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Mechanical metamaterials are valued for their diverse properties and potential applications. Due to the instability and large deformability of soft mechanical metamaterials (SMMs), geometric reorganization will occur and lead to some unusual properties. It is possible to change the properties of materials by varying the parameters. Conventional SMMs contain a periodic distribution of holes with the same size and shape, which can be changed to a lesser extent. Periodic dispersion of regular through-hole patterns of various sizes or shapes into elastomers, resulting in metamaterials with more mechanical functionality and deformation scenarios. In this paper, we investigated the influence of parameters on the buckling mechanical behavior of SMMs and the buckling mechanical behavior of structures with multiple sizes and geometric shapes. The parameters studied include geometric parameters (pore shape, porosity and area ratio) and physical parameters (Poisson's ratio and compression mode). Simulation of the buckling behavior of SMMs uses the finite element method. The finite element software ABAQUS is used, taking into account the almost incompressible characteristics of materials, the triangular quadratic plane strain hybrid element is selected (CPE6H). Numerical calculation gives the following results: Area ratio, pore shape and compression mode have obvious effects on buckling behavior, but Poisson's ratio has little effect; the influence of parameters on the buckling critical strains varied for SMMs with various pore shapes; very different buckling behaviors will result from swapping out the pattern of holes with the same size or shape for holes with two different sizes or shapes; the expression of buckling behavior is also varied when the mix of hole shapes is modified. These findings demonstrate that the design parameters may be used to achieve the desired buckling behaviors. This is a new method that can be used to control the deformation of structures; modify the properties of the SMMs without changing stiffness; simplify the structures without significantly changing the material properties. The design path of mechanical metamaterials is increased. [ABSTRACT FROM AUTHOR]

In the process of horizontal well construction, the working environment in the well is very complicated. It is difficult to determine the actual deformation and force of the coiled tubing in the wellbore from the load change at the wellhead along. In addition, the coiled tubing wrapped around the reel and entering the wellbore through the injection head may cause an initial residual bending. In this paper, the mathematical model of the coiled tubing under axial load during buckling deformation is established, and the analytical solution with the time term is derived by reasonable simplification of the model. The effect of residual bending on the post-sinusoidal buckling of the coiled tubing in the horizontal well was investigated using the separation variable method. The effect of residual bending variations on the well wall contact forces is analyzed. The research shows that the initial parameter Г is the main factor influencing the post-sinusoidal buckling of the coiled tubing with residual bending. The larger the parameter value Г, the greater the effect of the residual bending on the post-sinusoidal buckling deformation of the coiled tubing, and the earlier the critical point of the mixed sinusoidal-helical buckling of the coiled tubing appears. The compression velocity of the coiled tubing has a significant effect on the well wall contact force. The faster the compression, the greater the contact force. By introducing the time term and the separation variable, this paper provides a new method and theoretical basis for further study of the process of entering sinusoidal-helical buckling of the coiled tubing with initial residual bending. [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]

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]

This paper presents a theory for the buckling of short beams considering cross-sectional distortions due to transverse shear (i.e., shear warping), based on the consistent linearization of a geometrically nonlinear planar beam. The proposed deformation field considers the warping amplitude as an independent kinematic field, and the hyperelastic material assumes that the stresses normal and tangent to the deformed cross section are linear with respect to their work-conjugate finite strains. An approximate closed-form solution to the resulting quartic equation for the critical load is provided to facilitate practical implementation. Theoretical differences giving rise to distinct buckling theories for higher-order shear beams are discussed in terms of (1) the assumed deformation field, (2) variational consistency, and (3) material constitutive relation. The proposed formulation is applied to evaluate the stability of infinite strip unbonded fiber-reinforced elastomeric isolators (FREIs) with moderate-to-high shape factor, for which shear warping is expected to have a major influence due to the flexural flexibility of the fiber reinforcement. A homogenization procedure is described to obtain effective isolator rigidities considering rubber compressibility and fiber extensibility. Next, a finite element parametric study of the buckling of unbonded infinite strip FREIs is presented, and the results are used as a benchmark to evaluate the adequacy of the proposed and existing formulations. The theory presented herein and its approximate solution exhibit the best match with the numerical results, and the latter is deemed adequate for practical application. [ABSTRACT FROM AUTHOR]

The moving deformation of the strata and the redistribution of stope stress after mining show asymmetrical characteristics, which do not conform to the symmetrical structural characteristics of the original rock beam fracture. To further analyze the deformation of rock beams and the asymmetry law of stope pressure distribution after strata caving, the detailed process of instability and deformation of composite rock beams before failure was revealed through similar material simulation, theoretical analysis, and numerical simulation. Through similar simulation experiments, the structural characteristics of strata caving were observed. After excavation, the caving angle near the open-off cut side of the model is greater than that on the stop-mining line side. The maximum bending moment of the rock beam is located at the open-off cut side. The rock beam fracture is located on the partial open-off cut side in the middle of the rock beam. The rock beam on the open-off cut side is easy to shear slip and not easy to hinge. The rock beam in front of the advancing direction of the working face is easily hinged. Based on the structural characteristics of strata caving, considering the thickness of the composite rock beam, the two-hinged arch mechanical model for rock beam fracture is established. On this basis, the key parameters of rock beam instability and fracture such as limit load, additional horizontal stress, limit break distance, and break position are analyzed. Based on the deformation characteristics of two hinged arches, the caving structure and the asymmetric distribution mechanism of stress redistribution during the deformation of overburden in stope are explained. Finally, the deformation of rock beam and the asymmetry of stress distribution in stope are verified by numerical calculation. The results show that the concentrated stress value of the coal pillar at the open-off cut side is greater than that in front of the working face. There is a pressure relief area behind the working face, and the pressure relief area has a certain range. The range of stress concentration area, pressure relief area, and stress value tend to be stable, and only the range of the original rock stress zone expands when the working face is advanced to a certain distance. The asymmetric distribution of compaction stress in goaf is related to the buckling deformation of strata. [ABSTRACT FROM AUTHOR]

