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To investigate the mechanical deformation characteristics of the 'Segment-SCC-Steel Tube' combined bearing lining structure under internal and external pressure, the loading device and monitoring system for the stability analysis of the full-scale lining were proposed. The effect of cracked encased concrete and local external pressure on the instability mode of thin-walled steel pipes was explored by full-scale model experiment and three-dimensional FEM numerical simulation. The influence of SCC (Self-Compacting Concrete) and stiffening rings on the stability of steel pipes subjected to external pressure was discussed. The results show that SCC cracks occur and intensify with increasing internal pressure. The external water acts directly on the steel tube through cracking, resulting in wavy deformation, and the gap between the SCC and steel tube further increases. When calculating the critical external pressure for the steel pipe, the constraint of encased concrete can be ignored, and only the constraint effect of the stiffening ring can be considered. Therefore, the Von Mises formula was used to predict the critical external pressure between the stiffening rings with high accuracy. In addition, the stiffening ring can mitigate the crack propagation of nearby SCC. The steel tube remained in the elastic stage under internal pressure. In the full-scale experiment, the external pressure could not continue to rise after reaching 0.65 MPa. Nevertheless, the amplitude of the buckling wave continued to increase. It is considered that the steel pipe is in an unstable state, and the failure mode is dominated by single-lobe buckling. • According to the performance of the 'Segment-SCC-Steel Tube' lining structure, the influence of cracked encased concrete and local external pressure on the buckling mode of steel pipes is investigated. • The loading device of the full-scale model test is proposed for the external pressure stability analysis of the 'Segment-SCC-Steel Tube' lining structure, and the monitoring system combining distributed optical fiber and traditional vibrating wire sensors is established. • The mechanical deformation characteristics of the SCC and Steel Tube lining under internal and external pressure are revealed, and the influence of SCC and stiffening rings on the stability of steel pipes under external pressure is discussed. [ABSTRACT FROM AUTHOR]

This paper presents a large deformation Kirchhoff–Love shell model hierarchically enhanced with through-the-thickness warping functions, arbitrarily chosen by the user. Two unknowns are introduced for each of them, representing its amplitudes in two directions tangent to the shell surface. NURBS are used to approximate reference surface displacement and warping amplitudes in the weak form. The transverse shear strains are linear functions of the warping parameters only and naturally free from locking. A patch-wise reduced integration avoids membrane locking and improves efficiency. Particular attention is paid to the modeling of composites made up of multiple stiff layers coupled with soft interlayers. The alternating layup with high stiffness ratios induces a significant sectional warping with transverse shear strains concentrated in the soft layers. Two warping models are investigated: (WI) all stiff layers maintain the same director orthogonal to the deformed surface with independent transverse shear deformations of the soft layers; (WZ) a single zigzag function linking these deformations. The numerical tests confirm the great accuracy of the hierarchic shell model in reproducing the solid solution with a small number of discrete parameters, provided that the correct warping model is chosen. WI is reliable for all alternating layups. WZ reduces the unknowns to five per surface point, regardless of the number of layers, and is accurate for uniform soft layers. • The Kirchhoff–Love composite shell is enhanced with warping. • The hierarchic approach is used for large deformations. • Transverse shear strains and zigzag effects are included. • An accurate and efficient isogeometric formulation is proposed. • Two warping models are studied for stiff/soft layups. [ABSTRACT FROM AUTHOR]

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

Highlights • 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]

