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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]

A steel brace is effective to retrofit old reinforcement concrete (RC) buildings by increasing the horizontal load capacity of structures. However, concrete cracks that easily occur in the surrounding RC members under tension initiate early strength degradation, so this research aimed to develop a new self-centering brace (SCB) with the compression-only capacity such that no tension force is developed in the brace or to the adjoining RC members. Original SCBs have been developed to reduce the residual deformation of structures with a symmetrically flag-shaped hysteretic response. By altering the force transfer mechanism in the original SCB, a compression-only self-centering brace (C-SCB) can be developed under a symmetrically reversed cyclic loading, providing an alternative for the RC building retrofit. This paper first introduces the mechanics and deformation mechanism of the proposed C-SCB. A test program is then conducted on the cyclic tests of a buckling-restrained energy dissipating bar (EDB) to evaluate the energy dissipation. A 3,695-mm-long C-SCB is composed of posttensioning high-strength steel tendons, steel compression members, and buckling-restrained EDBs for the energy dissipation. The C-SCB in tests showed a good compression-only self-centering capability up to an axial displacement of 31 mm, with a maximum axial force of 1,530 kN. No damage of the steel tendons, compression members, or EDBs was found after three phase tests. Finite element analysis further validated the compression-only hysteretic response and mechanics of the C-SCB in a symmetrically reversed cyclic loading. [ABSTRACT FROM AUTHOR]

In the present paper, the effect of aspect ratio on the initial buckling response of an elastically supported rectangular FGM plate, the thin plate spline radial basis function (RBF) method can be used. This method involves the use of a thin plate spline to interpolate the displacement field of the plate, allowing for accurate analysis of the plate's behavior. The higher-order shear deformation theory (HSDT) is used for the analysis of the FGM rectangular plate resting on two parameters of elastic foundation. The displacement field consists of five unknown variables and approximately parabolic distribution of the transverse stress profile through the plate thickness and tangential stress-free boundary conditions on the plate surface. The governing differential equations (GDEs) of the plate are developed in the framework of Hamilton's principle. The thin plate spline radial basic function-based Meshfree method is used for discretizing the GDEs. To demonstrate the accuracy and efficacy of the present approach, the results obtained by the present approach are compared with the results given in the literature. The effect of various aspect ratios, grading index, span-to-thickness ratio, and two parameters of elastic foundations on the normalized buckling load is proposed. Some new results are also presented, which may be beneficial for future research works. The novelty of the present is the effects of aspect ratio on the elastically supported FGM plates. [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]

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]

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]

A full-scale, two-tiered steel buckling-restrained braced frame (BRBF) was tested to evaluate experimentally the seismic behavior of steel multitiered BRBFs, namely, column stability response, column seismic demands, and tier deformations under a loading protocol representing earthquake ground motions. The test specimen consisted of diagonal braces oriented in opposing directions in the two adjacent tiers to create the most critical multitier response. The test frame was designed in accordance with the 2010 AISC Seismic Provisions as a lateral load-resisting system of a single-story building. The frame was subjected to a three-phase loading protocol consisting of lateral displacement time histories corresponding to a far-field ground motion record and a near-field ground motion record applied sequentially achieving total frame drifts in excess of 3.5%, followed by a final monotonic lateral displacement corresponding to 4.5% story drift. The test frame exhibited a stable response despite a non-uniform distribution of frame inelastic deformation between the tiers, which induced significant in-plane bending moments in the columns. Flexural bending, combined with a large axial compression force, led to partial yielding in the columns. Large deformation demands were also observed in the BRB yielding in tension and attracting the majority of frame lateral deformation. On the basis of test results, a displacement-based analysis approach was proposed to relate column in-plane bending and flexural stiffness to relative inelastic tier deformations. [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]

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]

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]

