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In this research, the buckling behavior of long columns under dynamic load was investigated both experimentally and numerically, and an effective buckling criterion for dynamic load was derived from the results in terms of the impact velocity and the slenderness ratio. In the experiments, a free fall drop-weight type impact testing machine was employed. The dynamic buckling loads were measured by the load sensing block, and the displacements were measured by a high speed magnetic-resistance device. In the numerical analyses, dynamic FEM code 'MSC-Dytran' was used to simulate the typical experimental results, and the validity and the accuracy of the simulations were checked. The dynamic buckling loads at various impact velocities were then systematically investigated. From both experimental and simulated results, it was found that the dynamic to static buckling load ratios can be successfully described as a square function of the slenderness ratio of the columns, while they can be also described by a power law of the applied impact velocity.

This paper investigates the prebuckling dynamics of transversely isotropic thin cylinder shells in the context of propagation and reflection of axial stress waves. By constructing the Hamiltonian system of the governing equation, the symplectic eigenvalues and eigenfunctions are obtained directly and rationally without the need for any trial shape functions, such as the classical semi-inverse method. The critical loads and buckling models are reduced to the problem of eigenvalues and eigensolutions, in which zero-eigenvalue solutions and nonzero-eigenvalue solutions correspond to axisymmetric buckling and nonaxisymmetric buckling, respectively. Numerical results reveal that energy is concentrated at the unconstrained free ends of the shell and the buckling modes have bigger bell-mouthed shapes at these positions.

Performing a dynamic buckling analysis of structures is more difficult than carrying out its static buckling analysis counterpart. Some structures have a nonlinear primary equilibrium path including limit points and an unstable equilibrium path. They may also have bifurcation points at which equilibrium bifurcates from the primary equilibrium path to an unstable secondary equilibrium path. When such a structure is subjected to a load that is applied suddenly, the oscillation of the structure may reach the unstable primary or secondary equilibrium path and the structure experiences an escaping-motion type of buckling. For these structures, complete solutions of the equations of motion are usually not needed for a dynamic buckling analysis, and what is really sought are the critical states for buckling. Nonlinear dynamic buckling of an undamped two degree-of-freedom arch model is investigated herein using an energy approach. The conditions for the upper and lower dynamic buckling loads are presented. The merit of the energy approach for dynamic buckling is that it allows the dynamic buckling load to be determined without the need to solve the equations of motion. The solutions are compared with those obtained by an equation of motion approach.

Functionally graded carbon nanotube reinforced nanocomposites have drawn great attention in both research and engineering communities. The weak interfacial bonding between carbon nanotubes and the matrix, which traditionally hinders the application of carbon nanotube reinforced nanocomposites, can be remarkably improved through the graded distribution of carbon nanotubes in the matrix. Within the framework of classical beam theory, this paper investigates the dynamic buckling behavior of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes and integrated with two surface bonded piezoelectric layers. The governing equations of the beam subjected to an applied voltage, a uniform temperature and an axial periodic force are derived by applying Hamilton's principle. Numerical results are presented for beams with different distribution patterns and volume fractions of carbon nanotubes and end support conditions. The influences of the beam geometry, temperature change, applied voltage, static axial force component, boundary condition, carbon nanotube volume fraction and its distribution on the unstable regions of FG-CNTRC piezoelectric beams are discussed in detail.

This paper presents an analytical investigation on dynamic buckling of cylindrical shells with general thickness variations under exponentially increasing external pressure over the time. Different from the previous studies in literatures, the shell thickness varies arbitrarily and is common in actual engineering, which leads to failure of the existing methods. A new analytical method is first developed to solve the fourth-order governing partial differential equations with variable coefficients for the shell subjected to varying external pressure. Then the asymptotic formulae for dynamic buckling loads considering general thickness variations are derived and expressed by geometry sizes of the shell and thickness variation functions. To validate the presented results, two specific non-axisymmetric thickness cases are discussed in detail. The critical dynamic buckling loads show a great agreement with the previous ones by other researchers for simple and axial thickness variation situation. Finally, example calculations and parametric discussion are performed, and influences of thickness variation types, speed of external pressure and the power exponent of time on the critical dynamic buckling loads are discussed.

Unstiffened plates in structures are usually welded or fastened to supporting members, providing rotational restraint stiffness to the plate. Previous studies have shown that neglect of rotational restraint stiffness at the edges of a plate in a structure can introduce deviations in the analysis of dynamic elastic buckling. In this study, the in-plane impact-induced dynamic elastic buckling responses of isotropic imperfect unstiffened plates with four elastically restrained edges are analytically investigated, based on the large-deflection theory of thin plate. The evolution of the peak deflection predicted by the proposed analytical method is found to be consistent with the responses available from the literature. Then the method is further used to estimate the deformation map of an unstiffened plate with four elastically restrained edges, and the effects of rotational restraint stiffness, initial geometric imperfection and shock duration on the dynamic buckling response of the plate are examined. The results show that the critical dynamic buckling load and the maximum deflection response of the plates are significantly influenced by the rotational restraint stiffness as well as the first-order initial geometric imperfection, and thus cannot be neglected in the analysis of dynamic buckling.