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 • The differential system is solved with low computational cost. • The numerical results indicate a very good performance of the 6DE model proposed. • The 6DE model allows to obtain the equivalent properties for the beam-column model. • Practical expressions for the buckling loads exhibit an excellent agreement. Abstract Lattice towers and guyed masts are frequently used in the telecommunication industry, particularly to support antennas. These structural systems comprise a large number of elements (mainly, legs and diagonals) and for this reason, their representation by equivalent models is quite common and convenient. In a previous study, the authors derived a continuous model of a spatial lattice governed by nine differential equations (9DE). The legs trace forms a triangle and the diagonals with a zig-zag pattern are contained in three planes that join each two legs, defined as Pattern 1. Here and starting from an energy statement, the structural behavior of a 1D continuous model governed by six differential equations (6DE) which leads to a simpler representation of the lattice structure, is stated. This formulation considers the shear flexibility and the second order effect due to axial loads. Also, the inertial forces due to the legs and diagonals masses are taken into account. Numerical examples dealing with deflections, critical buckling loads and natural frequencies are solved with this 1D model. The results are compared with the outcomes found with finite element methods. A very good performance is attained with the proposed model. Finally, the equivalent properties for other patterns of diagonalization (Patterns 2, 3 and 4) different to the studied as well as the formulas to find the critical loads are included in Appendices. [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]

Abstract This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles. [ABSTRACT FROM AUTHOR]

Abstract The result of an experimental programme investigating a novel technique to strengthen web plates of steel plate girders against breathing fatigue due to shear buckling deformations is presented. An experimental test series is present in which six specimens were manufactured to simulate the end panel of a plate girder; these were strengthened with an optimized FRP retrofit panel that was developed in an earlier phase of the research project, and tested for plate girder web shear buckling deformation mitigation under repeated cyclic loading, as well as ultimate load capacity enhancement. Test results and non-linear finite element modelling demonstrated the efficiency of this technique for stiffening the web against these deformation and thus reducing the critical stresses, consequently increasing the fatigue life of the girders by a factor ranging between three and seven, depending on the applied stress range and the fatigue resistance assessment method. The research demonstrates the applicability of this novel FRP strengthening technique to prolong and extend the fatigue life of existing plate girder bridges. [ABSTRACT FROM AUTHOR]

Abstract A bio-inspired concept of non-uniform curved grid-stiffened composite structures with embedded stiffeners (embedded NCGCs) is proposed in the paper. Shallow curved stiffeners are embedded in the laminate skin to form an integrated structure to improve the skin–stiffener deformation compatibility. A method named streamline stiffener path optimization (SSPO) based on multiscale modeling is proposed for curved stiffener layout design of embedded NCGCs. Firstly, the homogenization-based global/local analysis is used to calculate structural responses on a global unstiffened model with the equivalent material properties obtained from local representative cell configurations (RCCs). Secondly, the discrete distribution of 2D curved stiffener paths is transformed into a continuous distribution of the streamline function values (SFVs) on a 3D level set surface. The stiffener path description using the streamline function is similar as the level set method with specific constraints. Projections of points with the same integral SFVs will form one stiffener path. Thirdly, optimal curved stiffener layout is achieved using shape design of local parallelogram representative cell configurations with analytical sensitivities calculated using the affine mapping from the square master domain to the parallelogram RCCs. Fourthly, stiffener spacing and angle constraints are added for manufacturing considerations and local buckling resistance, and optimization design is implemented to maximize the buckling load within a given weight. Finally, numerical examples of a square laminated panel under uniaxial and biaxial compressions validate the effectiveness of the proposed SSPO method and indicate the significant improvement of the buckling loads by steering the stiffener paths. Highlights • Bio-inspired shallow stiffeners embedded inside the laminate skin is proposed. • Curved stiffener layout optimization is solved based on multiscale modeling. • Curved stiffener paths are interpreted using the streamline functions. • Parallelogram representative cell configurations provide analytical sensitivities. [ABSTRACT FROM AUTHOR]