Floating liquefied natural gas (FLNG) cryogenic hoses can be employed for the transmission of liquefied natural gas (LNG). Usually, U-shaped metal bellows can be applied as the inner lining of FLNG cryogenic hoses. In installation, positioning and other working conditions, torsion is one of the main loads, and torsional buckling instability is a major failure mode of U-shaped metal bellows of FLNG cryogenic hoses. In the current research, the buckling instability of bellows under torsional loads has been investigated in detail, the mechanical mechanism of deformation in torsional buckling mode of bellows has been analyzed and the influence of the structural design parameters on the stability performance has been summarized. It was seen that the axis of the bellows was presented as a spiral line shape during the torsional buckling stage. At the same time, the torsional buckling properties of toroid and spiral bellows were analyzed. The obtained results showed that the torsional buckling stability of the spiral bellows was weaker than that of the toroid bellows and increase of the spiral angle of the spiral bellows intensified this trend. In addition, the post-buckling analysis of U-shaped bellows under torsional loads was carried out by means of experiments and finite element simulation. It was shown that the results obtained from finite element (FE) analysis in this research presented a relatively accurate critical torque value and a consistent buckling instability mode, compared with the experimental results. On this basis, the effects of common defects such as thickness thinning on the torsional stability of bellows were investigated. Considering the geometric defect of thickness thinning, the error of FE analysis was reduced further, and it was found that the defect could significantly decrease the stability of the bellows. The above analysis results could provide a reference for structural design and post-buckling analysis of bellows. [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]

This research is concerned with the free vibration and buckling analysis of carbon nanotube-reinforced beams (CNT-RBs) using a novel high-order shear deformation theory (HSDT). The current HSDT is modeled by a trigonometric function without a shear correction factor, and the displacement field has only four variables. Several different carbon nanotube distributions, including two uneven CNT distributions (X-CNT and O-CNT), are considered. The mixture rule is applied to express the effective material properties of carbon nanotube-reinforced beams. The CNTR beams are rested on two springs and a shear layer (Kerr foundation). Hamilton's principle is employed to derive the governing equations, which are then solved using the Navier technique. The current theory and several parameter effects are studied and validated in comparison to benchmark studies and theories. The main purpose of this study is to enhance understanding of high-order shear theories, such as third order, sinusoidal, exponential, etc. In this context, our theory yields excellent results when compared to other theories. The difference between our theory and the exact solution is so minimal that it is superior to other theories. The second part of the study focuses on investigating the distribution of carbon nanotubes to enhance understanding. This knowledge can assist panel manufacturers in determining the appropriate distribution shape. Our results indicate that the third distribution (X-CNT) significantly influences mechanical behavior, unlike the first and second distributions (UD-CNT and O-CNT). [ABSTRACT FROM AUTHOR]

In order to improve the resilience of structures subjected to strong earthquakes, a buckling-plate self-centering friction damper (BPSCFD) with low post-yielding stiffness is proposed, which consists of a group of post-buckling plates and a self-centering variable friction mechanism. The damper is intended to not only reduce the peak and residual deformation of structures, but also to limit the additional internal force of the structural elements. Through theoretical derivation and finite element simulation, the hysteretic damping and self-centering characteristics of BPSCFDs are studied. In order to examine the seismic performance of the BPSCFDs, the dampers are employed to retrofit a double-columns bridge bent, and the corresponding elastic-plastic time history analysis is conducted. The results show that the force-displacement relationships of BPSCFDs with different parameter combinations are characterized by typical flag-shaped self-centering hysteretic loops and low post-yielding stiffness, and the dampers can effectively reduce the peak and residual deformation of the bridge bent without increasing the peak acceleration and base shear. The research results could supply a guideline for the design and application of the damper. [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]

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]

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]

• Buckling strength of metamaterial is designed by deep learning and improved compared with benchmark models, validated by 3D printing and compression testing. • The optimization proceeds to transition in dominant buckling mode from in-plane to out-of-plane deformation, converging the eigenvalue of 2nd mode to 1st mode. • The mechanism of superior buckling strength shows that thickness of horizontal beam does not significantly affect buckling strength and post-buckling behavior. Metamaterials are specially engineered materials distinguished by their unique properties not typically seen in naturally occurring materials. However, the challenge lies in achieving lightweight yet mechanically rigid architectures, as these properties are sometimes conflicting. For example, buckling strength is a critical property that needs to be enhanced since buckling can cause catastrophic failure of the lightweight metamaterials. In this study, we introduce a generative machine learning based approach to determine the superior geometries of metamaterials to maximize their buckling strength without compromising their elastic modulus. Our results, driven by machine learning based design, remarkably enhanced buckling strength (over 90 %) compared to conventional metamaterial designs. The simulation results are validated by a series of experimental testing and the mechanism of the high buckling strength is elucidated by correlating stress field with the metamaterial geometry. Our results provide insights into the interplay between shape and buckling strength, unveiling promising avenues for designing efficient metamaterials in future applications. [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]