The stability of structures is an important aspect that the designer must pay particular attention to in order to ensure safety against collapse. This investigation is concerned with analytical and numerical analyses of the dynamic buckling of plane structures. A rigorous mechanical model is proposed, consisting of a beam-column element with nodal ends possessing two rotational springs of rigidities acting in parallel with the bending stiffness of the beam-column. The model is first analyzed with respect to the dynamic behavior by investigating the influence of the variation in the stiffness of the nodal springs on the fundamental frequency of the proposed mechanical model. Compression axial loading is applied to the beam-column in order to study the nonlinear dynamic behavior by introducing buckling. This novel approach is used to highlight the interaction between the fundamental frequency and the critical buckling load. Simple examples are treated using the approach and the results are compared with those obtained from a global analysis. The results revealed that it is possible to reproduce the stability analysis of a global structure by simply analyzing a target element, taking into account all elements adjacent to it with less than 1% error on the results.

This paper focuses on dynamic buckling of composite structures subjected to impulse loads. Using the Lyapunov exponent, the Budiansky–Hutchinson criterion is improved and its algorithm is constructed. Based on it, the nonlinear dynamic buckling loads are evaluated for typical composite structures such as a fiber-reinforced composite plate, composite laminated cylindrical shells and a laminated plate with delaminations and matrix cracks that are all subjected to impulse loads. The improved criterion of dynamic buckling is validated through comparisons with the results in the published literatures.

In this investigation, the nonlinear dynamic buckling analysis and the failure analysis of laminated composite cylindrical (LCC) panel with different shapes of cutouts under the action of rectangular in-plane pulse loads are performed in the finite element framework. Cross-ply laminates which are balanced symmetric are considered in the investigation. The first ply failure load (FPFL) of the panel is evaluated and checked whether it occurs before the nonlinear dynamic buckling phenomenon considering Tsai–Wu failure criterion. Convergence and validation studies are undertaken, and the results are compared with those from the existing literature. The effects of loading duration, cutout area and cutout geometry on the panel are investigated in detail and results are reported. The results indicate that for the panel with cutout, its dynamic buckling load (DBL), in certain cases, compared to the static buckling load (SBL), can be lower even if the loading duration is half of its first natural period. Additionally, the vibration and the static buckling analyses of the panels are carried out as and when required.

The buckling behaviors of drill string may cause serious down-hole problems, such as high friction during drilling, loss of weight on bit (WOB), and even drill string failure. This paper analyzes the dynamic buckling characteristics of drill string, considering the friction between drill string and wellbore. In the theoretical research, the key parameter expressions are determined, especially the contact behaviors of drill string and mathematical models are proposed, which include axial displacement, angular displacement and contact force. The numerical calculation results show that the influence of friction on the drill string buckling is mainly reflected in angular displacement. The influences of friction effect on the dynamic characteristics of drill string become greater with the increase of inclination angle, while become lower with the increase of drill string length. The friction effect appears to have insignificant influence on drill string condition with the accumulation of time. The comparison results indicate that the friction affects the action of axial load on drill string and delays the onset of buckling. On the other hand, the angular displacements decrease with drill string length increasing, while the axial displacements have an opposite effect. The research results provide theoretical references for studying dynamic buckling characteristics; furthermore, we can determine the methods and solutions to prevent drill string buckling based on this, and improve the safety of downhole drilling.

In this paper, the dynamic buckling of functionally graded (FG) porous shallow arches under hygro-thermal loading is studied through a numerical approach. Even and uneven porosity imperfections, hygroscopic stresses generated due to the nonlinear rise in moisture concentration, and the temperature dependence of material properties are all taken into account. The transient heat conduction equation is solved to derive the temperature profile. Hygro-thermo-mechanical properties of the arch are obtained applying the modified Voigt’s rule of mixture. The first-order shear deformation theory, the von-Kármán geometrical nonlinearity assumption, and the hygro-thermal strains are considered concomitantly to derive the equations of motions based on Hamilton’s principle. The generalized differential quadrature method (GDQM) and Newmark-beta integration schemes are also employed in conjunction with an iterative approach to solve the set of nonlinear governing differential equations of motion. The Budiansky–Hutchinson stability criterion is utilized to capture the dynamic buckling temperature of the structure. A parametric study is conducted in order to investigate the effects of porosity distribution, FG index, geometrical parameters, hygroscopic loading, and thermal/mechanical boundary conditions on arch’s dynamic buckling temperature.