Abstract Empirical expressions for estimating the maximum induced strain on buried steel pipelines crossing strike-slip faults are proposed. These expressions have been obtained through parametric studies involving finite element analyses of 18 different case loads of buried pipelines. The pipe and its soil surrounding were modeled in Abaqus software with shell and solid elements, respectively. Pipelines with different values of diameter, thickness, yielding strain and ultimate stress were analyzed under different values of fault displacement and pipe-fault crossing angle. The obtained response databank was used to develop empirical relations providing the maximum pipe strain in terms of geometrical, material and faulting characteristics of the problem. These expressions describe both the tensile and compressive modes of deformation and can be used in practice for the estimation of the maximum induced strain during the seismic design and/or evaluation of pipelines. It was found that the pipe type, bending angle and fault offset have pronounced effects on the behavior of the fault-crossing pipeline. On the other hand, the response of the pipeline was shown to be insensitive to the crossing angle due to the large strain caused by the section deformation, which occurs at any crossing angle. Highlights • The pipe-fault crossing problem is studied. • Empirical expressions for the prediction of maximum induced stain in pipe body are proposed. • Pipe type, bending angle, and fault offset have crucial effect on the induced strain in pipe body. • Pipe-fault crossing angle is less influential on the induced strain in pipe body. [ABSTRACT FROM AUTHOR]

Buckling is one of the main challenges in thickening the sidewall of a deep drawn cup. To overcome this problem, a novel sheet-bulk forming method, upsetting with a controllable deformation zone, was developed in this study to prevent the buckling during sidewall thickening. In this method, the material from the protective cavity of the die is pushed into the forming cavity under a counter force to establish a stabilised deformation zone, which can eliminate the limitation of the initial slenderness ratio in conventional upsetting methods. The experimental and simulated results reveal that the occurrence of buckling can be successfully avoided through upsetting with a controllable deformation zone. The forming load tends to remain unchanged because of the existence of a stable deformation zone. Additionally, the forming quality can be improved, and a uniform distribution of hardness in the cross section can be obtained, thereby improving the performance-in-service. [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]

Abstract Purlins are usually connected to roof sheeting by sliding-clips, while wall sheeting is often screw-fastened to girts. This paper investigates the buckling of such two types of parallel purlin/girt systems inter-connected by multiple lines of sag rods. One single purlin braced by one sag rod at any place along the span is first analyzed, and its buckling deformation at any cross-section is seen as a flexibility coefficient which is then used to study the buckling of the purlin braced by multiple sag rods along span. A flexibility matrix is constructed, whose eigenvalues are the base of critical equations. In the case where the sag rods are placed with equal spaces along span, the eigenvalues are expressed in explicit forms, of which each represents one buckling mode. Threshold stiffness of the sag rods are presented for multiple sag rod bracings for these two types of sheet-to-purlin connection. Based on the findings of this paper, the differences of buckling behaviors between these two types of purlin systems have been revealed. The effect of local deformation of the web at the sag rod connecting points on the sag rod stiffness is also included. Parallel purlin systems are then investigated in a compact matrix form. After carrying out matrix operations and slight approximations, a key parameter is found to be used to reflect the effect of the number of purlins and zig-zag layout of sag rods in adjacent bays on the effective sag rod stiffness. Highlights • Buckling of parallel purlins braced by multiple lines of sag rods is studied. • Rotational restraints of roof sheeting to purlins are considered. • The reduced effectiveness of the sag rods are revealed systematically. • It's found parallel purlins can be analyzed as if they one single-purlin-system. • Two types of purlin-to-sheeting connections are analyzed and compared. [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]

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]

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]

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]

This paper presents a two-variable first-order shear deformation theory considering in-plane rotation for bending, buckling and free vibration analyses of isotropic plates. In recent studies, a simple first-order shear deformation theory (S-FSDT) was developed and extended. It has only two variables by separating the deflection into bending and shear parts while the conventional first-order shear deformation theory (FSDT) has three variables. However, the S-FSDT provides incorrect predictions for the transverse shear forces on the insides and the twisting moments at the boundaries except simply supported plates since it does not consider in-plane rotation. The present theory also has two variables but considers in-plane rotation such that it is able to correctly predict the responses of plates with any boundary conditions. Analytical solutions are obtained for rectangular plates with two opposite edges that are simply supported, with the other edges having arbitrary boundary conditions. Numerical results of deflections, stress resultants, buckling loads and natural frequencies are presented with the FSDT, the S-FSDT and the present theory. Comparative studies demonstrate the effects of in-plane rotation and the accuracy of the present theory in predicting the bending, buckling and free vibration responses of isotropic plates. [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]