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]

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In this article, the vibration and buckling of a double-layer Graphene sheet (DLGS) coupled with a piezoelectric nanoplate through an elastic medium (Pasternak and Winkler models) are investigated. DLGS are subjected to biaxial in-plane forces and van der Waals force existing between each layer. Polyvinylidene fluoride (PVDF) piezoelectric nanoplate is subjected to an external electric potential. For the sake of this study, sinusoidal shear deformation theory of orthotropic plate expanded with Eringen's nonlocal theory is selected. The results indicate that nondimensional frequency and nondimensional critical buckling load rise when the ratio of width to thickness increases. Furthermore, incrementing the effect of elastic medium parameter results in increasing the stiffness of the system and, consequently, rising nondimensional frequency and critical buckling load. [ABSTRACT FROM AUTHOR]

In this article, the thermal buckling behavior of orthotropic circular bilayer graphene sheets embedded in the Winkler-Pasternak elastic medium is scrutinized. Using the nonlocal elasticity theory, the bilayer graphene sheets are modeled as a nonlocal double-layered plate that contains small scale effects and van der Waals (vdW) interaction forces. The vdW interaction forces between the layers are simulated as a set of linear springs using the Lennard-Jones potential model. Using the principle of virtual work, the set of equilibrium equations are obtained based on the first-order shear deformation theory (FSDT) and nonlocal differential constitutive relation of Eringen. Differential quadrature method (DQM) is employed to solve the governing equations for simply-supported and clamped boundary conditions. Finally, the effects of the small scale parameter, vdW forces, aspect ratio, elastic foundation, and boundary conditions are considered in detail. [ABSTRACT FROM AUTHOR]

Tape-springs – straight strips with transversely curved cross-sections – undergo a flattening of the cross-section upon bending, and accompanying torsional buckling in equal-sense bending which then "recedes" at greater deformation. The exact analytical solution for tape-spring bending was solved by Mansfield; however, the resulting expression for the twisting curvature at the onset and recession of torsional buckling cannot be solved in closed-form. Approximate closed-form expressions are therefore sought: firstly, by utilising Taylor series approximations of Mansfield's extensive functions; and secondly, by assuming a uniform transverse curvature, thereby rendering the problem algebraic in nature, and deriving new governing expressions. Further approximations assume the cross-section does not deform upon bending, and that the tape-spring remains a developable surface in the inextensible limit of zero thickness. All approximate solutions are shown to agree closely with Mansfield's solution at small curvatures, with the uniform curvature approximation also capturing the recession of torsional buckling to a reasonable degree of accuracy. The accuracy of the uniform curvature approximation is related to a pertinent dimensionless parameter, which governs the size of a boundary layer in Mansfield's exact solution: as this parameter tends to infinity, the uniform curvature approximation and Mansfield's exact solution are shown to converge; as it tends to zero, all solutions are shown to converge on the inextensible limit. • Approximate solutions for tape-spring bending assuming uniform curvature. • Closed form expressions for the onset and recession of torsional buckling. • Approximate solution in good agreement with exact Mansfield solution. • Exact and approximate solutions converge in the zero-thickness inextensible limit. [ABSTRACT FROM AUTHOR]

This research aims to establish the semi-analytical approach for nonlinear dynamic buckling and vibration responses of functionally graded graphene platelet reinforced composite (FG-GPLRC) circular plates and spherical shells subjected to time-dependent radial pressure and thermal loads. The higher-order shear deformation theory with von Karman’s nonlinearities and the nonlinear viscoelastic foundation model is used to establish the expression of the fundamental equations of considered structures. The shells and plates are considered with clamped and immovable edge, and shallow curvature of the shells is applied. The Lagrange function is applied to establish the total energy of structures, and the potential function of viscous damping of the viscoelastic foundation is expressed using the Rayleigh dissipation function. The motion equation of the structures can be formulated using the Euler–Lagrange function. The dynamic responses are obtained using the numerical method, and the critical dynamic buckling loads are obtained using the dynamic buckling criterion of Budiansky–Roth. The large effects of material parameters, geometrical parameters, and nonlinear viscoelastic foundation on dynamic responses of considered structures are investigated and discussed in many numerical examples. [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]

