress, Hz, and Bz responses. The thinner the plate thickness, the more pronounced the flexomagnetic effect. The flexomagnetic effect causes the thickness distribution of the stress components, Hz, and Bz to diverge from that of conventional structures (where this effect is disregarded), particularly for plates with CFFF boundary conditions. The longer the length of the compression zone increases, the lower the critical buckling load of the plate. The greater the stiffness of the elastic foundation, the better the plate can withstand compressive loads. Conclusion: The findings of this work provide a significant scientific foundation for the computation and development of nanoplates with magnetic properties. To design a structure that meets the necessary criteria, it is crucial to carefully choose geometric characteristics, boundary conditions, and stiffness parameters of the elastic foundation. According to this study, potential areas for additional research include investigating the impact of the flexomagnetic effect on nanoplates including fractures, optimizing nanostructures that exhibit flexomagnetic effects, and calculating the influence of flexomagnetic effects and temperature on nanostructures. [ABSTRACT FROM AUTHOR]

Purpose: This paper uses analytical methods to analyze the buckling behavior of sandwich nanobeams composed of three layers of material, with the central layer including a hollow hole. This study is the first instance of using such analytical techniques for investigating the buckling response of these specific FGM (functionally graded material) nanobeams. Methods: The calculation formulas have been derived using a novel third-order shear deformation theory. The equilibrium equation of the nanobeam is formulated based on the notion of virtual work. Analytical solutions have been used to get the precise answer for the ultimate load of the beam. Empirical evidence has substantiated the dependability of this particular approach. Results: This feature complicates the response of the beam and gives rise to several fascinating phenomena, including the idea of the virtual critical load which allows for the evaluation of the loss of the critical load. This research also looks at how the buckling behavior of the beam is affected by some geometric elements, material characteristics, hollow features of the intermediate layer, and viscous resistance-related parameters. Conclusion: Based on the findings of this investigation, several inferences can be inferred. The third-order theory employed in this investigation exhibits commendable reliability in the computation of the buckling issue pertaining to sandwich beams experiencing substantial deformations. The presence of a viscoelastic foundation has a significant impact on the critical buckling load of the beam, resulting in the inclusion of both real and fictitious components. The critical buckling load is influenced by various factors, including the core thickness, foundation parameters, material composition ratio, and the number of hollows, nonlocal characteristics, and core layer material. These factors not only impact the actual magnitude of the critical buckling load, but also affect the rate at which it is lost. The findings of this study hold considerable importance for engineers in their calculations and designs of similar structures within the field of engineering. Moreover, this serves as the foundation for other forthcoming study avenues that can serve as valuable sources of reference. [ABSTRACT FROM AUTHOR]

In this paper, the quantum effects of fine scaling on the buckling behavior of carbon nanotubes (CNTs) under axial loading are investigated. Molecular mechanics and quantum mechanics are respectively utilized to study the buckling behavior and to obtain the molecular mechanics coefficients of fine-scale nanotubes. The results of buckling behavior of CNTs with different chiralities with finite and infinite dimensions are given, and a comparison study is presented on them. The differences between finite and infinite nanotubes reflect the quantum effects of fine scaling on the buckling behavior. In addition, the results show that the dimensional changes highly affect the mechanical properties and the buckling behavior of CNTs to certain dimensions. Moreover, dimensional changes have a significant effect on the critical buckling strain. Beside, in addition to the structure dimensions, the arrangement of structural and boundary atoms have a major influence on the buckling behavior. [ABSTRACT FROM AUTHOR]

Purpose: This paper proposes a third-order shear deformation theory to study the static buckling of FG sandwich nanobeams, where the core layer of the beam has hollows in the z direction, and the two sandwich types mentioned in this paper are the hardcore and softcore types. Methods: Based on nonlocal theory, the size effect is considered, and two different solutions, as an exact solution and an approximate solution for calculating the critical buckling load of nanobeams, are presented. Results: The results show the advantage of calculating for beams with many different boundary conditions, which is completely different from the conventional analytical solution (usually only for beams subjected to the simply supported boundary conditions), this is also the new point of this work. This work uses the weighted average operator and approache to come up with an expression for figuring out the critical buckling load of FG sandwich nanobeams as an approximation. The data has shown that both solutions in this work are reliable compared to published works. At the same time, this work also shows that, depending on the material distribution of the layers and boundary conditions, one can find the appropriate core layer thickness for the maximum load-carrying capacity of the nanobeam. Conclusion: The static buckling response of sandwich FGM nanobeams with a homogeneous and porous core layer is studied. The the weighted average operator and analytical approaches, in addition to the novel shear deformation theory, were used to perform the investigation, which is something new that can be found in this article. Both of the computation techniques that are presented in this paper are quite flexible, which enables them to be used for the purpose of assessing beams under a wide range of boundary conditions. [ABSTRACT FROM AUTHOR]