Buckling phenomenon is a common failure mode for composite materials under the effect of compressive loading which is mainly investigated in two stages as pre – buckling and post – buckling. At the pre – buckling phase, the deformations take place temporarily in elastic range. However, load carrying capacity of a member can be increased by regarding the post – buckling process. Therefore, it is important to determine the final and maximum load carrying ability of the structure. Since, at the end of the post – buckling, the body cannot carry load and crippling failure takes place. In this review article, crippling behavior of the composite structures is investigated. After describing the crippling phenomenon, this study mainly investigates both experimental and theoretical points of views. In this scope, affecting parameters such as stacking sequence, geometrical properties and boundary conditions are determined. Then, the improved theoretical approaches are stated. The compatibilities of the test results are assessed with theoretical studies. [ABSTRACT FROM AUTHOR]

The compression load of straight bars, for which the cross-sections are smaller compared to their length, causes a phenomenon of bending along the longitudinal axis. Upon reaching a certain level, called the critical level of the stresses, the bending deformations begin to increase beyond the bearing limit of the bar. It yields instantly, due to an unstable elastic deformation state, although the material's resistance limit has not been exceeded. The irreversibility of the phenomenon is dangerous especially for the railway tracks and is not fully mastered by calculation methods. They can eventually establish the level of the critical demand, which has values specific to each rail configuration. It is accepted that for loads lower than this level, buckling of the respective rail does not occur. The longitudinal tension in the railway tracks occurs due to the expansion caused by their heating under the action of the sun's rays, but also due to the friction between the rails and the train wheels. This paper proposes the realization of a study model of the buckling of the railway tracks. This model is represented by an assembly, built in the SOLIDWORKS application for which a Buckling simulation was made. The imposition of two distinct temperatures on the rails and crossties is the source of the model's request. The increase in the temperature of the component parts of the assembly causes their expansion, so implicitly the appearance of some longitudinal deforming forces, specific to the buckling phenomenon. [ABSTRACT FROM AUTHOR]

The prebuckling deformation of structures is neglected in most of the conventional buckling theory (CBT) and numerical method (CNM), because it is usually very small in conventional concepts. In the preceding paper (Su et al., 2019), we found a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation became large and essential for determining the critical buckling load, and developed a systematic buckling theory for 3D beams considering the effects of finite prebuckling deformation (FPD). For bulk structures that appear vastly in the advanced structures, a few buckling theories consider the effects of the prebuckling deformation in constitutive equations by energy method, which are significantly important but not straightforward and universal enough. In this paper, a systematic and straightforward theory for the FPD buckling of bulk structures is developed with the use of two constitutive models. The variables for the prebuckling deformation serve as the coefficients of the incremental displacements, deformation components, and stress in the buckling analysis. Four methods, including the CBT, CNM, DLU (disturbing-loading-unloading method) method and FPD buckling theory, are applied to the classic problems, including buckling of an elastic semi-plane solid and buckling of an elastic rectangular solid, respectively. Compared with the accurate buckling load from the DLU method, the FPD buckling theory is able to give a good prediction, while the CBT and CNM may yield unacceptable results (with 70% error for the buckling of an elastic semi-plane solid). [ABSTRACT FROM AUTHOR]

Reduced beam section (RBS) connections are ductile connections that have been widely used in steel structures. Because of the reduction of web resistance, local buckling usually occurs under large deformations and is associated with decreased strength. In addition, the complex deformation of beams prevents determining the residual strength, hence posing a challenge in postearthquake repairs. In this study, a buckling-restrained system (BRS) including steel channels and a mortar was proposed for deformed RBS regions to provide lateral support on buckled plates so as to recover the connection strength. Two full-scale RBS connections with various cutting ratios were first tested, and then the connection was repaired with BRS loaded again. The test results indicated that the repaired connections were loaded at a drift angle of up to 4% without fracture or strength deterioration. The negative strength increased by approximately 18%, and the maximum strength was similar to that of the original connection, indicating that the column-to-beam flexural strength ratio of the connection did not change. The strain at the heat-affected area also did not increase and rather decreased because of the additional support of the restraint. The dissipated energy capacities of the repaired specimens were approximately 92% and 87% of the values of the original specimens. These results confirmed that BRS provided sufficient lateral resistance and helped recover the connection performance. • This paper proposed a new postearthquake repair method for recovering the performance of the locally buckled reduced beam section connections. • Two full-scale connection specimens with different cutting ratios were prepared and tested. • The results indicated that the method notably enhanced the strength of the locally buckled connection, and the maximum strength was similar to that of the original connection, indicating that the column-to-beam flexural strength ratio of the connection did not change. • The strain at the heat-affected area also did not increase, and the dissipated energy capacities of the repaired specimens were closed to the values of the original connections. • The repair method does not require field cutting, welding works, and temporally support structures. [ABSTRACT FROM AUTHOR]

Induction heating has many engineering applications. To accurately describe the induction heating process of thin steel sheets one needs to account for their mechanical deformation. This might strongly affect the magnetic configuration since thin sheets are prone to thermal buckling, leading to large supercritical deformations. We suggest a modelling strategy combining a computationally highly efficient structural mechanical shell description for the thin sheet with a standard continuum model for eddy current and thermal problems through an iterative coupling algorithm. All benchmark problems are solved numerically using the finite element method. [ABSTRACT FROM AUTHOR]

Buckling tests were conducted using slender specimens of western hemlock. In the tests, the slenderness ratio was varied from 132 to 418 in which elastic buckling was induced, and the values of the critical load for buckling were obtained. When the deflection of the specimen was calculated from the loading-line displacement based on elastica theory, the value of deflection/load initially decreased because the compressive deformation was more dominant than the bending deformation. In contrast, when the load increased, the bending deformation became dominant, and the deflection/load-deflection relation exhibited linearity. These tendencies indicated that the transition from compression to bending was induced around the minimum value of the deflection/load. Therefore, it was recommended to determine the critical load for buckling using the load at the minimum value of the deflection/load where the deflection was calculated from the loading-line displacement. [ABSTRACT FROM AUTHOR]

The out-of-plane buckling behavior of arches is closely related to the element torsional behavior. The traditional 12-degree-of-freedom second-order element stiffness matrix which uses a simplified element torsional stiffness GJ/ L (where G is the shear modulus, J the St. Venant torsion constant, L the element length) may significantly underestimate the out-of-plane buckling loads of funicular arches. This paper presents a simple and effective exact matrix stiffness method (MSM) for the out-of-plane buckling analysis of funicular arches. The developed MSM uses a 14-degree-of-freedom second-order element stiffness matrix of three-dimensional beam-columns considering both torsion and warping deformations. The out-of-plane buckling analysis of funicular arches is performed by using the global structural stability stiffness matrix, which combines the transformed second-order element stiffness matrices. The proposed MSM with the exact 14-degree-of-freedom second-order element stiffness matrix for the out-of-plane buckling analysis is verified by comparing with some classical solutions of funicular circular and parabolic arches with box sections and I-sections. Further discussions show that the 14-degree-of-freedom second-order element stiffness matrix may be reduced to a simplified 12-degree-of-freedom form only by deriving the exact element torsional stiffnesses, which could be significantly larger than GJ/ L for members with large cross-sectional torsional stiffness parameters (especially open cross-sections). [ABSTRACT FROM AUTHOR]