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]

Understanding the failure mechanisms of the buckling process of glass fiber composites based on acoustic emission (AE) signals is a challenging task. In this work, a method combining AE with digital image correlation (DIC) was used to monitor compressive buckling behaviors of delamination composites. The analysis of AE signals is based on the k-means algorithm and principal component analysis (PCA). According to PCA, three characteristic parameters of AE signals like amplitude, peak frequency, and RA value (rise time divided by amplitude), are selected for cluster analysis by k-means algorithm. The results show that the AE signals of the compression process can be divided into three clusters. The three clusters correspond to three kinds of damage modes such as matrix cracking, fiber/matrix debonding, delamination and fiber breakage. The characteristic frequency of each mode is found by cluster analysis. Besides, the size and position of delamination defects result in the reduction of mechanical properties of the glass fiber composites. The complementary technology combining AE with DIC is effective for damage monitoring of the composites. Clear changes of the displacement fields can accurately detect the damage location and degree of the specimen. [ABSTRACT FROM AUTHOR]

In the present work, elastic stability analysis of curved nanobeams is investigated using the differential constitutive law consequent to Eringen's strain-driven integral model coupled with a higher-order shear deformation theory accounting for through thickness stretching effect. The formulation developed here is general in the sense that it can be deduced to realise the influence of different structural theories and analyses of nanobeams. The governing equations derived are solved employing finite element method using a 3-nodes curved beam element. The model developed here is validated considering problems for which analytical/numerical solutions are available in the literature. For comparison purpose, results are also presented for various structural theories obtained from the present formulation. The influence of structural and material parameters such as thickness ratio, beam length, rise of the curved beam, boundary conditions, and size-dependent or nonlocal parameter are brought out on the buckling behaviours of curved nanobeams. It is observed that the type of buckling mode pertaining to the lowest critical value can be different depending on geometrical and internal material length scale parameter, and boundary conditions. [ABSTRACT FROM AUTHOR]

This paper reports on experiments addressing the buckling and collapse behavior of common built-up cold-formed steel (CFS) columns. The built-up column consists of two individual CFS lipped channels placed back-to-back and connected at the web using two self-drilling screw fasteners at specified spacing along the column length. The experiments aim to quantify ultimate strength, composite action, member end fixity, and buckling interactions and collapse behavior for common built-up CFS members. The testing also explicitly explores the effect of sheathing, as typically employed in cold-formed steel framing, on the response. The experiments provide benchmarks for design that include specific considerations for both thin-walled buckling and fastener behavior. A total of 17 monotonic, concentric compression tests with a column length of 1.83 m (6 ft) are completed with an array of position transducers monitoring displacements at key locations. Tests are conducted with the built-up member seated in CFS tracks. Results indicate a large range of deformation behavior, with local-global interaction and flexural-torsional modes common in many of the unsheathed specimens. Columns sheathed with oriented strand board on both flanges behave as braced against global buckling in the plane of the wall, and local buckling induced failures prevail. The end condition for the tested built-up members seated in track is determined to be semi-rigid, but generally closer to fixed than pinned. [ABSTRACT FROM AUTHOR]

A high-dimensional variable design space in optimization problems for tapered composite structures presupposes a development of efficient computational techniques to improve the design efficiency and flexibility. In this work, a mathematical model for optimization of tapered composite structures with buckling and manufacturing constraints is developed, then a ply-drop-based global blending model (GBM) is suggested to address the layers’ addition/deletion and blending problems. Within the framework proposed in Part I of this work (Compos Struct, 2016, 154: 106-128), by incorporating the global blending model, operations of add-layer, exchange-blend and sequence-adjustment are revised and enhanced. The GBM can not only characterize the global blending property, but also guide the maximum blending design. Accordingly, the design framework is simplified, and its computational cost is reduced significantly since there is no iteration of shape prediction and stacking-sequence optimization procedure. An 18-panel benchmark problem is adopted to verify the enhanced design framework, as compared with previous design results, the obtained better solution with higher efficiency implies its feasibility and potential for effective design of tapered composite structures. [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]