Jaya is a metaheuristic algorithm that uses a pair of random internal parameters to adjust its exploration and exploitation search behaviors. Such a random setting can negatively affect the search performance of the algorithm by causing inappropriate search behavior in some iterations. To tackle this issue, the present study deals with developing a new fuzzy decision-making mechanism for dynamic adjusting the trade-off between the exploration and exploitation search behaviors of the Jaya method. The new algorithm is named Fuzzy Reinforced Jaya (FRJ) method. The search capability of the FRJ is evaluated in solving a suite of unconstrained mathematical benchmarks and constrained mechanical and structural optimization problems with buckling and natural frequency constraints. Also, the relevant decision variables are selected from both continuous and discrete domains. To provide a deeper insight into the effect of the defined auxiliary fuzzy module, the performance of the algorithm is evaluated and discussed using normalized diversity concept and behavioral diagrams. Also, employing different statistical analyses (e.g., Q–Q diagrams, Wilcoxson and Friedman tests), the significance of the outcomes is evaluated. Also, the numeric achievements are compared with six other well-stablished techniques. Attained outcomes indicate that the proposed FRJ, as a self-adaptive and parameter-free method, provides superior and promising results in the terms of stability, accuracy, and computational cost in solving mathematical and structural optimization problems. [ABSTRACT FROM AUTHOR]

In the current research, we delve into the intricate realm of bifurcation analysis for Föppl–von Kármán plates, employing a precise numerical tool. This innovative numerical approach melds the power of spectral discretization with the prowess of a high-order continuation method-based Taylor series development (HODC). It is worth noting that combining the high-order continuation method with such discretization techniques offers an efficient path-following approach, complete with adaptive step lengths, capable of tackling a wide array of nonlinear problems. Despite the extensive applications of nonlinear elasticity, the spectral method remains relatively uncharted territory within this context. However, our deep-rooted understanding and expertise in the field drive us to embrace this method alongside high-order development continuation for bifurcation analysis of Föppl–von Kármán plates. The governing equations governing thin elastic plates experiencing significant elastic deflections manifest as a pair of coupled nonlinear differential equations, famously known as the von Kármán (vK) equations, presented in a strong form with two principal unknowns: deflection (w) and the Airy stress function (F). Leveraging Chebyshev decomposition matrices, we approximate these fourth-order elliptic nonlinear partial differential equations. Subsequently, we harness high-order development continuation techniques to morph these nonlinear systems into linear ones. Our rigorous evaluation and validation of this numerical approach's precision and performance come to fruition through a comprehensive buckling analysis encompassing multiple illustrative examples. [ABSTRACT FROM AUTHOR]

Piezoelectric nanobeams are important components in micro-nano electromechanical systems. They are often used as mechanical structures such as wireless sensors, biological probes and transistors. And their mechanical performance is a very important research topic. Based on the theory of surface elasticity and the "core–shell" model, post-buckling behavior of porous piezoelectric nanobeams is analyzed using the first-order shear deformation beam theory, where the surface effect is introduced by employing the surface energy model. The governing equations and boundary conditions of post-buckling of porous piezoelectric nanobeams under mechanical loading were derived by introducing the concept of median surface in physics and the principle of minimum potential energy. The influence of surface effect on post-buckling configuration, post-buckling path, amount of induced charge and critical load of porous piezoelectric nanobeams with different external constraints and porosities were discussed. The results show that considering surface effects, the effective elastic modulus and critical load of porous piezoelectric nanobeams will be increased, and the post-buckling configuration, post-buckling path and amount of induced charge will be reduced. Meanwhile, the mechanical properties of porous piezoelectric nanobeams can be effectively improved by appropriate pore distribution. These findings can be used as a theoretical basis for the accurate design and manufacture of micro-nano mechanical and electronic devices. [ABSTRACT FROM AUTHOR]

A detailed assessment is made here of a recently proposed buckling model for a drillstring that remains in conformal contact with an axially toroidal borehole. Suitable rescaling of the relevant equations allows us to identify a particular regime of interest, which is subsequently explored in depth with a multiple-scale asymptotic strategy. In particular, the localisation phenomena previously reported in the literature are placed on firm ground and explained with the help of a small number of analytical formulae. Two new sets of qualitatively different solutions are also identified and discussed in detail. Our asymptotic predictions of the critical loads are shown to be in very good agreement with the direct numerical simulations of the corresponding linear bifurcation problem. [ABSTRACT FROM AUTHOR]

Based on the shell and plate theory, this paper uses the divide-and-combine method (DCM) to derive an analytical out-of-plane compression buckling limit expression of the basic unit of the core layer of a grid beetle elytron plate (GBEP); the accuracy of expression and the mechanism of GBEP unit buckling are investigated through experiments and finite element (FE) simulation. The results show that: (1) the theoretical expression of the out-of-plane compression buckling limit of a GBEP unit obtained by DCM is applicable and is closer to the test results than the classical solution of the out-of-plane compressive buckling of a cylindrical shell and the theoretical result of Flügge. Based on this, a modified expression of the theoretical result of Flügge's compressive buckling limit load is proposed. (2) Given the significant differences between the theoretical values obtained in this paper and the experimental values, the out-of-plane compressive buckling resistance of the GBEP unit and its mechanism are investigated from the viewpoints of structural parameters η (the ratio of the radius of the trabeculae to the width of the element) and deformation process; the synergistic mechanism of the honeycomb-trabeculae structure is also studied. This paper contributes to improving the bionic system derived from the beetle's forewing. [ABSTRACT FROM AUTHOR]