This study investigates a complex slope failure that occurred in Chongqing Xi railway station. The studied slope belongs to a under-dip shale slope. Onsite surveys and UDEC numerical modelling were conducted to describe the deformation characteristics and potential failure mechanism of this slope. The simulated results suggest that sliding, buckling and toppling can occur in the deformation process, which is verified by the actual deformation characteristic of the slope and monitoring results. Moreover, the effects of bedding dip angle, slope angle, bed thickness on the deformation characteristics of the slope were also investigated with UDEC models. Finally, the possible slope structure for occurrence of slide-buckling-toppling failure and several numerically validated remedial measures were proposed. [ABSTRACT FROM AUTHOR]

Abstract A Ritz approach for the analysis of buckling and post-buckling of plates with through-the-thickness cracks is presented. The plate behavior is described by the first order shear deformation theory and von Karman's geometric nonlinearity. The admissible functions used in the displacements approximation are series of regular orthogonal polynomial supplemented with special functions able to decribe the dicontinuity across the crack and the singularity at the crack tips; boundary functions are used to fullfill the homogeneous essential boundary conditions. Convergence studies and analysis results are presented for buckling and post-buckling of plates with a central through-the-thickness crack evidencing differences in the structural response between pre- and post-buckling regimes, which can substantially affect the plate residual strength. The performed analyses show the efficiency and potential of the method, which provides accurate results in conjunction with a reduced number of degrees of freedom and simplified data preparation. [ABSTRACT FROM AUTHOR]

Highlights • In situ study on the buckling and post-buckling of Cu–Zr amorphous films. • A unique buckling and post-buckling behavior is observed. • A buckling map has been developed, including four buckling modes. • Formation of buckling modes are related to the size-dependent deformation. Abstract The buckling and post-buckling behavior of the Cu–Zr amorphous films is highly dependent on film thickness (h) and applied strain (ε). A buckling map has been developed with h and ε as axes, where four buckling modes are detected, including uncracked triangular buckle, cracked rectangular buckle, cracked triangular buckle, and patches. Formation of the four buckling modes will be discussed in terms of the film thickness and size-dependent deformation. [ABSTRACT FROM AUTHOR]

Highlights • A finite element is developed for beam-column distortional lateral torsional buckling. • Effects captured are pre-buckling deformation, global/local warping, and load height. • Investigated are second-order moments effects due axial forces on lateral buckling. • Assessed is the beneficial effect of transverse stiffeners on beam buckling strength. Abstract The present study develops a unified distortional lateral torsional buckling finite element formulation for the elastic analysis of beam-columns with wide flange doubly symmetric cross-sections. The solution captures several non-conventional features including the softening effect due to web distortion, the stiffening effect induced by pre-buckling deformations, the pre-buckling nonlinear interaction between strong-axis moments and axial forces, the contribution of pre-buckling shear deformation effects, the destabilizing effects due to loads being offset from the shear centre, and the presence of transverse stiffeners on web distortion. In the present theory, it is possible to evoke/suppress any combination of features and thus isolate the individual contribution of each effect or quantify the combined contributions of multiple effects. The effects of beam span-to-depth, flange width-to-thickness, web height-to-thickness, and flange width-to-web height ratios on the critical moments are investigated. Comparisons with conventional lateral torsional buckling solutions that omit distortional and pre-buckling effects quantify the influence of distortional and/or pre-buckling deformation effects. The theory is also used to investigate the influence of P-delta effects of beam-columns subjected to transverse and axial forces on their lateral torsional buckling. The solution is adopted to quantify the beneficial effects of transverse stiffeners in controlling/suppressing web distortion in beams. [ABSTRACT FROM AUTHOR]

Amorphous carbon probably is the most-known and widely used carbon allotrope. However, unlike crystalline carbon such as graphene or carbon nanotubes, amorphous carbon generally is brittle and unable to sustain large mechanical deformation due to the inherent lack of long-rang order. In this work, we demonstrate a significant delay of failure on an amorphous carbon hollow nanosphere due to the buckling and post-buckling deformation of the spherical shell. Both in situ experiments and finite element analyses are conducted to probe deformation mechanism of buckling and post-buckling, suggesting a strong dependence of the shell thickness on the buckling process. A unified deformation energy-based mechanics model is developed to extract the critical buckling and post-buckling force, and shows good agreement with in situ experiments and finite element analyses. Extension of the model to inhomogeneous hollow nanospheres is also discussed and confirmed with finite element analyses. [ABSTRACT FROM AUTHOR]

Tubular steel structures with slender compression cross-sections are prone to local buckling. In this paper the axial compression is investigation of the innovative fabricated structural steel column consisting of sinusoidal corrugated pattern. When it comes to the design of compressive individuals, buckling is a crucial layout provision. The paper describes the effect of variation in the sectional properties like mean diameter, thickness, amplitude, and frequency of corrugation on the buckling axial load. A quadratic model was developed to correlate the independent variables for maximum buckling load by using central composite design (CCD) method. Subsequently ANOVA, a statistical tool is used to analyse and compare the different combinations and finding the most influential factor on buckling load. Response surface methodology is adopted to review the interaction models between the different combinations. [ABSTRACT FROM AUTHOR]

