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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]

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]

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]

• 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]

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]

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]

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]

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]

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]

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]

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]

Dynamic buckling prediction of submerged structures under impact loads is a challenging problem for both theoretical and numerical approaches, and the experimental data is very limited. In the present paper, dynamic buckling of grid-stiffened cylindrical shells submerged in a large opening pond at a depth of 5 m and subjected to radial intermediate-velocity impact was experimentally investigated. In order to increase load durations under the condition of fixed peak pressure, explosive depth and standoff distance, airbags composed of O 2 and C 2 H 2 were used and exploded underwater to generate impact load. Amplitudes and durations of shock waves and pulsating bubbles were characterized by using pressure transducers. Measurements of hoop and axial strains reveal that global buckling of skin and stiffeners of the grid-stiffened cylindrical shell occurred under bubble pulsation loads, which features mutation and separation of strains and a sudden change in the vibration period of the stiffened shell with a small increment of impulse. 6 half waves and 1 half wave are observed along the circumferential and axial directions of the shell, respectively. Larger bubble pulse impulse, greater deformation and vibration of the shell under larger impact are the main reasons for global dynamic buckling of the grid-stiffened cylindrical shell. [ABSTRACT FROM AUTHOR]

A general analytical model is developed to evaluate buckling behavior of a bilayer beam-column with a through-the-width asymmetric delamination under simply supported boundary conditions. Both transverse shear deformation and local deformation at delamination tip are taken into account in the model by considering two sublayers in both delaminated and intact regions as two individual shear deformable ones. Interface continuity conditions, which account for effect of interface normal and shear stresses, are also introduced in the intact regions. Furthermore, the present model is capable of dealing with the case of delamination located arbitrary through thickness and along length of beam-columns. In comparisons with the results of classical Euler-Bernoulli beam model, Timoshenko beam model (rigid joint model) and finite element analysis, better agreements are achieved for the present flexible joint model, which captures local deformation at delamination tip due to consideration of interface normal and shear stress components. Parametric studies are conducted to evaluate influences of sublayer thickness ratio, delamination length, delamination location, specimen length, and material parameters on the critical buckling strain with emphasis on transverse shear deformation and local deformation at delamination tip. The developed model can be used with confidence in buckling analysis of layered structures with an arbitrary delamination through the length and thickness. [ABSTRACT FROM AUTHOR]

Large steel silos are typical kinds of thin-walled structure which are widely used for storing huge quantities of granular solids in industry and agriculture. In the present analyses, buckling design of circular steel silos subject to large eccentricity filling pressure is demonstrated in accordance with Eurocode: EN1990, 1991, 1993 . The finite element model is established by using the commercial general purpose computer package ANSYS. Five types of buckling analyses are carried out for the geometrically perfect and imperfect models, with and without the consideration of the material plasticity, which are designated as LBA, GNA, GMNA, GNIA, and GMNIA in EN 1993 Part 1–6. Buckling behavior of five example steel silos with capacity of 40,000 to 60,000 m 3 is investigated whose slenderness ranges from 1.89 to 0.46, comprising intermediate slender and squat silos widely applicable in practical engineering. The results show that the buckling deformations are nonsymmetrical and the GMNIA analysis gives out the least buckling load factor for all example silos from all proposed buckling analysis types, and the load displacement curves are highly nonlinear and predict a distinct maximum load followed by a descending path, in which the maximum load is taken as the critical buckling point λ cr for the equilibrium path. The buckling mode in GMNIA analysis takes the form of the well-known elephant-foot deformation at the bottom part of the shell wall, combined with nonsymmetrical waves in meridional direction throughout the whole height of the silo wall due to the distribution of weld imperfection. The geometrical nonlinearity is beneficial while material nonlinearity is strong and detrimental to buckling behavior of example silos. The effect of weld imperfection is also harmful to buckling resistance of silo, which is more serious for relatively slender silos than squat silos. The buckling is mainly governed by the nonuniform distribution of the solid pressure other than other influential factors as the weld imperfection, geometrical and material nonlinearity, compared with the load case of symmetrical filling. The economical design of steel silos can be effectively measured by the economic index called the ratio of capacity to steel consumption (RCS). It is validated that the index RCS increases rapidly with the decrease of silo slenderness, and the storage efficiency of example silos is increased by about 2.1 times with the slenderness varying from 1.89 to 0.46. It also suggests that the eccentricity in filling of steel silo should be reduced as far as possible for improvement of buckling strength of structure under eccentric filling. [ABSTRACT FROM AUTHOR]