This paper investigates the size-dependent vibration and buckling behavior of nanoplates described by the nonlocal Kirchhoff model analytically. The nonlocal and local constitutive relations, governing equations and boundary conditions are comprehensively discussed. A shifted governing equation in terms of local stress resultants with associated local boundary conditions is chosen in the current work. The direct separation of variables method is formulated based on the Hamiltonian dual form of the governing differential equation to address the eigenvalue problems of nonlocal rectangular plates with each edge either simply supported or clamped. The closed-form eigen-solutions are acquired for the first time for the cases where two adjacent clamped edges exist. The validity and accuracy of the present approach are verified by comparison with published analytical and numerical results. Parametric studies are performed to investigate the influences of nonlocal parameter and boundary conditions on the size-dependency of natural frequencies and critical buckling loads of nanoplates. [ABSTRACT FROM AUTHOR]

In the context of architected materials, it has been observed that both long-wavelength instabilities leading possibly to localization and short-wavelength instabilities leading to the apparition of a deformation pattern could occur. This work proposes for the first time a comparison of the ability of two families of higher order equivalent media, namely strain-gradient and micromorphic media, to capture both patterning and long-wavelength macroscopic instabilities in those materials. The studied architected material consists in a simple one-dimensional arrangement of non-linear springs, thus allowing for analytical or nearly analytical treatment of the problem, avoiding any uncertainties or imprecisions coming from a numerical method. A numerical solution of the problem is then used to compare the post-buckling prediction of both models. The study concludes that, micromorphic media are the appropriate choice of equivalent continuum models to emply when dealing with the possibility of patterning inside a structured medium, but if long-wavelength global instability is of interest, a strain-gradient type equivalent medium is well suited. [ABSTRACT FROM AUTHOR]

The classical theory of elastic critical buckling stress works well for slender columns and thin flat plates under compression; however, the situation is different for longitudinally compressed thin-walled circular cylindrical shells, and the issue has plagued us despite considerable efforts over the last 100 years. We noticed that all such buckling analyses thus far, both linear and nonlinear, in terms of the main philosophy, inherited and were confined to Euler's pioneering solution for the slender column model that focuses on the longitudinal buckling deformation mode and should be classified as the 'longitudinal open-loop' eigenmode because the deformations of the two longitudinal ends are physically independent of each other. In view of this, for an ideal linear-elastic buckling model of a thin-walled perfectly circular cylindrical shell under uniform longitudinal compression on the foundation of the longitudinal open-loop eigenmode solution, it is also necessary to consider a 'circumferential closed-loop' eigenmode simultaneously to physically avoid violating the reality of its ideal periodic deformation on the entire perimeter and to mathematically redefine the biunique and precise relationship for each distinct eigenmode by the critical circumferential wavelength. Originating from such a case study, the mathematical uniqueness issue hidden in the general solution of the Donnell equation is further discussed. The authenticity of the competing eigenmode characterized by the Koiter circle is also discussed. Furthermore, a preliminary attempt was conducted to interpret the discrepancy between theoretical and experimental buckling loads, mainly initiated by the characteristic type of longitudinally generated circumferential local inward displacement in initial geometric imperfections, using the insights herein. [ABSTRACT FROM AUTHOR]

In this work, a nonlocal strain gradient model for the buckling analysis of functionally graded Euler–Bernoulli beam subjected to thermo-mechanical loads is developed. The governing equations are derived by incorporating the effects of nonlocal and strain gradient parameters. Thermal properties over the cross section are graded using the power law. The resulting sixth-order differential equation is solved analytically for various boundary conditions. The effect of strain gradient and nonlocal parameters on the variation of critical buckling temperature under three different boundary conditions and three different thermal loading conditions is studied. The proposed model compares well with the existing literature in the limiting sense of no nonlocal and gradient effects. [ABSTRACT FROM AUTHOR]

This article addresses the problem of determining the solicitation and deformation of beams with geometric imperfection, also called real beams under a compression action. This calculation is performed by applying the Finite Transfer Method numerical procedure under first-order effects with the entire compression action applied instantaneously and applying the action gradually under second-order effects. The results obtained by this procedure for real sinusoidal or parabolic beams are presented and compared. To verify the potential of the numerical procedure, the first and second-order effects of a beam with variable section are presented. New analytical formulations of the bending moment and the transverse deformation in the beam with sinusoidal imperfection subjected to compression are also obtained, under first and second-order analysis. The maximum failure load of the beams is determined based on their initial deformation. The results of solicitation and deformation of the real beam under compression are compared, applying the analytical expressions obtained and the numerical procedure cited. The beams under study are profiles with different geometric characteristics, which shows that it is possible to obtain maximum failure load results by varying the relationships between lengths, areas and slenderness. The increase in second-order bending moments causes the failure that originates in the beam, making it clear that this approach reproduces the buckling phenomenon. The article demonstrates that through the Finite Transfer Method the calculation of first and second-order effects can be addressed in beams of any type of directrix and of constant or variable section. [ABSTRACT FROM AUTHOR]