Abstract The prebuckling deformation of structures is usually very small in conventional concepts, and is always neglected in the conventional buckling theory (CBT) and numerical method (CNM). In this paper, we find a class of structures from the emerging field of stretchable electronics, of which the prebuckling deformation becomes large and essential for determining the critical buckling load. Although great progress has been made for the buckling theory in the past hundred years, it is still challenging to analyze the buckling problems with finite prebuckling deformation (FPD buckling) straightforwardly. Here, the experimental stretch of a series of serpentine interconnects was firstly conducted as a representative example to show the FPD buckling behaviors and inapplicability of the CBT and CNM. The CNM can yield a huge error of 50% on the critical buckling load for the case with thickness-to-width ratio of the cross section h / b = 0.6. Most importantly, a systematic and straightforward theory (FPD buckling theory) is developed to analyze the FPD buckling behaviors of beams with the coupling of bending, twist and stretch/compression. As a comparison, various theoretical and numerical methods are applied to three classic problems, including lateral buckling of a three-point-bending beam, lateral buckling of a pure bending beam and Euler buckling. Our FPD buckling theory for beams is able to give a good prediction, while the CBT (by Timoshenko et al.) and CNM (by commercial program packages) yield unacceptable results (with 70% error for a three-point-bending beam with h / b = 0.8, for example). Discussion on the FPD buckling of bulk structures is deferred to a following paper. [ABSTRACT FROM AUTHOR]

Highlights • The Perforated Core Buckling Restrained Brace, an all-steel BRB, is investigated. • Two new expressions are proposed to predict the core buckling wavelength. • A new expression is proposed to distribute the stabilizing bridges along the core. • Two low-cycle fatigue models are proposed to predict the failure of the PCBRB. Abstract The Perforated Core Buckling-Restrained Brace (PCBRB) is an all-steel BRB whose core has been split into two lateral bands connected by stabilizing bridges. The core, with a constant cross-section perimeter, can slide along the restrainer so that it can be inspected or replaced by simply removing a centering pin. We analyzed the behavior of two different Perforated Core (PC) geometries which we tested to failure with different load protocols of several maximum deformation amplitudes. The main difference between both geometries was the radius of the lateral band connections. The experimental results show how a low radius, despite offering a higher constant cross-section yielding length, leads to a lower dissipation capacity and to a closer distance between stabilizing bridges. The results also show a gradual drift of the internal and the external lateral band segments into permanent negative and positive elongations, respectively, which increases the minimum gap required between the core and the restrainer. We also analyzed the in-plane and the out-of-plane wavelength of the high-mode buckling of the PC and validated two wavelength prediction equations that would prevent the uncontrolled second-order deformations and the buckling failure of the PC. Finally, based on experimental data, we propose two low-cycle fatigue relationships for the PCBRB that would be valid for elastoplastic devices with uniform uniaxial strain distribution, such as BRBs and TADAS devices. [ABSTRACT FROM AUTHOR]

The buckling capacity of uniformly compressed flat plates has been investigated in this study. Material properties were characterized based on parameterization of the stress-strain curves using a simple and novel mathematical expression. Idealized stress-strain relationships were developed using the proposed material model and extensive parametric numerical analyses were conducted to investigate the effect of the material stress-strain properties on the buckling capacity of flat plates. For stress-strain curves with a yield plateau, the results of the parametric study showed a minimal influence of the material properties on the buckling capacity of the plates whereas a significant effect of the strain-hardening properties was observed in plates with round-house curves. Ultimately, the proposed stress-strain model was shown to be remarkably useful for capturing the relevant intricacies associated with material nonlinearity when predicting the buckling capacity and post-buckling behavior of uniformly-compressed flat plates. [ABSTRACT FROM AUTHOR]

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobeam. The twoparameter elastic foundation model including linear Winkler's springs along with Pasternak's shear layer is in contact with the beam in deformation. Material properties of FG nanobeam are supposed to vary gradually along the thickness according to both power-law and Mori-Tanaka laws. Small-scale effect of Eringen's nonlocal elasticity theory has been considered. Nonlocal equilibrium equations are obtained based on the minimum potential energy principle and solved analytically. The accuracy of current method is examined by comparing current results with the available ones in literature. Effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio on buckling behavior of FG nanobeams are examined. [ABSTRACT FROM AUTHOR]

An attempt is made in the current research to obtain the fundamental buckling torque and the associated buckled shape of an annular plate. The plate is subjected to a torque on its outer edge. An isotropic homogeneous plate is considered. The governing equations of the plate in polar coordinates are established with the aid of the Mindlin plate theory. Deformations and stresses of the plate prior to buckling are determined using the axisymmetric flatness conditions. Small perturbations are then applied to construct the linearised stability equations which govern the onset of buckling. To solve the highly coupled equations in terms of displacements and rotations, periodic auxiliary functions and the generalised differential quadrature method are applied. The coupled linear algebraic equations are a set of homogeneous equations dealing with the buckling state of the plate subjected to a unique torque. Benchmark results are given in tabular presentations for combinations of free, simply-supported, and clamped types of boundary conditions. It is shown that the critical buckling torque and its associated shape highly depend upon the combination of boundary conditions, radius ratio, and the thickness ratio. [ABSTRACT FROM AUTHOR]

Abstract A finite strip method was developed for buckling and free vibration analysis of piezoelectric laminated composite plates based on various plate theories such as Zigzag, Refined plate and other higher order shear deformation theory by variation of transverse shear strains through plate thickness in the form of parabolic, sine and exponential. The plate edge conditions are considered to be simply supported and the polynomial shape functions are used to evaluate the in–plane and out–of–plane deflection and rotation of the normal cross section of plates in transverse direction. Numerical results were obtained based on various shear deformation plate theories to verify the proposed method. The effects of length to thickness ratio and fiber orientation of cross–ply and angle–ply laminate were presented. Also, the effect of different electrical conditions on the critical buckling load under in–plane forces and strains is investigated and electrical buckling load and natural frequency of piezoelectric laminate composite plates are calculated through numerical examples. In addition, the new results on the effect of piezoelectric layers thickness, placement of piezoelectric layers and also the effect of length to thickness ratio in the interaction of biaxial in–plane loading on critical buckling load were studied. Highlights • The buckling load of CC electrical conditions, unlike of OC, is close to elastic solutions. • The rate of decreasing in buckling load of OC is higher than CC with locating piezoelectric layers close to mid-surface. • In anti-sym angle-ply with locating the piezoelectric layers closer to the mid-surface the buckling load would increase. • The natural frequency would be increased or decreased with locating pzt in mid-surface for different thickness of plate. • The linear behavior is obtained for all electric boundary conditions and length to thickness ratio for biaxial loading. [ABSTRACT FROM AUTHOR]