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]

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]

The purpose of this paper is to present optimal designs for variable stiffness laminated composite truncated cones under lateral external pressure. The objective is to maximize the failure load which is defined as the minimum of the buckling load and the first-ply failure ( FPF ) load. The numerical results are obtained using a semi-analytical degenerated shell element based on a refined first-order shear deformable shell theory and the influences of the pressure stiffness ( PS ) and the thickness/radius ratio are taken into account. A 2D degenerated shell element is also used for verification purposes. Results are presented for the related verification problems solved and the semi-analytical shell element is validated. Optimal designs, where FPF and buckling are imposed as design constraints, are presented for laminated composite thin and relatively thick cones having variable thickness and ply-angle. A simple graphical optimization technique and a modified Micro-Genetic Algorithm are employed. It is shown that, FPF constraint may be active for thicker cones having lower cone angles, PS slightly decreases the buckling pressures, and the stacking sequence has considerable influence on the failure load. The numerical results presented show that restraining the large end against rotation significantly increases the failure load. [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 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 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]

This study investigates the stability of the structural systems assembled by system scaffolds. Loading tests were conducted on the indoor single-bay system scaffolds and the outdoor full-scale structural system assembled by system scaffolds. Test results were compared with the second-order inelastic analysis with semi-rigid joints to determine the reliability of various analytical parameters. The study reveals that, while the failure model of the single-bay two-storey system scaffold without diagonal braces is overall buckling failure of the structure, the failure model of the same structure with diagonal braces is buckling failure of the vertical standards between the upper and lower storeys. The critical load of the configuration with diagonal braces is about double that of the same structure without diagonal braces. At the moment of buckling failure of the outdoor full-scale two-row, two-bay, six-storey structural system assembled by system scaffolds, the vertical standards at the four corners appeared to have large horizontal displacements owing to without diagonal braces. However, the vertical standard in the center did not exhibit obvious horizontal deformation because it was reinforced with diagonal braces on four sides. In addition, the use of diagonal braces can significantly increase the load capacity of vertical standards. This study recommends that all vertical standards be reinforced with diagonal braces to ensure the load capacity of the structural systems assembled by system scaffolds. A second-order inelastic analysis with semi-rigid joints and various notional lateral forces is recommended to determine the critical loads of full-scale structural systems assembled by system scaffolds. [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]

This study investigated the buckling of nontypical prolate domes subject to hydrostatic external pressure. The domes were shells of revolution with an egg-shaped configuration, with a base diameter and height of approximately 160 and 121 mm, respectively. Four laboratory-scale egg-shaped domes, cold-pressed from a 1-mm 304 steel sheet, were measured for geometry, tested to collapse, and analysed numerically. The experimental results and numerical evaluations were well consistent. Furthermore, the buckling behaviours of a perfect egg-shaped dome, a capacity-equivalent hemisphere, and a mass-equivalent hemisphere were numerically studied. The results indicate that the prolate egg-shaped dome has a relatively large load-carrying capacity that is not highly sensitive to material plasticity and geometrical imperfections. [ABSTRACT FROM AUTHOR]