The direct strength method (DSM) has become an alternative to the effective width method (EWM) to compute the bending moment capacity of cold-formed channel sections. The traditional EWM examines the nominal moment capacity by the PURLIN program. DSM uses a signature curve from tests on many Australian channel sections to obtain design moment capacity for local and distortional buckling modes. Moreover, the non-linear analysis performed by Strand7 will be compared with the current DSM curve. In general, these comparisons of results are in good agreement: the THIN-WALL program results and the linear static analysis results in Strand7; the moment capacity calculated by the PURLIN program (EWM) and the DSM curve in the local buckling mode; the non-linear analysis results in Strand7 and the DSM curve for each buckling mode. The outcome of this study will benefit structural engineers by providing them with design methods analysis. [ABSTRACT FROM AUTHOR]

Using a three-variable higher-order shear deformation theory (HSDT), this research proposes an analytical method for studying the free vibration and stability of perfect and imperfect functionally graded (FG) beams resting on variable elastic foundations (VEFs). Unlike the other HSDTs, in this study, the number of unknown functions involved is only three, while the other HSDTs include four unknown functions. Besides, this theory meets the boundary requirements of zero tension on the beam surfaces and allows for hyperbolic distributions of transverse shear stresses without the need for shear correction factors. The elastic medium is supposed to have two parameters (i.e., Winkler–Pasternak foundations), with the Winkler parameter in the longitudinal direction being variable variations (linear, parabolic, sinusoidal, cosine, exponential, and uniform) and the Pasternak parameter being fixed, at first.1 The effective material characteristics of the FG beam are assumed to follow a simple power-law distribution in the thickness direction. Furthermore, the influence of porosity is investigated by considering four distinct types of porosity distribution patterns. First, the equations of motion are derived using Hamilton's principle, and then Navier's method is used to solve the system of equations for the FG beam with simply supported ends analytically. The correctness of the current formulation is demonstrated by comparing them with the results of open literature. Finally, parametric studies are done to explore the impacts of various parameters on the free vibration and buckling behaviors of FG beams. The new theory is shown to be not only correct but also simple in predicting the free vibration and buckling responses of FG beams resting on VEFs. [ABSTRACT FROM AUTHOR]

The paper aims to develop a unified modeling to analyze the free vibrations and buckling of laterally functionally graded material columns. The columns of rectangular cross-section, in which the mass density and Young's modulus vary along the depth as a power-law function, were considered. The differential equation governing a mode shape of a deformed column was derived with the relevant boundary conditions, including the effect of rotatory inertia. The computation results for the natural frequencies and buckling load were compared well with those available in the open scientific literature. The effects of geometrical and material properties on natural frequencies and buckling loads with the mode shapes are highlighted. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to study the nonlinear buckling behavior of carbon nanotube-reinforced (CNT-reinforced) cylindrical shells with the CNT-reinforced stiffeners under external pressure taking into account the effects of uniform temperature rise. A new design of stiffener system is proposed for CNT-reinforced cylindrical shells with five cases of the CNT distribution law for shell and stiffeners. A modified homogenization technique for CNT-reinforced stiffeners is developed and presented. Based on the Donnell shell theory and the von Kármán nonlinearity assumption, the Galerkin method is applied with the solution of deflection approximated in threeterm form, the critical buckling, and load-deflection postbuckling curves can be achieved in explicit expressions. Effects of the CNT-reinforced stiffeners, the thermal temperature, and the CNT-reinforced parameters on the external pressure buckling responses are numerically indicated and validated. [ABSTRACT FROM AUTHOR]

A buckling analysis of functionally graded plates of a complex form resting on an elastic foundation and subjected to an in-plane nonuniform loading is performed by the R-functions method for the first time. The mathematical formulation of the problem is presented within the framework of the classical laminate plate theory. The plates considered consist of three layers. The middle layer (core) is ceramic or metal, a face layers are fabricated of functionally graded materials (FGMs). The power-law distribution of volume fraction of constituents is used to compute the effective material properties of FGM layers. The approach proposed and the software developed consider the heterogeneous subcritical state of the plates. First, the problem of in-plane elasticity problem is solved, and then the stability problem is considered. To solve both the problems, the Ritz method combined with the R-functions theory is used. The method proposed and the software developed are verified by comparing the buckling loads of square plates subjected to a nonuniform loading. The critical loads for sandwich FG plates of a complex geometry in a nonuniform edge compression are calculated. The effects of boundary conditions, the scheme of layer arrangement, and the type of FGM on the critical load are studied. [ABSTRACT FROM AUTHOR]

A first attempt is made to study the free vibrations and the buckling response of functionally graded plates using a refined hyperbolic shear deformation theory. This theory incorporates high-order effects of shear and normal deformation with accounting for thickness stretching. A combination of hyperbolic and polynomial functions ensures a parabolic profile of shear stresses and the enforcement of zero shear stresses at the top and bottom surfaces of the plates. The need for a shear correction factor is eliminated. The plates are made from advanced composites consisting of a functionally graded material varying from a ceramic to metallic phase across the thickness. The mechanical properties of the plates are homogenized by the Voigt rule of mixtures and the Mori- Tanaka scheme. A C0 finite-element model is developed for the present theory and is included in the MATLAB code. A convergence study is performed and the efficacy of the model is validated. [ABSTRACT FROM AUTHOR]