The non-linear hygrothermal and mechanical buckling responses of FG sandwich plates resting on two-parameter elastic foundations are presented in this study. Non-linear Fourier temperature distribution is considered as a special case. A hyperbolic displacement model is proposed in the present investigation. The present model involves four unknown variables, and the shear stresses on the bottom and top of the plate surfaces are equal to zero. The effective material properties of the FG sandwich face sheets are presumed to be varied in the direction of the thickness using a simple power law distribution, while the core is supposed to be purely ceramic. The stability equations are deduced by the principle of virtual work, containing the effect of foundations interaction and hygrothermal effects based on the present model. The hygrothermal effects are considered as non-linear, linear and uniform distribution through the plate thickness. Comparison examples are presented to verify the accuracy of the present model. The effects played by the temperature rise, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio of the plate, the inhomogeneity parameter on the critical buckling of FG sandwich plates are investigated. [ABSTRACT FROM AUTHOR]

The compressive deformation is mainly contributed by axial compressive deformation and high-order in-plane and out-of-plane global buckling deformation for conventional buckling-restrained braces (BRBs). A novel type of all-steel BRBs with perforated core plates, termed as perforated BRBs (PBRBs), are proposed in this study, where shear deformation can occur in addition to the aforementioned deformations in a conventional BRB under compression. Experimental study was carried out using five specimens with different configurations of holes under cyclic loading. Stable hysteretic properties, high ductility, and energy dissipation capacity were obtained for the PBRBs. The effects of two parameters, i.e. the slenderness ratio of the chord and hole spacing factor defined as the ratio of the hole length to the hole spacing, on seismic performance of the specimens were investigated. The compressive deformation mechanisms of the PBRBs were further investigated through a numerical study. The compressive deformation was found to be composed of axial compressive deformation, flexural deformation owing to in-plane and out-of-plane global buckling, and in-plane shear deformation of the latticed core plate. [ABSTRACT FROM AUTHOR]

Highlights • This work deals with non-conventional energy-dissipating system of biaxial plastic buckling. • The goal is to enhances the energy dissipating capacity of thin-walled square aluminum tubes. • Several the well-developed ACTP device was employed. • The greater the interaction between the loading complexity and the strain rate, and the greater the energy absorbed by the tubes. • The total energy absorbed is increased by more than 100% for of the most complicated loading path (i.e., Biaxial-60°). Abstract Motivated by the biaxial plastic dynamic buckling behavior of tubular structures, the particular interest of this work was to develop a non-conventional energy-dissipating system. This system is based on the studying of the experimental behavior of square metallic tubular structures under dynamic complex loading paths. This non-conventional solution aims to enhance the strength properties of the used structures. Accordingly, the well-developed device (the ACTP: Absorption par Compression-Torsion Plastique) has been employed where biaxial loading paths (combined compression-torsion) with different complexities were generated from a uniaxial compressive load. Thus, five inclination angles (30°, 37°, 45°, 53° and 60°) were used to study their effect on the biaxial plastic buckling of square aluminum tubes. This new comprehensive experimental study aimed to investigate the effect of three loading boundary conditions (i.e., simple, intermediate and severe) on the tubes' behavior. The dynamic deformation, mean collapse load (P m) and energy absorbed are key parameters that require investigation. They are largely affected by the loading path complexity, applied strain rate and their interaction. The results showed that the higher the biaxial loading complexity provided by the ACTP, the greater the interaction between the loading complexity and the strain rate, and the greater the energy absorbed by the structures. Changes in local deformation mechanisms induced by the loading complexity thus lead to the energy absorbed enhancement. The latter was higher than 100%, in favor of the most complicated loading path (i.e., Biaxial-60°) compared to the classical uniaxial case for an axial deflection of 20 mm. Simple mathematical equations were proposed predicting the P m of buckled tubes. These equations can describe the tubes' behavior fairly well. [ABSTRACT FROM AUTHOR]

Highlights • A coupled mechanochemical model is proposed for buckling simulation. • The buckling behavior is strongly dependent on SOC & electrochemical process. • Lithiation-soften of active material remarkably reduces the buckling stability of cell system. • Design insights into enhancing the buckling resistance of electrode are provided. Abstract This work has proposed a coupled mechanochemical model to investigate the buckling performance of electrode and thereby enhance the mechanical integrity of lithium-ion batteries. This method based upon finite deformation theory is capable to simulate the state of charge (SOC) and path dependent buckling phenomenon of the layered structure. It is revealed that the buckling behavior of an electrochemical loaded electrode depends not only on the material properties and the electrode geometry but also on the charging/discharging process, SOC as well as the operation current rate. Moreover, with regarding to the lithiation stiffening active material, the results show that increasing the current density in lithiation while decreasing it upon delithiation can increase the relatively critical buckling load, and contribute the electrode to withstand buckling failure. As for the lithiation softening one, it is disclosed that the bucking resistance would be impaired in lithiation and recovered upon full delithiation. In addition, to eliminate the adverse effect of lithiation soften on the electrode buckling resistance, design insights into the current collector have been provided. [ABSTRACT FROM AUTHOR]

An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Kármán’s theory to account for geometric non-linearities; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results from finite elements simulations, confirming the accuracy and potential of the formulation. [ABSTRACT FROM AUTHOR]

Cold Formed Steel (CFS) sections are widely used in construction of residential and industrial buildings owing to higher strength to weight ratio. The failure modes generally observed in CFS sections are local, distortional, or lateraltorsional buckling. Though ample works have been reported in the literature, experimental work on distortional buckling is limited. In view of this, an experimental investigation on CFS lipped Channel (C) section under four-point loading has been carried out to assess the distortional buckling behaviour under monotonic loading. Seven specimens were identified based on a parametric study carried out using CUFSM so that the specimens fail due to distortional buckling/local buckling. The flexural capacities of the C-sections were predicted using various codes and compared with the respective experimental results. Also, the experimental results are compared with the modified direct strength method proposed in the literature and it is found that the predicated strengths are in close agreement with experimental ultimate loads. [ABSTRACT FROM AUTHOR]