In this paper, under the condition of bidirectional stress, the buckling deformation of the side plate in a rectangular concrete-filled steel tube (CFST) column has been studied in detail. We have conducted a theocratical analysis, an experimental validation and a finite element simulation to investigate the influences of the height-width ratios and Nominal Poisson's ratios on the buckling form of the side plate, and we also try to explain the change of buckling form between unidirectional and bidirectional stress, both of them can provide a good reference and basis for design and application of the CFST column. The specific work can be summarized as follows: Firstly, a theoretical analysis has been conducted to study the buckling coefficient solution method of the thin plate under the conditions of axial compress and transverse tension. Then, under the conditions of the unidirectional and the bidirectional stress, a comparative study is carried out to investigate the changing relationship of the buckling coefficient (k) of the side plate; the results indicate that the buckling characteristic is changed due to the bidirectional stress, meanwhile, the buckling coefficient and the number of buckling half-wave will increase. Furthermore, the existing outcomes and the numerical simulations are adopted to study the relevance between the number of the elastic buckling half-wave in the side plate and the corresponding height-width ratio of the component; the results indicate that the former is larger than the latter. Finally, based on the obtained, the buckling relationship curve, the conclusion can be drawn as follows: when the bidirectional stress has been applied to the side plate, there is an equal interval between the different buckling half-waves; meanwhile, the interval shows a quadratic function reduce trend with the increase of nominal Poisson's ratio. [ABSTRACT FROM AUTHOR]

This work aims to reveal the in-plane-compressive characteristics of Glass Fibre based single face corrugated Structure Sheet (GFSS) by developing a loading holder of the both ends of the panel of GFSS in the direction of the cross machine direction. A grooved end-support device was developed and exmined. In order to set stably and quickly a straight panel of GFSS on the compressive-testing apparatus, the width and the depth of the holder's groove were varied against the geometrical size of the panel, and the stability and reproducibility of compressive deformation of the panel was experimentally investigated. When changing the height of the panel and reinforcing the both ends of the panel by dipping instant adhesives, the deformation behavior and the buckling strength was characterized in three modes: a short height crushing without lateral deflection, a small lateral deflection mode as the intermediate state, and a triangle-like folding as a long height crushing. [ABSTRACT FROM AUTHOR]

In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of DP500 and DP980 dual-phase steels, and AZ31B magnesium composite under tension–compression cyclic loading. The advantage of the device lies in the possibility of monitoring friction between the specimen and supporting blocks during the test. In consequence, it allows to avoid an error during stress determination. The full cyclic loading capacity for each material can be executed at the displacement amplitude within the range ± 2.5 mm which corresponds to the maximum strain amplitude of ± 0.2 for the specimen with the gauge length of 21.5 mm. It is concluded, that the technique proposed is promising since the thin sheet material can be tested under tension–compression in a wide range of deformation without the buckling effect. Furthermore, useful data for modelling cyclic deformation behaviour for shell structures can be obtained. [Display omitted] • Proposed fixture enables to avoid buckling during thin metal sheet compression. • The friction force is continuously registered during the test. • Complex characteristics could be successfully and precisely determined. • Useful data for modelling cyclic deformation can be obtained. [ABSTRACT FROM AUTHOR]