We investigate the mechanical stability of L-section and T-section composite struts with single edge delamination. We propose a solution procedure based on a layerwise theory and the first order shear deformation theory by taking into consideration of the von Karman geometrical nonlinearity. We derive the nonlinear equilibrium equations according to the minimum total potential energy principle, and solve them using Rayleigh–Ritz method and Newton–Raphson method. In modeling the delaminated L-section and T-section struts, we divide the structures into regions, and exert continuity conditions between different regions. The proposed model is capable of analyzing both local buckling of the base laminate and sublaminate as well as the global buckling of the whole structure. We present numerical results to provide an insight into effects of size of delamination on buckling mode and post-buckling behaviors of the struts. We perform the three-dimensional finite element analysis using the ABAQUS commercial software. The results show a very good agreement with those obtained by the analytical method. The results indicate that the presence of delaminations not only reduces the load-carrying capacity of open section struts remarkably, but also plays a pivotal role in the critical buckling load and buckling mode shape of the struts. [ABSTRACT FROM AUTHOR]

A finite element method is developed for the stiffened multi-layered airfoil/hydrofoil structure for the large deformation and finite strain problem. The kinematics of the airfoil/hydrofoil is set up. The Consistent Orthogonal Basis Function Space is applied for the airfoil/hydrofoil structure. Given the airfoil/hydrofoil configuration and boundary conditions, the basis function space can be uniquely determined, such that the diagonal mass matrix is obtained accurately and the basis functions are very identical with the mode shape functions of the structure. In order to satisfy the displacement compatibility condition between adjacent layers of the airfoil/hydrofoil, the traction degree-of-freedom is also induced. The post buckling analysis is presented for the wing (hydrofoil) structure of the underwater glider. The water pressure is applied on the outer surface and the critical buckling pressure is calculated. The post buckling equilibrium path is also given. The results are verified with ANSYS. The present study of the buckling analysis of the airfoil/hydrofoil under water pressure is helpful to the design of underwater glider. [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]

Thin-walled composite beams of complex sectional contour are widely used along with the traditional elements of reinforced structures. Based on the generalized theory of elasticity of thin-walled beams, the mathematical model of flexural–torsional deformation of open-profile thin-walled composite beams of non-uniform cross section under thermo-mechanical loading has been developed. To confirm the reliability of developed approach to determination of the spatial displacements of thin-walled composite beams of non-uniform cross section, several experimental studies were conducted. Based on the analysis of the range of typical profiles, for the further analysis we selected several compound cross sections for which the analytical dependences were obtained regarding displacements of their characteristic points. Our studies can serve as a base for development of the practical recommendations for the optimal designing and manufacturing of thin-walled anisotropic profiles, as well as proposing the measures to reduce the value of deformations caused by the production process. [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]

It is the aim of this paper to show the mechanisms behind the experimental observations of rather smooth sigmoidal deformations in bi-crystal micropillar tests (in contrast to single crystal micro-compression tests) and to point out that the appearance of such deformation modes are a further reason for being careful when interpreting the force-axial displacement behavior in terms of stress-strain curves. Instabilities, i.e., buckling and subsequent post-buckling deformations, inhomogeneous strain fields and substantial deformations of the base as well as pronounced free surface effects are considered. The influences of imperfections and of friction as well as a possible clearance in the guidance of the loading device are taken into account, too. From these studies, the experimenter may get information how and with which limitations material parameters can be obtained from such compression tests in combination with simulations. [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]

Buckling behaviors of elastoplastic ceramic/metallic functionally graded material (FGM) rings are investigated by using the first order shear deformation theory. The hydrostatic-pressured rings are assumed to be in both the plane-stress case and the plane-strain case, which lead respectively to a uniaxial and a biaxial elastoplastic stress states in prebuckling stage. A uniform strain hypothesis helps to deal with the elastoplastic stress states. By introducing in the graded material properties, the constitutive model of FGMs is formulated under the framework of J 2 deformation theory. By considering the kinetic relations of von-Kárman type and employing the principle of virtual displacement, the equilibrium equations and the buckling governing equations of FGM circular rings are formulated, and the analytical solution of the anisotropic rings is obtained. Finally, the elastoplastic buckling problem is numerically solved through a semi-analytical method, which is proposed to seek the real circumferential strain of FGM rings at the buckling point and determinate the elastoplastic buckling critical hydrostatic pressure. The effects of the inhomogeneous and geometrical parameters on the buckling critical load and the position of the elastoplastic interface are discussed. Results show that, in both the plane-stress and the plane-strain cases, the elastoplastic critical loads are generally lower than their elastic counterparts due to material flow, and the plane-strain critical load is generally larger than the plane-stress one. The elastoplastic critical load does not always decrease monotonously with the increase of the inhomogeneous parameters, which is quite different from their elastic counterparts. [ABSTRACT FROM AUTHOR]