To reveal the atomistic scale mechanism of buckling of single-walled carbon nanotubes (SWCNTs) under axial compression, we carried out molecular dynamics (MD) simulation and atomistic structural instability (ASI) analysis. The ASI analysis enables us to reveal the development of ‘latent’ instability modes until buckling of structure, which cannot be clarified with MD alone. Euler-type buckling was found in relatively thin and long nanotube models, while buckling triggered by change of cross-sectional shape (i.e., radial buckling) was found in thick and short models. With growing radius, a crossover between the Euler-type and radial buckling modes was clearly found in the ASI analysis. Even when the deformation behavior was apparently the same, the buckling can be triggered by different instability modes. We also analyzed the structural instability using the Flügge theory based on linear continuum mechanics (LCM) to compare the results with the ASI analysis. Initial eigenvalues and development of instability modes were different between the ASI and LCM results, leading to a significant deviation of buckling strain and instability crossover points. We investigated the effect of chirality of CNT which is difficult to explain by LCM. [ABSTRACT FROM AUTHOR]

Studies on buckling of steel tubular truss arches are lacking in contrast to steel arches with solid web sections, although they have been widely applied in long-span structures. This paper deals with the in-plane elasto-plastic buckling and strength design of circular steel tubular truss arches with triangular sections by using finite element analyses (FEA). Firstly, the in-plane buckling failure modes are explored to reveal the buckling mechanics of truss arches. By introducing the normalized slenderness of the entire arch and the chord tube, as well as the interactive coefficient that accounts for the effect of chord tube buckling, the unified buckling curve for truss arches in uniform compression are obtained. Lastly, an interactive equation is proposed for in-plane buckling resistance of steel tubular truss arches under combined compressive and bending actions. It is found that, the buckling of diagonal web tubes greatly reduces the load-carrying capacity and deformation ability of truss arches hence should be prevented in design. The chord tube deformation always exists during the buckling failure of the truss arch and its effect on the buckling resistance is inevitable. The buckling curve b in the codes can used for truss arches in uniform compression, and the interactive equation can provide satisfactory lower bound predictions for truss arches under general loading. [ABSTRACT FROM AUTHOR]

Highlights • Axial buckling of taxol- and MAP-stabilized microtubules is investigated. • Both surface and nonlocal effects are taken into consideration. • SLS model is used to describe the viscoelastic surrounding cytoplasm. • A good agreement is found between the results and available experimental data. • Stabilizing microtubules with taxol reduces the critical buckling load. Abstract In this paper, an orthotropic elastic shell model is developed for the buckling analysis of protein microtubules subjected to an axial force in living cells. Surface effects are taken into consideration based on the Gurtin–Murdoch elasticity theory. To incorporate the small scale effects, the nonlocal elasticity theory is also used. The influences of the viscoelastic surrounding cytoplasm are taken into account employing standard linear solid model. The governing differential equations are derived using the first-order shear deformation theory and the principle of virtual work. A numerical solution is obtained for the governing equations by employing differential quadrature method. To verify the accuracy of the numerical results, the present results for the axial buckling of microtubules stabilized with microtubule-associated proteins and taxol are compared with those of experimental observations in the literature. It is found that the orthotropic shell model with both surface and nonlocal effects can describe the buckling behavior of microtubules accurately, while the nonlocal shell model without surface effects fails to predict the buckling loads. [ABSTRACT FROM AUTHOR]

Results of an investigation on the effects of crack and length perturbations of a twospan column on buckling analysis with different boundary conditions are presented. The external and internal supports were represented by a rotational spring which models the reduced flexural stiffness due to crack. This study emphasises the exploitation of the localization concept and curve veering effect for a two-span weakened column. A set of numerical examples is presented to highlight the effect of imperfections on the buckling mode of structures. [ABSTRACT FROM AUTHOR]

• The bi-modular FGMs UMAT is developed for the first time and successfully conducted to validate the perturbation solution. • The rise-to-thickness ratio and corresponding critical load are two factors influencing the snap-through buckling. • The rotation constraint and radial constraint at the shell edge have opposite effects on the snap-through buckling. • The bi-modular FGM effect may speed up or slow down the snap-through buckling. Functionally graded materials (FGMs) enable structures to achieve a smooth transition between different material properties, providing an optimized combination of functions to meet the diversity of engineering needs. However, the presence of bi-modular effect in FGMs is often neglected due to the complexity in the analysis. In this paper, the curvature correction equivalent method based on the von Kármán theory will be applied to the theoretical study for the large deformation problem and the resulting snap-through buckling of functionally graded revolutionary shallow thin shells with bi-modular effect under different boundary constraints. Furthermore, a bi-modular FGMs user material subroutine (UMAT) is developed for the first time to simulate the real material model, thus validating the theoretical solution. The results show that except for the bi-modular effect of materials, boundary constraints of shells also have important influences on the relationship of load vs. central deflection and snap-through buckling. The research of boundary constraints brings new conclusions to snap-through buckling: the rotation constraint and radial constraint at the shell edge have opposite effects on snap-through buckling. This work will contribute to the analysis of the snap-through buckling of functionally graded revolutionary shallow thin shells with an obvious bi-modular effect and under various boundary constraints. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of buckling-restrained braces (BRBs), namely shuttle-shaped buckling-restrained braces (SS-BRBs). The proposed SS-BRB is composed of a circular steel tube as the inner core, and a shuttle-shaped thin-walled steel tube as the external restraining member. The space between them is filled by a steel-plate isolation system. The shuttle-shaped restraining member of the SS-BRB significantly improves load-carrying efficiency and saves material in its strength design. Moreover, the SS-BRB is more aesthetically appealing and can be utilized as an exposed BRB in long-span or spatial structures. In terms of the concept of restraining ratio of a BRB, no design method of an SS-BRB is available currently because it concerns the solution of the elastic buckling load of an SS-BRB. Therefore, the elastic buckling load of a pin-ended SS-BRB is initially studied by adopting the equilibrium method and is further verified through finite element (FE) method. The lateral displacement function of an SS-BRB, and the longitudinal stress at the extreme fiber of the external restraining member are derived by considering an initial geometric imperfection that is consistent with the first order overall buckling shape of the SS-BRB. A correction factor considering shear deformation has been incorporated for a more accurate prediction. The lower limit of the restraining ratio for a load-bearing type of SS-BRBs is further obtained based on yielding of the extreme fiber of the restraining member. Furthermore, the proposed formula has incorporated a strain hardening factor for the SS-BRB that experiences strain hardening of the core after its initial yielding. The proposed formulas have been validated through FE numerical analysis. The findings in this paper provide fundamentals to develop the design method for an energy-dissipation type of SS-BRBs. [ABSTRACT FROM AUTHOR]