Bone column-buckling is known as due to the loss of trabecular connectivity such that vertical weight-bearing trabeculae lose their cross attachments with each other. It has been considered as a predominant mechanism accounting for skeletal fragility disproportional to the degree of bone loss. Here, we focus our attention upon the improvement of our understanding of the relationships between bone degradation and fracture risk assessment (i.e., buckling load) which is both timely and at the core of important clinical problems such as osteoporosis and age-related bone fragility. With respect to well-known existing literature, there is a great need for a theoretical framework that provides new insights into the bending–buckling process when coupled to continuum damaged-bone adaptation. Within the limitations of our assumptions, it is clearly shown that damage occurs preferentially in regions where bone resorption activity dominates and the existence of a bone density gradient helps to maintain the stability of the bone-column deflection. For another, predicted buckling stress as a function of slenderness ratio is satisfactorily appreciated through experimental results. In our knowledge, this contribution is an original first attempt, at the scale of the single trabecula, which used adaptive elasticity in order to state an original but simplified adaptive-damage bone column buckling theory. [ABSTRACT FROM AUTHOR]

The aim of the paper is to propose a new approach for the optimization of grid shell structures based on a mixed sizing/topologic process, which specifically accounts for the global buckling behavior. The approach consists of merging a sequence of sizing and topological optimization processes where local and global buckling phenomena are opportunely introduced. Indeed, in addition to the removal of some members and the increase/decrease of the cross section size of the remaining ones, the proposed approach accounts for the possibility to convert some of the elements composing the grid shell structure, generally trusses, into beam elements with the aim of having an optimized solution also with respect to the global buckling behavior. The selection of the truss members to convert into beams is made by considering two different strategies presented in detail in the paper. Numerical analyses referring to some case studies derived from the current literature are developed by considering the proposed approach and a traditional sizing/topologic mono objective approach. The results obtained from the numerical analyses clearly underline the reliability of the proposed approach and its efficiency in comparison to traditional approaches of structural optimization. [ABSTRACT FROM AUTHOR]

This paper studied buckling of parallel Z - and C-purlin systems inter-braced by sag-rods at mid-span under pure hogging moment. The purlins are connected to metal sheeting by self-drilled screws and the lateral movement of the top flange is prevented. The paper studied first in detail the buckling of a single purlin, and then buckling of parallel purlin systems. The alternate offset of the sag-rods in adjacent bays and the local deformation of the purlin web have been taken into consideration in parallel purlin systems. For one-purlin system, the buckling moments are given, valid for different combinations of sag-rod and distributed rotational stiffness. The threshold stiffness of the sag-rod, at which the buckling mode changes from symmetrical buckling to anti-symmetrical buckling, is also given. For parallel purlin systems, the buckling moments are calculated by the formulas of one-purlin system, but with a reduced equivalent sag-rod stiffness used in the calculation. Numerical examples for the reduced sag-rod stiffness reveal that an astonishingly large reduction of the sag-rod effective stiffness occurs when the purlin number and the sag-rod offset increase, and the sag-rod stiffness is maximum if the sag-rod is set as close to the bottom flange as possible. And finally some strengthening practices and details are recommended. [ABSTRACT FROM AUTHOR]

Understanding the effects of water absorption on the geometry of a paper sheet is important for inkjet printing applications, since internal moisture content differences may cause unacceptable out-of-plane deformations. The present work focuses on moisture-induced deformations due to a moisture content that is uniform over the thickness of the sheet. Large enough in-plane differences will cause the sheet to buckle, leading to a wavy pattern at the edges of the sheet. Two approaches are utilized to study this for levels of moisture content up to and including the threshold for buckling. An analytical approach, based on geometrically nonlinear plate theory (von Kármán theory), and a numerical one, using commercially available finite element software, are presented. As a first reference problem an isotropic circular plate, wetted uniformly at its center, is solved both analytically and numerically for the in-plane stress distribution, the buckling threshold, and the resulting buckling mode. Secondly, the same is done for an orthotropic rectangular plate, wetted at its edges. Here, in the analytical approach a Rayleigh–Ritz analysis is employed to approximate the buckling threshold. The latter is also calculated by numerical means. The results show that the methods provide results consistent with each other. [ABSTRACT FROM AUTHOR]