In this paper, we study some comparisons of Dirichlet, Neumann and buckling eigenvalues on Riemannian manifolds. By introducing a new parameter, we provide some new relationships, which improve corresponding results of Ilias and Shouman in [Calc. Var. Partial Differential Equations, 2020, 59: Paper No. 127, 15 pp.] in some sense. [ABSTRACT FROM AUTHOR]

A mini basket type mapping catheter consists of thin film flexible sensors and is applied in the medical field to measure the electrocardiography (ECG) signals in order to localize and quantize the physiological condition/status of heart. The flexible nature of the thin film changes the configuration with respect to the contact boundary conditions when it contacts a target surface. Therefore, to accurately localize the flexible sensor, the thin film flexible sensor's configuration must be determined accurately in an on-line fashion. As a study of localizing the thin film flexible sensor, this study proposes an on-line thin film buckling configuration determination method using parametric optimization and interpolation technique. With the specific modulus of elasticity and dimensions of the thin film flexible sensor of the mapping catheter prototype, the buckling configuration with two point boundary condition under axial load can be calculated in desktop environment. The proposed calculation method is validated by mapping catheter sensor prototype test. The calculation/test results showed that the maximum overall length L, x a , and y a value error between the calculation and experiment are approximately 0.16 mm, − 0.12 mm. − 0.10 mm in 50 ms calculation time. The calculation result of the proposed method is also compared with that of the numerical simulation by FEM, which has approximately 0.44 mm y a value error compared with that of the experiment. [ABSTRACT FROM AUTHOR]

The stability behaviour of unsymmetrical laminated structures made of fibre-reinforced plastics is significantly influenced by bending–extension coupling and the comparatively low transverse shear stiffnesses. The aim of this work is to improve the analytical stability analysis of unsymmetrically laminated structures. With the discrete plate theory, the stability of laminated structures can be reduced to single laminated plates. The structure is divided into individual segments, and the surrounding structure is modelled by rotational elastic restraints. The governing equations for single plates under specific boundary conditions can be solved exactly with Lévy-type solutions. In this study, Lévy-type solutions for the mentioned boundary conditions under biaxial compressive load is described for the classical laminated plate theory, the first-order shear deformation theory and the third-order shear deformation theory (TSDT). In addition to transverse shear, bending–extension couplings of unsymmetrical cross-ply and antisymmetrical angle-ply laminates are considered. For the implementation of boundary conditions for the rotational restraints in the context of TSDT, a new set of conditions is formulated. The investigation shows very good agreement of the buckling load with comparative finite element analyses for different layups. [ABSTRACT FROM AUTHOR]

In this work, the nonlinear post-buckling of an advanced porous nanocomposite plate with and without imperfection subjected to a hygro-thermo-mechanical load and lying on elastic foundation is carried out using third-order shear deformation theory (TSDT). Also, a modified form of a Halpin-Tsai (M-H-T) micromechanical model is proposed to characterize the mechanical properties of graphene oxide powder (GOP)-reinforced polymer nanocomposite. To this aim, the influence on random distribution, non-straight shape and agglomerated state of the GOPs is adequately incorporated into the M-H-T model. Also, two porosity distributions including symmetric and asymmetric are considered. Both the linear and nonlinear influence of temperature and moisture concentration on the bending response are probed. Large deflection theory is considered to extract the stress field and displacement field for the perfect and imperfect nanocomposite plate. Navier solution is used to solve the large deflection nonlinear equations. Numerical results are validated by existing results in the literature. A parametric investigation is established to discuss the effects of the temperature rise and moisture concentration, elastic foundation coefficients, nanoparticle geometry, aspect ratio, porosity distributions, and geometry imperfection on the GOP-reinforced polymer composite post-buckling behaviors. [ABSTRACT FROM AUTHOR]

Using a nonlinear theory of sandwich shells with a transversely soft core, approximate analytical solutions were found to the one-dimensional linearized stability problem for a sandwich beam in the case of axial compression of its outer layer. The equations applied are based on the introduction into consideration unknown contact forces of interaction of the outer layers with core, of outer layers and core with stiffening elements at all points of their interfaces. A numerical solution of the nonlinear problem formulated was obtained invoking the method of finite sums (integrating matrices) by reducing the original problem in a differential form to a system of integroalgebraic equations. [ABSTRACT FROM AUTHOR]

Background: The modelling of the sheet metal forming operations requires accurate and precise data of the material plastic behaviour along non-proportional strain paths. However, the buckling phenomenon severely limits the compressive strain range that could be used to deform thin metal sheets. Objective: The main aim of this paper was to propose an effective device, that enables to determine of accurate stress-strain characteristics of thin metal sheet specimens subjected to axial deformation without buckling and with a special emphasis on friction correction. Methods: In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of X10CrMoVNb9-1 (P91) power engineering steel, and DP500 and DP980 dual-phase steels, under compression loading. The fixture enables monitoring of the friction between the specimen and supporting blocks during the test, and thus the precise stress response of the material could be determined. Results: The effectiveness of the fixture was evaluated under tension–compression cyclic loading and during the compression tests in which high-strength thin metal sheets were successfully deformed up to 10% without specimen buckling. Furthermore, the successful determination of a friction force variation between supporting blocks and the specimen during tests enabled to determine an actual force acting on the specimen. Conclusions: The proposed testing fixture was successfully assessed during the compression and cyclic tension–compression of high-strength thin metal sheets as no buckling was observed. Its advantage lies in adapting to change its length with specimen elongation or shrinkage during a test. The friction force generated from a movement of both parts of the device could be effectively monitored by the special strain gauge system during testing and thus its impact on the stress-strain characteristics could be successfully eliminated. [ABSTRACT FROM AUTHOR]