In this paper, the free vibration and mechanical buckling analyses of the metal foam plates with porosities via a moving Kriging meshfree method based on the higher-order shear deformation theory are studied. The displacement fields are approximated by the moving Kriging shape functions, which satisfy Kronecker's delta property. Thanks to that property, the essential boundary conditions can be directly imposed the same with finite element method. In this study, the porosities are distributed by uniform, symmetric, and asymmetric distributions along the thickness direction. The natural frequency and critical buckling load of the metal foam plate are determined by solving the explicit governing equations, which are derived through the variational formulation. The influence of the porosity distribution, porous coefficient, width-to-thickness ratio and boundary condition on the natural frequency and critical buckling load of the porous metal foam plate is investigated and discussed in detail. Numerical examples indicate that the present approach is stable and well accurate predictions for investigating vibration and buckling behaviors of the porous metal foam plate. Moreover, an increase of the porous coefficient makes a decline of the natural frequencies and critical buckling loads of the plate. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation on the evaluation of the seismic performance of a new hybrid buckling restrained brace (HyBRB) under cyclic load. Detailed design steps adopted for the HyBRB design are reported in this paper. The analytical method for estimation of critical loads corresponding to buckling mode formation of the steel core inside the restrainer has been presented. The design targets achieved for the HyBRB are ease of inspection of the detachable BRB core to facilitate replacement of the steel core after a seismic event, if necessary, and enhanced energy-dissipation capacity through restrained buckling about both weak and strong axes of the core. The proposed HyBRB has displayed stable hysteretic behavior with good energy-dissipation capacity in low to high levels of the core strain range. Permanent deformation about the strong axis of the core was observed on unfastening of the restrainers, although restrained buckling of the core was observed about the weak axis in lower displacement amplitudes. Analytical simulation was carried out using a phenomenological model to simulate the experimental behavior. The simulated axial force-deformation hysteresis loops were found to be in close agreement with those obtained from experimental investigation. [ABSTRACT FROM AUTHOR]

• Comparing between the finite element simulation and the actual buckling is aneffective way to determine the loading forms of the buckling. • The casing can lead to the redistribution of deformation and the concentration of deformation of pipelines. • The variation of ground load will lead to buckling deformation of road crossing pipeline. • A small deformation of pipeline will evolve into serious buckling due to the change of ground load and geological disaster. As one of the main forms of pipeline deformation and failure, buckling poses a threat to the service safety of pipelines, seriously leads to oil and gas leakage, pipeline shutdown and environmental pollution. It not only brings huge economic losses, but also leads to fire, explosion and other accidents, which threaten the property and life safety of the country and people. Therefore, it is necessary to study the buckling deformation mechanism and failure rule, so as to lay a foundation for the evaluation and protection of pipeline buckling deformation. In this paper, theory and finite element simulation method has been used to study the buckling failure mechanism of the pipeline crossing road. The form and magnitude of the local load causing pipeline buckling are obtained through theory and vilified by the finite element simulation. The analysis results show that the boundary conditions and stiffness of the pipe are locally changed by the casing, and the deformation of the pipe is concentrated under the external load, such as road load and seismic wave, which leads to buckling. Therefore, the existence of casing will affect the deformation distribution of pipeline, and it is necessary to optimize the design and protect it in practical engineering to avoid buckling caused by deformation concentration. [ABSTRACT FROM AUTHOR]

Large deformations can easily occur when tunneling through weak surrounding rock with high underground stresses. Under high-stress environments, the surrounding rock stores a large amount of strain energy, and the strain energy stored in the soft and weak surrounding rock enclosure is dissipated through the large traveling plastic deformation. Therefore, the effective use of the surrounding rock's bearing capacity and energy dissipation is a feasible solution to the large deformation problem. Based on the energy principle, this study designs a high compressibility, large stroke energy-dissipation element, which transforms the traditional support into energy-dissipation support and solves the problem of large deformation by reasonably utilizing the "displacement" of the surrounding rock. The experimental results showed that the steel plate assembled structure had an initial peak value of about 15 MPa, a constant resistance of about 2 MPa with a large stroke, and a compression rate of more than 75%, with good post-compression flexural peak characteristics. Elastic–plastic buckling analyses of defective steel plate composite structures were carried out using finite element analysis software, and the deformation and force characteristics of a variety of steel plate composite structures after buckling under actual field conditions were investigated. Based on the 3D laser scanning system, the thickness of the upper and lower steel plates of the steel plate composite structure was set to 1 cm, the height of the vertical plate was set to 28 cm, and the thickness was set to 8 mm. The original rigid supporting method was converted into one of compression support by circumferentially embedding the steel plate composite structure into the initial support structure. The resulting support configuration offered a high safety factor because the pressure of the surrounding rock was released by the deformation of the steel plate composite structure. [ABSTRACT FROM AUTHOR]