This paper deals with the vibration and buckling behaviour of orthotropic double -layered graphene sheets with various boundary conditions in a hygrothermal environment. Two graphene sheets are coupled by an elastic media and also limited to the external Pasternak elastic foundations. The governing equations of motion and equilibrium are derived using Hamilton's principle and then solved using Galerkin's method. The general equations for transverse vibration and buckling of orthotropic double-layered graphene sheets subjected to in-plane edge hygrothemal loadings are formulated on the basis of Eringen's differential nonlocal elastic law and the new first order shear deformation theory. The accuracy of the present solutions is demonstrated by comparison with solutions available in the literature. Numerical results are presented to show variations of the frequency and critical buckling load corresponding to various values of the nonlocal parameter, temperature rise, moisture rise, elastic foundation parameter, and aspect ratio. Also, seven different boundary conditions are discussed in the paper. [ABSTRACT FROM AUTHOR]

This paper presents the Hencky bar-net model (HBM) for elastic buckling analysis of rectangular plates with any combination of edge conditions. HBM comprises a grid (or net) of rigid bar segments joined by rotational springs as well as a torsional spring system in each grid panel. The HBM is developed from the finite difference plate model that allows researchers to perform plate buckling analysis via solving a set of algebraic equations instead of solving a fourth order partial differential equation. The elastic spring stiffnesses for the HBM that provides the flexibility for deformation are established for the first time for elastic rotationally restrained edges and free edges. Some plate buckling problems were solved by using the developed HBM and the solutions shown to converge to those of the continuum plate counterparts when the grid size becomes very small; thereby verifying the validity of the model. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for elastic buckling problems of thick rectangular transversely isotropic simply supported plates subjected to uniaxial or biaxial uniformly distributed in-plane load, one of which could also be tensile. Governing equations are simplified to two partial differential equations using displacement potential functions (DPF) which are solved using the separation of variables method with exact satisfaction of boundary conditions. The presented solution is applicable to any plate with no restriction on its thickness ratio and also to any composite plates which have the same in-plane mechanical properties in all directions of the plate. Obtained results for critical buckling loads are compared with other analytical results for thin and moderately thick, and with numerical results for thick plates which show excellent agreement between them. Then, the effects of loading conditions aspect and thickness ratios for four transversely isotropic materials and also the engineering constants on the buckling of plates are discovered. The results show that the presented method is applicable and reliable for various kinds of material properties, thickness ratios, and loading conditions. Results also show that in comparison with a uniaxially loaded plate, adding a compressive load in second direction decreases the critical buckling load and the plate buckles in lower modes, while for adding a tensile load it is vice versa. Among materials engineering constants, in-plane modulus of elasticity and transverse shear module have the most effects on the critical buckling load of plates. [ABSTRACT FROM AUTHOR]

Classic snap-through of curved beams, plates, and shells has long been an object of attention in structural engineering. Euler buckling under axial loading is perhaps an even more entrenched part of the canon of engineering education and practice. In this paper we introduce a relationship between the two phenomena, that to our knowledge has not been directly addressed before. The relationship shows that Euler buckling configurations are connected by the force–displacement curve under transverse loading. The results are used to develop a very simple metric to estimate the number of unstable static equilibria of a buckled structure based only on its geometry with no need for static or dynamic solvers. The study is focused on beams as this allows for an unambiguous discussion of the idea on the simplest possible structure. [ABSTRACT FROM AUTHOR]