The behaviour of collapsed or stenotic vessels in the human body can be studied by means of simplified geometries like a collapsible tube. The objective of this work is to determine the value of the buckling critical pressure of a collapsible tube by employing Landau's theory of phase transition. The methodology is based on the implementation of an experimentally validated 3D numerical model of a collapsible tube. The buckling critical pressure is estimated for different values of geometric parameters of the system by treating the relation between the intramural pressure and the area of the central cross-section as the order parameter function of the system. The results show the dependence of the buckling critical pressures on the geometric parameters of a collapsible tube. General non-dimensional equations for the buckling critical pressures are derived. The advantage of this method is that it does not require any geometric assumption, but it is solely based on the observation that the buckling of a collapsible tube can be treated as a second-order phase transition. The investigated geometric and elastic parameters are sensible for biomedical application, with particular interest to the study of the bronchial tree under pathophysiological conditions like asthma. [ABSTRACT FROM AUTHOR]

Purpose: The present research work aims to analyze the vibration and buckling behaviour of multidirectional FG porous structures engrained with damage. Power-law (P-FGM), sigmoid (S-FGM) and exponential (E-FGM) gradings are considered to compute the material properties of the cracked FG plate. The porosity effect on the structural strength has been modelled to explore the realistic influences. Methods: In the current study, the eigenvalue analysis of the cracked FG plate with porosities is performed computationally with the help of a numerical model. The multidirectional porous structural model is repaired in ABAQUS via python script to meet the batch input. The study used the ABAQUS kernel instead of the standard GUI for better control. Results: The adequacy of the current model has been verified initially by comparing the eigenvalues (frequency and buckling load) with those of available published data with and without damages (crack). The results have been calculated for different grading patterns, porosity values, geometrical data, grading index, and crack-dependent parameters to understand their influence on the eigenvalues of the damaged multidirectional porous graded structures. Conclusions: A few generalized understandings are obtained based on the parametric study, i.e., the cracks cause a substantial decrement in total structural stiffness, which, in turn, reduces the final results adequately. Structural components are affected due to the presence of a crack in specific orientations, like in the lengthier edge of the rectangular shape. Similarly, the porosity affects the total stiffness and associated responses like the frequency and the critical buckling load. [ABSTRACT FROM AUTHOR]

For the first time, the finite integral transform (FIT) approach is extended to predict thermal buckling behaviors of orthotropic thin plates with various edge restraints. A rational strategy of accurate solution procedure is proposed to tackle plate problems, and no assumption of trial function is imposed, which is different from traditional semi-inverse solution framework. Performing the transformation introduced on the plate thermal buckling equation to produce systems of linear algebraic equations easily solved, which can provide useful benchmark results for the critical temperature and the associated thermal buckling mode shape of orthotropic plates. Good agreement between the present result with data offered by finite element method (FEM) is found, which validates the accuracy of the approach employed. Thermal buckling behaviors of plates are also investigated parametrically, with the parameters involved being the aspect ratio and edge restraint. All the present numerical and graphical results are expected to give better design for orthotropic plate structures subjected to uniform thermal load. Furthermore, in view of the generality of the present method, it is hopeful to be extended for more complex plate and shell problems. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical investigation on the buckling behaviour of corroded cold-formed steel (CFS) channel section columns under axial compression. 7 stub columns and 7 medium long columns were accelerated corrosion by the outdoor periodic spray test. Prior to compression tests, the mass, residual thickness, surface morphology and initial geometric imperfection of the corroded CFS columns were measured. The failure modes, load–strain curves and load–axial displacement curves obtained from axial compression tests were discussed. Based on the corrosion morphology, the non-linear finite element (FE) model for the corroded CFS columns was then developed. Finally, the calculation method for corroded CFS channel section columns was proposed. The results indicated that with the increasing mass loss rate, the irregularity of residual thickness increased rapidly at first, and then increased slowly due to uniform corrosion. The failure mode of the corroded specimens may change from distortional buckling to local buckling as the mass loss rate increased. With the increase in mass loss rate, the buckling critical load, ultimate load, post-buckling strength and axial displacement corresponding to ultimate load decreased. The failure positions of distortional buckling and local buckling were mainly related to the corrosion degree of the flange and web, respectively. The FE results were compared against the experiment results showing a good match in terms of both the ultimate strength and failure modes. [ABSTRACT FROM AUTHOR]