This paper discusses the buckling and post-buckling of thick composite plates having large initial geometrical imperfections. Within the theory of large transformations, the proposed formulation uses generalised forces and deformations derived from the energy conjugacy of the second Piola-Kirchhoff stress and Green-Lagrange strain. In addition, it provides partial differential equations of equilibrium that are easy to solve using common techniques such as the Galerkin-Ritz method. Unlike existing contributions, which are (i) limited to imperfections that are proportional to current deformations, (ii) address small to moderate initial imperfections only, and/or (iii) require advanced and time consuming numerical methods, the present approach is based on analytical solution and takes into account large initial imperfections. Despite the complexity of the energy balance formulation, the resulting governing equations are simple and applicable to design practical composite structures. The proposed model was compared to numerical results obtained using the finite element method. Overall, good agreements have been obtained when the assumptions fall within the range of validity of the commercial software used for simulation. [ABSTRACT FROM AUTHOR]

In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler–Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details , the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields. [ABSTRACT FROM AUTHOR]

Highlights • Incompressible functionally graded rectangular thick plates are studied. • Material properties vary through the thickness based on the power law function. • Higher order shear and normal deformable plate theory is developed. • Legendre polynomials are used in the expansion of displacement field components. • Bending, buckling and free vibration are investigated for simply supported plates. Abstract In the present study, higher order shear and normal deformable plate theory is developed for analysis of incompressible functionally graded rectangular thick plates. Also, The effect of incompressibility is studied on the static, dynamic and stability responses of thick plate. It is assumed that plate is incompressible and the incompressibility condition is considered in addition to the governing equations for determining the unknowns. Since the plate is thick, higher order shear and normal deformable theory is applied so that the Legendre polynomials are used for expansion of displacement field components in the thickness direction. Also, it is supposed that material properties vary through the thickness based on the power law function. Utilizing the variational approach, governing equations for static, stability and dynamic analysis of plate are derived. Resulted equations are solved analytically for simply supported plates. Finally, the effects of material properties and dimensions on the response of incompressible plates are investigated in details. [ABSTRACT FROM AUTHOR]

Buckling behavior of a bonded, uni-axially compressed double-nanoplate-system is investigated in this work. Both the synchronous and asynchronous-type buckling is considered in detail. The two nanoplates are assumed elastically bonded by a polymer resin. The nano-scale effects of nanoplates are dealt with in the analysis by using nonlocal elasticity theory. The theory is utilized for deriving the expressions for a buckling load of a double-nanoplate-system. A simple analytical method is introduced for determining the buckling load of a nonlocal double-nanoplate-system. Explicit closed-form expressions for the buckling load are derived for the case when all four ends are simply supported. Single-layered graphene-sheets are considered for the study. The study highlights that the nonlocal effects considerably influence the buckling behavior of the double-graphene-sheet-system. Unlike the buckling behavior of a single graphene sheet, the double-graphene-sheet-system undergoes both synchronous as well as asynchronous buckling. The nonlocal effects in the double-graphene-sheet-system are higher with increasing values of the nonlocal parameter for the case of synchronous buckling modes than in the asynchronous buckling modes. The increase of the stiffness of the coupling springs in the double-graphene-sheet-system reduces the nonlocal effects during the asynchronous modes of buckling. Different aspect ratios of the double-graphene-sheet-system and higher buckling modes are also considered in the work. [ABSTRACT FROM AUTHOR]

Microtubules (MTs) in living cells are frequently bend, e.g., with a mean curvature of about 0.4 rad/μm in fibroblast cells [Odde et al., J. Cell Sci. 112, 3283 (1999)]. This raises a natural question whether bending buckling can occur in a MT. In this paper, an orthotropic model is developed to investigate buckling of MTs upon bending and torsion. A critical buckling curvature for a bent MT is predicted to be about 0.03 rad/μm (to which the corresponding bending moment is 0.85 nN nm), indicating that MTs in living cells are likely buckled. Buckling behavior of torsional MTs is also studied, and a critical buckling torque of 0.077 nN nm is obtained. Comparison to the results from an isotropic model shows that anisotropic properties of the MT wall have severe effect on the mechanical behavior of MTs. [ABSTRACT FROM AUTHOR]

Explicit formulas are obtained to describe the buckling behavior of triple-walled carbon nanotubes (CNTs) that are embedded in an elastic matrix, with van der Waals (vdW) interaction taken into consideration. The investigation is based on the continuum shell theory in which the individual tube is treated as a cylindrical shell. The elastic matrix surrounding the outermost tube is modeled as a Pasternak foundation to account for not only the normal stress, but also the shear stress between the outermost tube and the surrounding matrix. Numerical analyses are carried out to estimate the critical buckling load of triple-walled CNTs, and the results indicate that the critical buckling loads approach a constant of around 0.26 N/m with the increase of the innermost radii regardless of whether or not the triple-walled CNT is embedded in an elastic matrix. The effects of vdW interactions before and after buckling on the critical buckling load are also examined for triple-walled CNTs with various innermost radii. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical study and finite element simulation for the buckling of a thin film on the compliant substrate. First, we develop a continuum mechanics approach for large deformation buckling analysis based on minimizing the total energy of the film/substrate structures, and considering the precise curvature of the buckled film and the Poisson's ratio of the substrate. The predicting results using this proposed theory agree quite well with previous experimental results. Then, we make a modification for the model to simplify the expressions for the wavelength and amplitude of the buckled geometry. Furthermore, considering a thin Si film on shape memory polymer (SMP) substrate, we investigate the buckling behavior of the thin film through theoretical analysis and finite element method. Through the investigation, it is found that the evolution rate of the buckling geometry of thin film depends on the temperature of the SMP substrate, and the buckling geometry changes faster at a higher temperature. Finally, a programmed method to control the buckling of thin Si film on the SMP substrate is proposed and is realized with finite element simulation in ABAQUS. [ABSTRACT FROM AUTHOR]