Presence of flaws or cracks may cause substantial decrease in the strength of a component or structure. This kind of structural damage will accumulate over time, leading to significant decrease in ultimate load carrying capacity of structural members and premature brittle failure. In this paper, a coupled analytical and numerical study is implemented in order to evaluate buckling load of cracked cylindrical shells which is often encountered in the fields of civil engineering, offshore engineering and mechanic engineering. In the first phase of the study, buckling load of cylindrical shells with circumferential crack is investigated by treating the symmetric model as a cracked rectangular beam-column on an elastic foundation. The cracked beam-column is modelled as two beam elements on elastic foundation connected by an equivalent rotational spring and governing characteristic equation is obtained. Finite element models are used to verify analytical results and assess their accuracy, based on which good agreement is observed between analytical and numerical results. Effect of different parameters such as the length of cylinder, radial stiffness of cylinder, crack location and crack severity is studied on the axial load carrying capacity of such members. A simplified equation is proposed in order to calculate buckling load of tall cylindrical shells with a circumferential crack. In the second phase, the buckling load of cylindrical shells with a partial crack is studied using the results of finite element analysis on models with varying crack length. Based on the results of numerical analysis, an empirical equation is proposed to interpolate buckling load of these members between two limiting values, namely the buckling loads of same uncracked cylinder and the cylinder with circumferential crack. [ABSTRACT FROM AUTHOR]

This paper presents results of a numerical parametric study on elastic shear buckling of cold-formed steel channels with flat slotted webs. The study was performed on finite element models developed in ANSYS and validated against test data. The effects of perforation pattern, channel flange width, flange lip length, and aspect ratio on the elastic shear buckling load were investigated on the models with realistic and test setup boundary conditions. Equations for predicting the elastic shear buckling load of slotted channels were developed. The equations account for the effects of the studied parameters on the elastic shear buckling load of cold-formed steel channels with flat slotted webs and showed a good agreement with the finite element analysis results. [ABSTRACT FROM AUTHOR]

In practical engineering, the measured differential settlement can be gained by monitoring the points beneath the tank wall and it can induce the buckling of the tank even with a small amplitude. In general, Fourier series is adopted to decompose the measured differential settlement into harmonic components with various wave numbers. However, the question that which harmonic components should be considered is a main challenge for buckling investigations of the tank under measured differential settlement. In this work, a recommendation for harmonic components needed for consideration was proposed when decomposing measured differential settlement into harmonic components in terms of Fourier series. Moreover, the effects of the harmonic components considered on buckling behavior of floating roof tanks and conical roof tanks were discussed. The results presented that three monitoring points can make a first estimate of ovalling and the harmonic components considered should be smaller than and equal to [ N ]/3 ([] is the rounding function and N is the number of the monitoring points). The introduction of the harmonic component with a high wave number can cause the change of the buckling modes of the tanks under differential settlement, including floating roof tanks and conical roof tanks. Meanwhile, it can decrease the buckling strength of the floating roof tank more significantly than that of the conical roof tank. [ABSTRACT FROM AUTHOR]

The design of unbraced cold-formed steel beams must consider lateral-torsional buckling due to the low torsional stiffness associated with open cross-sections. The American Iron and Steel Institute incorporated design equations for the critical elastic lateral-torsional buckling stress in the North American Specification for the Design of Cold-Formed Steel Structural Members. These equations are based on elastic theory for singly-symmetric and doubly-symmetric sections. However, the equation for point-symmetric sections is only a rough approximation. Furthermore, there are no provisions for lateral-torsional buckling of non-symmetric sections, or sections oriented to non-principal axes. This paper investigates and develops a general formulation of the lateral-torsional buckling equation to broadly cover all cold-formed steel cross-sections. [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]

The Koiter–Newton method has been proved to be a computationally efficient method for buckling and post-buckling analysis of structures, using a novel reduced-order modeling strategy. In this paper, the existing method is extended for laminated composite plates with delamination. We develop a 4-node quadrilateral element S4DE as a geometric linear element in the co-rotational formulation of the Koiter–Newton method. The assumed layerwise displacement model of the developed element is enriched with Heaviside unit step functions to model delamination. The displacement fields of each layer are described using the superposition of first-order shear deformation and layerwise functions. The zig–zag theory is applied to enhance the numerical accuracy and computational efficiency of the developed element. The construction of the reduced order model requires derivatives of the strain energy with respect to the degrees of freedom up to the fourth order, which is two orders more than traditionally needed for a Newton based nonlinear finite element technique. The geometrical nonlinearities are taken into account using derivatives of the local co-rotational frame with respect to global degrees of freedom. Various laminated plates with different thicknesses, delamination lengths and stacking sequences are considered to validate the good performance of the present method in terms of numerical reliability, accuracy and computational effort. [ABSTRACT FROM AUTHOR]