Buckling due to diffusion-induced compressive stress has been observed during the lithiation of various nanowires, and can affect the mechanical and electrochemical performance of nanowire-based electrodes. This study is focused on the diffusion-induced buckling of nanowires. Two diffusion paths are analyzed; one with radial diffusion only, and the other with axial diffusion. For the diffusion-induced buckling of nanowires with radial diffusion, the theory of large deformation is used in the description of the coupling between mass transport and deformation in large deformed solids. Using the linear theory, analytical solution of the critical length of a nanowire, below which there is no buckling, is obtained, which is dependent on the constraint of the ends of the nanowire and the volumetric strain of the nanowire at the fully lithiated state. The comparison between the linear analytical solution of the critical length and the numerical solution from the theory of large deformation shows that the linear analytical solution is valid for the influx less than 1 mol · m −2 · s −1 and configurations considered in the work. Numerical analysis shows that the critical buckling time decreases with the increase of nanowire length and current density, and the nanowire with two fixed ends has a larger critical buckling time than that for the same nanowire with a fixed end and a pinned end. The nanowire length plays a bigger role in determining the critical state of charge for the onset of the buckling than that of the diffusion flux. The state of charge ( SOC ) at the state of critical buckling decreases with the increase of the nanowire length and increases with the increase of current density. For the diffusion-induced buckling of nanowires with axial diffusion, numerical analysis is performed. The numerical result reveals similar trend, i.e., the critical buckling time decreases with the increase of nanowire length and current density. The comparison of the critical buckling times for the conditions with axial diffusion, radial diffusion and diffusion from all sides, respectively, reveals that the contribution from axial diffusion is negligible even for small aspect ratio, and it does not change significantly with the increase of the aspect ratio. [ABSTRACT FROM AUTHOR]

The worst geometric imperfection is a mathematical concept which should deliver in theory a lower bound for the buckling load of unstiffened cylindrical shells. The corresponding knock-down factors could be used as base for improved shell design guidelines in order to reduce weight and cost of unstiffened shells. Commonly used worst geometric imperfections include eigenmode or axisymmetric imperfection pattern. However, experimental results show that buckling failure is induced by an isolated single dimple which can be classified as a realistic worst geometric imperfection. It is hypothesized that the interaction between single dimple motion and the deformation behavior in the pre-buckling range of cylindrical shells significantly influences the buckling load. A numerical model is proposed in order to study the before mentioned thesis. The results show that the proposed numerical model induces a physical meaningful and realistic buckling response in a cylindrical shell. It can be validated that the interaction between single dimple motion and the deformation behavior of a cylinder in the pre-buckling range significantly influences the buckling load. Based on experimental data it can also be shown that the lower bound of the buckling load is accompanied by a characteristic post-buckling pattern shortly after collapse. [ABSTRACT FROM AUTHOR]

This paper presents a finite element model based on the first-order shear deformation theory for free vibration and buckling of functionally graded beams. The present element has five nodes and ten degrees-of-freedom. Material properties vary continuously through the beam thickness according to the power-law form. Governing equations are derived with the aid of Lagrange's equations. Natural frequencies and buckling loads are calculated numerically for different end conditions, power-law indices, and span-to-depth ratios. Accuracy of the present element is demonstrated by comparisons with the available results. [ABSTRACT FROM AUTHOR]