Buckling instability refers to a significant limit on the structures with I-section members, which causes severe decreasing of critical buckling load. Many mechanisms and techniques have been developed to increase the loading capacity of I-section structures, e.g., using composite materials or changing web geometry. This study aims at theoretically investigating the effect of geometry on the buckling capacity of wood composite I-beams with sinusoidal corrugated web. Experiments and numerical simulations are carried out to validate the theoretical predictions. The presented model is also reduced to flat web to validate with an existing study. Good agreements are observed from the validations. Parametric study is conducted to indicate the effects of web geometry on the critical buckling load. A significant increasing of buckling load (minimum 17.7%) is obtained between flat and sinusoidal web I-beams. Sensitivity study is carried out to evaluate the influences of web thickness, beam length and beam height on the loading capacity of sinusoidal I-beams. Optimal design is conducted to investigate the impact of the ratios of wavelength-to-beam length ( a L ) and wave amplitude-to-flange width ( A T ) on the critical buckling load and volume of wood corrugated I-beams. The findings in this study can be further used as guidance for the design of composite I-beams with sinusoidal corrugated web. [ABSTRACT FROM AUTHOR]

The exact consideration of the global buckling behaviour of HSS steel structures is very important in the design because due to the higher yield strength smaller cross sections can be used, which might be more sensitive to stability failure. According to the previous research results, the flexural buckling behaviour of HSS and NSS columns can be significantly different, however, these differences are not considered in the current design methods. The application range of the current EN 1993-1-1 [1] is limited for steel grades up to S460. The EN 1993-1-12 [2] gives design rules for materials up to steel grades of S700, however, for the determination of the flexural buckling resistance of welded box section members there are no improved design guidelines for HSS structures. Therefore, the purpose of the current study is to investigate the column buckling behaviour of HSS welded box section columns based on previous and current experimental investigations and on numerical simulations. This paper focuses on the effect of the different material properties, imperfections and residual stresses on the global buckling behaviour of HSS members and gives design proposal for the applicable column buckling curves for steel grades between S420 and S960. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we investigate the numerical simulation of the whole buckling transition process during unloading and loading of the compression load with quasi-static method. By using a smaller load increment step, longer calculation time and appropriate damping, this buckling transition is calculated. We find that the tubular deformation evolves from continue-line contact to bottom-top-point, continuous-point, spatial two-point, spatial one-point, planar one-point contact, and finally back to vertical configuration during unloading. This deformation sequence is reversed during loading. During the transition from planar one-point contact to spatial two-point contact deformation, the buckling shape and related physical quantities change abruptly. During unloading and loading, the dimensionless critical loads of the first three buckling deformations are basically the same. For the buckling deformations with spatial two-point and planar one-point contact, and for spatial one-point contact deformation, the critical loads of loading are about 5% and 50% larger than that of unloading, respectively. For the spatial one-point contact deformation with dimensionless length greater than 40 and other buckling deformations with dimensionless length greater than 20, the critical loads obtained in the buckling process remain almost unchanged. It is noted that since the friction effect is not considered in our numerical simulation, the critical loads obtained are the minimum values in the process of buckling transition. Highlights • Quasi-static method is used for buckling transition process. • Six buckling modes during loading and unloading. • For dimensionless length more than 40, the critical load with spatial one-point contact is constant. • For dimensionless length more than 20, the other critical loads remain unchanged. [ABSTRACT FROM AUTHOR]

Highlights • Analytical solution of flexural-torsional buckling of arches with shear deformation. • Neglect of shear deformations causes a higher buckling load for arches under radial load alone. • Neglect of shear deformations causes a lower critical temperature for arches under temperature field alone. • Flexural-torsional buckling load decreases with increase of temperature field. • Critical temperature field decreases with increase of radial point load. Abstract This paper presents an analytical investigation of the thermoelastic lateral-torsional buckling of circular arches under an arbitrary radial point load in a uniform thermal environment accounting for shear deformations, which has not been reported in the literature. The interaction of thermal environment with the arbitrary load and elastic end restraints produces complex non-uniform compressive, bending, and shearing actions in the arch. The theoretical solutions of the critical load and temperature field for the elastic lateral-torsional buckling of arches accounting for shear deformations are derived. Comparisons of theoretical solutions with finite element results show that their agreements are excellent. Effects of various factors on the lateral-torsional buckling are investigated. An increase of the temperature field reduces the buckling load, while an increase of the radial load reduced the critical temperature field for buckling. The effect of shear deformations on the lateral-torsional buckling load is also explored. It is shown that the neglect of shear deformations causes errors in the prediction of the critical buckling load. When shear deformations are considered, the buckling load for arches with a small and intermediate lateral slenderness ratio under the radial point load alone is shown to be lower than that without consideration of shear deformations. However, under the uniform temperature field alone, the critical temperature field for lateral-torsional buckling of the arches considering shear deformations is higher than that neglecting shear deformations. [ABSTRACT FROM AUTHOR]

In the current work, an innovative fixture was designed and made to test local buckling of the notched plates under tensile loading. The conducted experimental measurements include the symmetric and for the first time the anti-symmetric modes of the buckling. Both monotonic and cyclic loading were applied on the specimens and the effect of the buckling on the fracture capacity and fatigue life of the specimens were investigated. The main interest of the paper is to describe the fixture and some experimental techniques. The buckling load was obtained from the tests as well as fracture capacity and fatigue life. Based on the obtained results, the buckling can reduce the fracture capacity as well as the fatigue life by 35% and 59%, respectively. Due to the mix mode of I-III, the anti-symmetric buckling shows a greater effect on the fracture capacity, however, the sliding crack closure due to mode III prevents the crack growth in the case of anti-symmetric buckling. [ABSTRACT FROM AUTHOR]

Present research investigates the thermal postbuckling of sandwich plates containing a stiff core and two thin carbon nanotube reinforced composite (CNTRC) face sheets. Properties of the core, carbon nanotubes (CNTs) and polymeric matrix of the faces are assumed to be temperature-dependent. It is assumed that CNTs as reinforcements may be distributed according to a functionally graded pattern. Plate is formulated based on the first-order shear deformation theory and von Kármán type of geometrical nonlinearity. The governing equations are obtained by the energy method with the aid of the Conventional Ritz method. Shape functions of the Ritz method are estimated according to the Chebyshev polynomials. A set of nonlinear eigenvalue equations is achieved. The obtained equations are homogeneous, coupled, and nonlinear in terms of both displacements and temperature. A successive displacement control strategy is implemented to trace the thermal postbuckling equilibrium path of the plate. It is shown that, with increasing the volume fraction of CNT, critical buckling temperature of sandwich plate increases and postbuckling deflection decreases. Furthermore, through a functionally graded distribution of volume fraction of CNTs across the thickness, critical buckling temperature of the sandwich plate may be enhanced and thermal postbuckling deflection may be alleviated. [ABSTRACT FROM AUTHOR]