Abstract When the sinusoidal buckling of suspended tubular strings is transforming to helical buckling, the deformation changes drastically, which makes the tubular strings extremely unstable. The quantitative description of this buckling configuration in previous theoretical studies is not precise enough. In our current study, dynamic relaxation method is applied to carry out numerical simulation of buckling transition of suspended tubular strings. To obtain stable buckling configurations, larger Rayleigh damping is used to attenuate the dynamic effect. With the increase of axial compression load, the lateral buckling of the suspended strings suddenly becomes spiral shape with two contact points. As the string length increases, the position of the lower contact point remains almost at the same position. While the upper contact point gradually moves upward, and the helix angle between the two points increases and gradually tends to be constant. The maximum contact force is located at the lower contact point, the maximum shear force is located at the bottom of the strings, and the dimensionless distance between the location of the maximum bending moment and the well bottom is about 1.0. These loads, including the maximum contact force, maximum shear force and maximum bending moment, gradually decrease with the increasing string length and tend to be constant. The dimensionless critical load is reduced from 4.41 to 3.81 with the effect of string length. The critical load calculated in this paper is the minimum value when helical buckling just occurs. The results obtained in the current study have wide engineering applications, particularly in failure analysis and prevention of helical buckling. Highlights • Stable buckling configuration is obtained by using dynamic relaxation method. • Quantitative description of buckling deformation, shear force, bending moment and contact force are obtained. • The critical load obtained is the minimum one when the helical buckling just happens. [ABSTRACT FROM AUTHOR]

Highlights • Thermal buckling analysis of FGM plates and cylindrical shells are investigated. • Finite element formulation based on a modified FSDT shell formulation is elaborated. • Introduction of parabolic distribution of transverse shear strains. • Applicability and usefulness of the present formulation is highlighted through numerical simulations. Abstract In this paper, the thermal buckling behavior of functionally graded plates and cylindrical shells is investigated. By considering a modified First order Shear Deformation Theory, the governing equations are elaborated. The kernel idea of the proposed model consists on assuming a parabolic distribution of the transverse shear strains across the shell thickness and imposing a zero condition of the transverse shear stresses on the top and bottom surfaces of the shell structure. Four nodes shell elements are adopted to solve the thermal buckling problem. The material properties are assumed to change continuously through the thickness according to a power-law distribution. In order to highlight the potentials of the present formulation, numerical investigations are conducted and compared with results available from the literature. The computation of the critical buckling temperature of structures under non-uniform temperature rise is based on Gauss numerical integration. The effects of material compositions, power law index, thermal loading, boundary conditions and geometrical parameters of shells on the thermal buckling behavior of FGM structures are also examined. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the thermal and mechanical buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates by using isogeometric analysis (IGA) based on modified couple stress theory (MCST). A refined hyperbolic shear deformation theory is used for buckling analysis, which satisfies free transverse shear stress conditions on the top and bottom surfaces of plate without a need for shear correction factor. The material properties of carbon nanotube reinforced composite plates are assumed to be temperature-dependent. For numerical analysis the IGA method using B-Spline or Non-Uniform Rational B-Spline (NURBS) functions is employed. The obtained results are compared with those available in the literature. Also, the influence of different parameters on mechanical and thermal buckling analysis is investigated. These parameters include material length scale parameter, boundary conditions, aspect and length-to-thickness ratios of plate, different types of FG-CNTRC distribution, volume fraction of CNTs and temperature dependency. [ABSTRACT FROM AUTHOR]

Abstract Buckling-Restrained Braced Frames (BRBFs) are among the common seismic resistant systems with many beneficial characteristics such as stable cyclic behavior and high energy dissipation. However, recent studies have shown that BRBFs are susceptible to residual deformations during earthquakes which makes them vulnerable to aftershock events. The aim of the current study is to investigate the aftershock collapse capacity of BRBFs. In the first part of the paper, simplified procedures including IDA and collapse fragility analyses are carried out to gain more insight regarding the residual drift and collapse capacity of the intact frames. Then, aftershock fragility assessment is conducted for several damage states, to highlight the influence of post-mainshock residual drifts on the collapse of the structures. As for the second part, a detailed probabilistic framework is introduced and utilized to include the effects of upcoming aftershocks on the annual collapse probability of the structures. Results show that aftershock can highly intensify the structural response especially when the structure tolerates large residual drifts during the mainshock. Highlights • Aftershock collapse fragilities of BRB frames have been calculated. • A simple methodology has been introduced to calculate the overall collapse risk. • Collapse risk of BRBFs were determined based on MS-only and MS-AS scenarios. • The proposed methodology can be utilized for any general structural system. [ABSTRACT FROM AUTHOR]