Submarine pipeline is one of the most popular research filed that many researchers focus on solving the issue of buckling of pipeline. The snaked laying is an effective method to control the lateral buckling. The scour below offshore pipeline may affect the efficiency and performance of the snake lay pipeline. The objective of this study was to investigate the effect of scour hole on the buckling of seawater pipelines. A three-dimensional numerical model developed to investigate the effect of scour below offshore pipeline subjected to wave and current by using Abaqus software and Aqua Module. The results indicated that vertical deformation of straight pipeline increased by increasing scour hole depth. This value changed 4.85 cm to 32.87 for holes 11 to 200 cm respectively, but these parameters of the snake lay pipelines were not affected by the presence of scour hole. Moreover, the effective axial force of snacked lay pipelines reduced 5 times in comparison to straight pipeline by applying wave and current. The results indicated that the value of stress of snaked-lay pipeline was independent on scour hole depth. Therefore, this pipeline was effective method to limit and control buckling even in the presence of scour below it. [ABSTRACT FROM AUTHOR]

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For this study, the geological engineering features and possible failure modes of the Dabenliu quarry slope in the Jinping-I Hydropower Station were qualitatively analyzed before a method for setting viscous boundary and an algorithm for modeling pre-stressed cables were embedded into a DDA (Discontinuous Deformation Analysis) computer code to analyze the deformation of the slope under seismic loading. Our simulation results revealed that the middle and upper parts of the slope slipped along the bedding joints (interlayer shear zones) and that the lower part buckled and collapsed after the slope was excavated. This is a typical slipping–buckling failure mode characterized by upper-slipping followed by lower-buckling. Based on the distribution of the simulated internal force of the anchor cables, the reinforcement scheme was adjusted by strengthening the support for the middle and lower parts of the slope, whereas the length and pre-stress of the anchor cables were reduced for the upper part of the slope. The adjusted reinforcement scheme can ensure the stability of the slope under the action of a magnitude 7 earthquake, and the slope may lose stability with no evident collapse under the action of a magnitude 8 earthquake. Finally, the simulation results were verified via a comparison with the monitoring data regarding the slope. [ABSTRACT FROM AUTHOR]

Rail vehicles generate huge longitudinal impact loads in collisions. If unreasonable matching exists between the compressive strength of the intermediate coupler and the structural strength of the car body, the risk of car body structure damage and train derailment will increase. Herein, a four-stage rigid–flexible coupling finite element model of the coupler is established considering the coupler buckling load. The influence of the coupler buckling load on the train longitudinal–vertical–horizontal buckling behavior was studied, and the mechanism of the train horizontal buckling instability in train collisions was revealed. Analysis results show that an intermediate coupler should be designed to ensure that the actual buckling load is less than the compressive load when the car body structure begins to deform plastically. The actual buckling load of the coupler and the asymmetry of the structural strength of the car body in the lateral direction are two important influencing factors for the lateral buckling of a train collision. If the strength of the two sides of the car body structure in the lateral direction is asymmetrical, the deformation on the weaker side will be larger, and the end of the car body will begin to deflect under the action of the coupler force, which in turn causes the train to undergo sawtooth buckling. [ABSTRACT FROM AUTHOR]

This work investigates the interplay between viscoelasticity and instabilities in soft particulate composites undergoing finite deformation. The composite is subjected to in-plane deformation at various constant strain rates, and experiences microstructural buckling upon exceeding the critical strain level. We characterize the dependence of the critical strain and wavelength on the applied strain rate through our numerical analysis. In the simulations, we employ the single and multiple-branch visco-hyperelastic models. We find that the critical strain and wavelength – characterized by the single-branch model – show a non-monotonic dependence on the strain rate, reaching a maximum at a specific strain rate. Remarkably, different buckling patterns (with different critical wavelengths) can be activated by changing strain rates. The space of admissible buckling modes widens in composites with higher instantaneous shear modulus. In the composites characterized by the multiple-branch model, the critical strain function exhibit multiple local maxima following a superposition of the single-branch responses. Typically, the branch with a larger relaxation time has a more significant effect on the critical strain. Moreover, the local maximum (of the critical strain function) is amplified by increasing the strain–energy factor of the corresponding branch term. Finally, we perform the experiments on the 3D-printed particulate soft composite characterized by a broad spectrum of relaxation times. The comparison of the experimental and simulation results demonstrates the ability of the numerical model to predict the critical buckling characteristics. [ABSTRACT FROM AUTHOR]