The study of natural and human-made processes often results in long sequences of temporally-ordered values, aka time series (TS). Such processes often consist of multiple states, e.g. operating modes of a machine, such that state changes in the observed processes result in changes in the distribution of shape of the measured values. Time series segmentation (TSS) tries to find such changes in TS post-hoc to deduce changes in the data-generating process. TSS is typically approached as an unsupervised learning problem aiming at the identification of segments distinguishable by some statistical property. Current algorithms for TSS require domain-dependent hyper-parameters to be set by the user, make assumptions about the TS value distribution or the types of detectable changes which limits their applicability. Common hyper-parameters are the measure of segment homogeneity and the number of change points, which are particularly hard to tune for each data set. We present ClaSP, a novel, highly accurate, hyper-parameter-free and domain-agnostic method for TSS. ClaSP hierarchically splits a TS into two parts. A change point is determined by training a binary TS classifier for each possible split point and selecting the one split that is best at identifying subsequences to be from either of the partitions. ClaSP learns its main two model-parameters from the data using two novel bespoke algorithms. In our experimental evaluation using a benchmark of 107 data sets, we show that ClaSP outperforms the state of the art in terms of accuracy and is fast and scalable. Furthermore, we highlight properties of ClaSP using several real-world case studies. [ABSTRACT FROM AUTHOR]

Functionally graded (FG) sandwich plates have been spotlighted as an advanced composite structure so that the vast amount of research efforts have paid on the study of their thermo-mechanical behaviors. Among them, the thermal buckling has emerged as an important research subject because it is directly related to the safety of structural system. In this situation, this paper examines the thermal buckling behavior of ceramic-metal FG sandwich plates with a homogeneous core and two FGM face sheets. The thermal buckling problem is formulated according to 3-D thermo-elasticity and approximated by making use of a (1,1,0) hierarchical model and 2-D natural element method (NEM). The NEM-based numerical method was compared with the reference methods, from which its reliability was verified. In addition, the critical buckling temperatures (CBTs) of ceramic-metal FG sandwich plates subject to uniform, linear and nonlinear temperature loads are parametrically examined. The parametric experiments informed that the CBT is strongly influenced by the width/thickness, core thickness and aspect ratios, the ceramic and nonlinearity indices, and the boundary condition type. [ABSTRACT FROM AUTHOR]

Analytical methods cannot find the exact solution for inelastic lateral torsional buckling. This study aims to develop innovative solutions by creating closed-form equations. A series of numerical studies (ANSYS) have been conducted for buckling load calculation on European I-section cantilever beams reinforced with transverse stiffener plates at different intervals. Formulations were developed using two methods to estimate the found load values more practically. Multiple linear regression analysis and multigene genetic programming methods were used to obtain these formulations. According to the error statistics, the multigene genetic programming method gave more accurate results than the multiple linear regression analysis methods in buckling load estimation. The estimates obtained from the multigene genetic programming method and the numerical results calculated in the ANSYS program were found to be compatible with each other. The scientific novelty brought by the research is to develop more original formulations for cantilever beams instead of using the buckling load calculation described for simply supported beams in the specifications. The scientific difference is that the developed formulations can calculate in a way that can consider the contribution of transverse stiffeners to the buckling load. This study will show that formulations designed with computer technologies can be an alternative calculation method for estimating the lateral buckling load according to the transverse stiffener plate spacing for European I-section cantilever steel beams. [ABSTRACT FROM AUTHOR]

Buckling is the most common type of failure associated with circular cylindrical shells (CCSs) subjected to axial compressive forces. This is mainly due to large radius-to-thickness (R/t) ratio of such shells, making them very thin structures. The buckling stress of these kinds of shells highly depends on the geometric imperfections which are practically hard to be avoided throughout the service life of the structure. The presence of a localized damage (dent) is found to reduce the buckling strength considerably. In this study, the effect of dent imperfection on the buckling strength of CCSs having large R/t ratios is numerically investigated. The R/t values are selected to be large enough to ensure elastic buckling for the entire parts of the shell except near the dent where it is hard to be avoided due to the stress concentration. A finite element (FE) simulation is used to study the effect of the different dent parameters: size, depth, and position on the buckling strength. The obtained results indicate that for the case of shells with large R/t ratios, the amount of reduction in buckling strength due to dent ranges from 13 to 53% without a remarkable trend for its relationship with the size, depth, position of the dent; and R/t. [ABSTRACT FROM AUTHOR]

In this study, the post-buckling behavior of a transverse functionally graded beam is investigated. Euler–Bernoulli beam theory (EBT) and shear deformable beam theories are taken into account in deriving the mathematical models of the beam using the vector approach. Timoshenko theory (TBT) and six different higher order beam theories (HOBT), namely Reddy, Touratier, Soldatos, Karma, Akavcı and Violet, are considered as shear deformable beam theories. It has been shown that mathematical models of shear deformable beam theories can be obtained using the vector approach. There are two different models developed for shear deformable beam theories depending on normal and shear forces and moment. It is found that the model which is named as Model 2 in this study yield inappropriate results. The functionally graded materials are characterized by using power law functions. The non-dimensional integro-non-linear differential equations system is solved analytically. The critical load values calculated for EBT, TBT and HOBT theories depending on different material conditions and slenderness ratio values are presented in tables. In addition, pitchfork bifurcation diagrams are drawn showing the post-buckling behavior of the beam. In addition, the regions where the examined beam theories are valid depending on the slenderness coefficient are shown. [ABSTRACT FROM AUTHOR]