Abstract This study introduces a new quasi-3D (three-dimensional) higher-order shear deformation theory (HSDT) capable of accounting for the through-thickness deformations with only four unknowns, which is suited to the numerical method for buckling analysis of functionally graded material (FGM) plates in thermal environments. The refined quasi-3D HSDT is incorporated into the improved meshless radial point interpolation method (RPIM) in order to scrutinize the thermal buckling responses of FGM plates. In the improved RPIM, the radial basis function is presented in a compactly supported form to build the shape functions without any fitting parameters. Parametric studies on the buckling behavior of FGM plates under various types of through-thickness temperature changes are conducted and the effects of temperature distribution on the plate surface are investigated. Results illustrate the accuracy of the proposed meshless method based on the refined quasi-3D HSDT and the improved RPIM for predicting the thermal buckling behavior of FGM plates. [ABSTRACT FROM AUTHOR]

Time depended deformation and critical buckling load of viscoelastic thick plates were studied using finite strip method with the trigonometric functions in longitudinal direction and the polynomial functions in transverse direction. The plates were considered to be thick and the third order shear deformation theory was used to consider the effect of shear stresses in thickness. The mechanical properties of the material were considered to be linear viscoelastic by expressing the relaxation modulus in terms of Prony series. Time history of maximum deflection of viscoelastic plates subjected to transverse loading and unloading on plates was calculated using a fully discretized formulation. In addition, the critical in–plane load of plates was calculated by a nonlinear procedure in different times of loading. Moreover, the effect of thickness and the interaction of biaxial in–plane loading on critical load of plate were studied. [ABSTRACT FROM AUTHOR]

Abstract In this study, bending, free vibration, and buckling response of functionally graded porous micro-plates are investigated using the classical and first-order shear deformation plate theories. The Navier solution technique is utilized to obtain analytical solutions to simply supported rectangular plates. A power-law distribution is used to model the variation of two material constituents through the plate thickness. Three different porosity distributions are considered and assumed to take forms of cosine functions. The microstructure-dependent size effects are captured using the modified couple stress theory. Numerical results of bending, free vibration, and buckling are presented to determined the effects of constituent material variation, microstructure-dependent size effects, and porosity distributions on the mechanical response of functionally graded porous micro-plates. [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]

An effective way for improving the global load-carrying capacity of a steel arch with a welded hollow section is to increase the height of its webs. However, the high and thin web may buckle locally, which will affect the global load-carrying capacity and should be taken into account in predicting the global strength of the arch. This paper presents a numerical investigation for the in-plane strength and design for pin-ended circular steel arches with a welded hollow section, focusing on the effects of web local buckling by the large deformation inelastic analysis in association with a finite shell element model. The circular steel arches subjected to a radial load uniformly distributed along the arch length, a load uniformly distributed over the full span of the arch, or/and over the half span of the arch and their various combinations are considered in the investigation of their failure modes and strengths. The initial global and local geometric imperfections as well as residual stresses are included in the finite element model. It is found that web local buckling influences the global strength of the steel arches significantly and needs to be accounted in formulate their strength design formulas. The parameters related to the web local buckling and global buckling of the arch are thoroughly explored. It is found that the stability coefficients of arches under the nominal uniform axial compression are related to the equivalent normalized web height-to-thickness ratio of the cross-section and the normalized slenderness of the arch, and accordingly the design formula of the stability coefficients is proposed by including their effects. In addition, a design formula for predicting the strengths of the arches under a load uniformly distributed over the full span is developed by introducing a corrective coefficient into the stability coefficient, and it is found that the corrective coefficient is related to the arch rise-to-span ratio and slenderness of the arch. Furthermore, a general interaction design formula is developed for predicting in-plane strength of the arches under general in-plane loading such as a load uniformly distributed over the half span of the arch and various combinations of a full span uniform load and a half span uniform load. Comparisons with the finite element results demonstrate the proposed design formulas can provide good predictions and/or lower bound predictions for the strengths of the steel arches with a welded hollow section [ABSTRACT FROM AUTHOR]