To simplify the construction of traditional self-centering buckling-restrained braces (SC-BRBs) and achieve efficient recovery function, an innovative type of single-tube self-centering buckling-restrained braces (ST-SC-BRBs) is proposed. The ST-SC-BRBs only require one outer tube for the prestressed system. The detailed structure and working principle of the ST-SC-BRBs are described, and it is emphasized that the restrained steel tube should be checked as a compression-bending member to ensure its overall stability. Low-cycle fatigue tests are conducted on scaled models of one traditional BRB and two ST-SC-BRBs. The results show that the residual deformation of the ST-SC-BRBs is significantly reduced compared to that of the traditional BRB, with comparable energy dissipation capacity. The ST-SC-BRB works stably with a full hysteresis curve and an obvious "flag-shaped" pattern within the inter-story drift ratio of 2%. The self-centering ratio is the key factor affecting the recovery effect of the ST-SC-BRB. To achieve smaller residual deformation, the self-centering ratio is suggested to be greater than 1. Overall, the ST-SC-BRB presents a more simplified and effective approach to constructing a recoverable functional structure. • A new type of single-tube self-centering buckling restrained brace (ST-SC-BRB) is proposed. • Axial low-cycle tests show that the ST-SC-BRB structure achieves significantly reduced residual deformation. • The self-centering ratio of the ST-SC-BRB is the key factor affecting its self-centering effect. [ABSTRACT FROM AUTHOR]

• A modified concrete damaged plasticity model is proposed considering the deformation and mechanical characteristics of LRS FRP-confined concrete. • The 3D finite element analysis of longitudinal reinforcement buckling in LRS FRP-confined RC columns is realized. • The effect of longitudinal reinforcement buckling on member is illustrated by the FEA results. • The factors affecting the buckling of longitudinal reinforcement are studied, and an empirical formula for determining the failure of members by the buckling of longitudinal reinforcement is proposed. Large rupture strain (LRS) FRPs have great potential to be used for seismic retrofit of RC columns because of its high rupture strain (i.e., > 5%) that provides better confinement effects. However, in FRP-confined RC columns, the longitudinal reinforcements may buckle before the LRS FRP rupture, especially in the case of large stirrup spacing. This study aims to present a 3D finite element (FE) model for simulating the buckling effect of longitudinal reinforcements in LRS FRP-confined RC columns. A modified concrete damaged plasticity model (CDPM) is proposed to consider the deformation and mechanical characteristics of LRS FRP-confined concrete. Removal of failed concrete elements is considered to facilitate the buckling of longitudinal reinforcements in LRS FRP-confined RC columns. The FE analysis accuracy was verified by comparisons with test results. The factors affecting the buckling of longitudinal reinforcements were discussed through an extensive parametric study. Empirical formulas for the stress and strain values at which the longitudinal reinforcement starts to soften were developed. An empirical formula for the ultimate axial strain of LRS FRP-confined RC columns determined by longitudinal reinforcement buckling was also obtained by regression analysis. [ABSTRACT FROM AUTHOR]

This present study consists to analyze the mechanical buckling and the free vibration stabilities of antisymmetric cross-ply and angle-ply laminated composite plates using a refined high order shear deformation theory of four variables against five in other high order theories. Among the advantages of this new theory it takes into consideration the shearing effect in the calculation of deformation without the need for shear correction factors and giving rise to a variation of the shear stresses along the thickness and satisfying the zero shear stresses condition in faces of the plate. The laminate resting on the Pasternak elastic foundation, including a shear layer and Winkler spring, are considered. The equations of the motion are derived from Hamilton's principal. The closed form solution of simply supported rectangular plates has been obtained by using the Navier method. In addition, the effects of various parameters of the laminated composite plate on static buckling and dynamic are presented. [ABSTRACT FROM AUTHOR]