Seismic structural fuses such as buckling restrained braces (BRBs) are highly nonlinear members that need a detailed finite element model (FEM) to represent their actual behavior. On the other hand, making detailed model for the whole building from solid or shell elements to be consistent with the model of BRBs would require expensive computational time and large storage space especially when performing nonlinear time history analysis (NTHA). Therefore, a mixed FEM is developed in this research so that the solid elements are used for the core plate and the restraining system only. The non-yielding segments of the BRBs and the conjoined girders and columns are simulated using beam elements with nonlinear material properties while the effect of large deformations is taken during analysis and this was able to represent plastic hinge formation, plastic rotations and residual displacements in such members. A beam-solid transfer mechanism is developed to properly transfer forces between the non-yielding segments of BRB and the inner solid plate. The core plate is connected to the surrounding restraining system with contact elements to simulate the normal and frictional forces generated upon contact based on the penalty algorithm. This model was validated using the data and the results of an experimental work mentioned in the literature where very good agreement was achieved. Thereafter, a rehabilitation study for the SAC 9-storey building was performed. The results showed how the BRBs work as structural fuses during earthquakes and confirmed the ability of the model to represent inelastic behavior of multi-story BRBFs. [ABSTRACT FROM AUTHOR]

A novel analytical approach for predicting the buckling load with its mode shape of friction piles fully embedded in soil is proposed, in which the lateral subgrade and axial friction resistances change linearly. The proposed approach considers uniform rectangular piles that are either free or pinned or fixed at the pile and toe. The differential equation that governs the mode shape of the buckling pile along with the boundary conditions was analytically derived and numerically solved using the Runge–Kutta method and the Regula-Falsi method. The buckling loads of this study agreed well with those reported in the literature. The buckling behavior of piles was discussed as factors affecting the end condition, aspect ratio, subgrade ratio, friction ratio, subgrade parameter and friction parameter. [ABSTRACT FROM AUTHOR]

Buckling is a critical phenomenon in structural members under compression, which could cause catastrophic failure of a structure. To increase the buckling resistance in structural design, a novel topology optimization approach based on the bi-directional evolutionary structural optimization (BESO) method is proposed in this study with the consideration of buckling constraints. The BESO method benefits from using only two discrete statuses (solid and void) for design variables, thereby alleviating numerical issues associated with pseudo buckling modes. The Kreisselmeier-Steinhauser aggregation function is introduced to aggregate multiple buckling constraints into a differentiable one. An augmented Lagrangian multiplier is developed to integrate buckling constraints into the objective function to ensure computational stability. Besides, a modified design variable update scheme is proposed to control the evolutionary rate after the target volume fraction is reached. Four topology optimization design examples are investigated to demonstrate the effectiveness of the buckling-constrained BESO method. The numerical results show that the developed optimization algorithm with buckling constraints can significantly improve structural stability with a slight increase in compliance. [ABSTRACT FROM AUTHOR]

The nonlinear dynamics of composite plates with thermomechanical coupling is analytically addressed in order to describe the main bifurcation phenomena triggering the involved pre- and post-buckling response scenario. The static buckling occurrence and two resonance conditions around the unbuckled and buckled equilibria are investigated by means of the asymptotic multiple scale method, together with the double-zero bifurcation marking the occurrence of dynamical buckling. The resulting modulation equations and the steady-state mechanical and thermal responses are determined and compared with the numerical outcomes in order to verify the adequacy and effectiveness of the refined scalings adopted in the multiple scale analyses to describe the various bifurcation scenarios. [ABSTRACT FROM AUTHOR]

A laboratory experimental program has been conducted to investigate three hinge buckling failure (THB) using a newly developed THB testing apparatus and methodology. The novel apparatus differs from buckling experimental programs used in the past in that it allows for direct control of axial load throughout the test similar to a horizontal in situ stress. The objective of the study was to gain quantifiable insight into the THB failure mechanism under a range of controlled axial stress conditions to inform future development of stability analysis methods. Specimens (two block) of the relatively homogeneous Wallace sandstone formation were selected and a total of seven tests were conducted to parametrically explore a range a specimen thickness (3.2 to 5 cm) and two levels of axial 'clamping' stress (10 and 15 MPa). In addition to load and displacement monitoring, high-speed camera images and acoustic emission (AE) data was collected during each test. The tests revealed relatively consistent characteristic behaviour with identifiable thresholds of yield, peak and failure (collapse). A brittle-ductile response transition was observed based on the tested parameters, although not clearly identified from the limited testing. A clear relation was developed for specimen thickness and axial stress. A calibrated distinct element modelling simulation of the experiment was conducted that showed a reasonable match to the characteristic experimental behaviour. This provided greater insight into the THB failure mechanism and showed that this method of simulation is suitable for this mode of failure. Highlights: Three Hinge Buckling of laminated rock was investigated experimentally using a novel testing apparatus. A parametric testing program was conducted to explore the effect of specimen thickness on buckling under different axial 'clamping' loads. The experimental tests were supported by high-speed video image capture and acoustic emission hit count monitoring. The tests revealed several characteristics regions of the lateral load – lateral displacement response. Micro-mechanical distinct element modelling using UDEC Voronoi tessellated simulation provided further insight into the experimental results. [ABSTRACT FROM AUTHOR]