The contradiction of high subducting plate rate (ranging from 4 to 9 cm/yr on Earth's surface) and low slab sinking rate (about 1 and 2 cm/yr in lower mantle) calls for significant slab deformation in the middle mantle. However, mechanisms that can account for both the deformation and the rate discrepancy have not been fully explored. Here, using 2‐D numerical models that incorporate grain size evolution, we propose a new slab deformation mode, slab segmentation and stacking, to accommodate the differential slab sinking rates. Our results show that the segmented slab due to faulting and grain‐size reduction may further break off and stack over itself as it encounters the high‐viscosity lower mantle. Stacked slabs slowly sink in the lower mantle, while periodic slab tearing hinders upward stress transmission, allowing shallow plates to subduct at a higher rate. This discovered mode also provides an alternative explanation for slab thickening in the lower mantle. Plain Language Summary: According to observations and analysis, the velocities of plates entering the trench are much higher than the slab sinking rate in the lower mantle. Inconsistent velocities at the slab's two ends must be accommodated by slab deformation or accumulation in the middle mantle to ensure mass conservation. We have considered three different deformation modes: slab buckling, horizontal deflection, segmentation and stacking. Compared to the diffusive plastic weakening in the mode of slab buckling, previous studies have shown that slab faulting and grain size evolution can induce stronger localized weakening within slabs. Our study goes a step further by finding that the segmented slab can break off and stack over itself periodically when it encounters the lower mantle. This allows the slab to deform more easily in the mantle transition zone, enabling the plate to subduct at a higher rate while keeping the lower‐mantle slab sinks at a low rate. We also find that this mode of slab deformation can equally well explain the thickening of the slab in the lower mantle. Key Points: The discrepancy between the subducting plate rate and lower mantle slab sinking rate calls for slab accumulations in the middle mantleSimple buckling explains the accumulation but is not sufficient to accommodate the rate discrepancyThe mode of slab segmenting, breaking off, and stacking is a possible solution to the slab accumulation and rate discrepancy [ABSTRACT FROM AUTHOR]

During the operation of the drill string, it displays a degree of flexibility. Simultaneously, its dynamic properties, influenced by complex stress conditions, manifest nonlinearity and uncertainty. A comprehensive investigation into the dynamics of flexible drill strings is imperative for deep well drilling. This paper presents a model that simulates random interactions between a flexible drill string and the borehole wall, simplifying the actual drill string model using analogous principles. Dynamic simulation software is utilized for analysis, and an indoor experimental setup has been established. The results reveal that with a constant weight on bit (WOB), higher drill string rotational speeds correlate with increased susceptibility to buckling deformation. Additionally, the critical time for deformation onset exhibits a nearly linear relationship with rotational speed. Maintaining a constant rotational speed, an increase in WOB enhances the likelihood of buckling deformation. The experimental findings suggest a correlation between the drill string's rotation frequency and the WOB. [ABSTRACT FROM AUTHOR]

The general theory of slender structure buckling by Grabovsky and Truskinovsky (Cont. Mech. Thermodyn. 19(3–4):211-243, 2007), (later extended in J. Nonlinear Sci. 26(1):83–119, 2016 by Grabovsky and the author), predicts that the critical buckling load of a thin shell under dead loading is closely related to the Korn's constant (in Korn's first inequality) of the shell under the Dirichlet boundary conditions resulting from the loading program. It is known that under zero Dirichlet boundary conditions on the thin part of the boundary of positive, negative, and zero (one principal curvature vanishing, and one apart from zero) Gaussian curvature shells, the optimal Korn constant in Korn's first inequality scales like the thickness to the power of −1, − 4 / 3 , and − 3 / 2 respectively. In this work we analyse the scaling of the optimal constant in Korn's first inequality for elliptic shells that contain a finite number of points where both principal curvatures vanish. We prove that the presence of at least one such point on the shell leads to the scaling drop from the thickness to the power of −1 to the thickness to the power of − 3 / 2 . To our best knowledge, this is the first result in the direction for constant-sign curvature shells, that do not contain a developable region. In addition, under the assumption that a suitable trivial branch exists, we prove that in fact the buckling deformation of such shells under dead loading, should be localized at the vanishing curvature points, as the shell thickness h goes to zero. [ABSTRACT FROM AUTHOR]