Buckling may cause drill string damage or even drilling failure. For the 3000-m-long horizontal section drill string, a simplified analysis model of drill string in horizontal well is established, and the dynamic response results of axial displacement, angular displacement and contact force are obtained. When buckling, the closer the position of drill string is to the bottom, the later the buckling time, the smaller the buckling deformation degree, the slower the growth rate of axial displacement, and the smaller the attenuation degree of angular displacement and contact force amplitude. After buckling, drill string undergoes tensile deformation and eventually remains stable in the tensile state. After stabilization, from the top of drill string to the bottom of drill string, axial displacement increment increases first, then remains unchanged and then decreases, and the relative torsion angle between different positions gradually decreases. The drill string is always in horizontal contact with the wellbore, resulting in the same contact force values at different locations. The change of well inclination angle does not affect the change law of displacement and contact force. The absolute value of angular displacement is negatively correlated with the change of well inclination angle, and the value of axial displacement increment and contact force is positively correlated with the change of well deviation angle, but the value of contact force is quite close. The research results can provide reference for alleviating the buckling of drill string in horizontal wells.

This paper presents a dynamic analysis of trusses with an initial length imperfection of the elements, considering geometrical nonlinearity. In the nonlinear analysis of trusses, the hybrid finite-element formulation considers the initial length imperfection of the elements as a dependent boundary constraint in the master equation of stiffness. Moreover, it was incorporated into the establishment of a modified system of equations. To overcome the mathematical complexity of dealing with initial length imperfections, this study proposes a novel approach for solving nonlinear dynamic problems based on a hybrid finite-element formulation. In this study, the unknowns of the dynamic equilibrium equations were displacements and forces, which were obtained using virtual work. The hybrid matrix of elements of the truss is established based on the hybrid variation formulation with length imperfections of elements, considering large displacements. The authors applied Newmark integration and Newton–Raphson iteration methods to solve the dynamic equations with geometrical nonlinearity. An incremental iterative algorithm and calculation programming routine were developed to illustrate the dynamic responses of trusses with initial-length imperfections. The results verified the accuracy and effectiveness of the proposed approach. The uniqueness of the proposed method is that the length imperfection of the truss element is included in the stiffness matrix and is considered a parameter that affects the dynamic response of the system. This helps to solve the problem of the dynamic response of trusses with length imperfections becoming simpler. The numerical results show that the effect of length imperfection on the dynamic response of the trusses is significant, particularly on the dynamic limit load. In addition, to completely evaluate the behavior of the trusses, this study also developed formulas and analyses to consider the inelastic and local buckling of the truss structures, named ‘Inelastic post-buckling analysis (IPB).’

Instability is one of the major failure modes of long span arch bridges, and its possibility of occurrence will be increased as triggered by earthquake excitations. However, the randomness of each ground motion causes the difficulty in achieving a reliable assessment of the safety of the bridges in regard to its stability issue based on certain time history analysis. Therefore, a failure probability-based instability evaluation method and corresponding instability damage index are proposed in this study to solve this problem, converting the deterministic analysis of a ground motion into a probability analysis of a group of random ground motions. The results find that the input direction, the velocity pulse and the pulse period of the ground motion have a significant impact on the stability of the bridge, while seismic moment and PGV/PGA ratio do not. The fragility curves show that the bridge has more than 60% probability of slight instability when input PGA reaches 0.2 g, 50% probability of moderate instability when input PGA reaches 0.6 g, and 20% probability of collapse when input PGA reaches 1.0 g. Moreover, when the PGA approaches 1.0 g, it is discovered that the velocity pulse and the pulse period can increase the chance of the occurrence of bridge instability by 20%–30%.

In the present investigation, the dynamic instability regions of shear deformable cross-ply laminated and composite cylindrical panels subjected to periodic nonuniform in-plane loads are reported. Since the applied in-plane load is nonuniform, initially the static part of the nonuniform in-plane loads are applied and the stresses (σ_x, σ_y and τ_xy) within the panel are evaluated by the solution of cylindrical panel membrane problem. Subsequently, superposing the stress distribution due to static and dynamic in-plane loads, the stress distributions within the panel are obtained. Using these stress distributions the governing equations of the problem are derived through Hamilton's variational principle based on higher-order shear deformation theory of elastic shell theory incorporating von Kármán-type nonlinear strain displacement relations. The governing partial differential equations are reduced into a set of ordinary differential equations (Mathieu-type of equations) by employing Galerkin's method. The instability boundaries of Mathieu equation corresponding to periodic solutions of period T and 2T are determined using Fourier series. Effect of various parameters like static and dynamic load factors, aspect ratio, thickness-to-radius ratio, shallowness ratio, linearly varying in-plane load, parabolic in-plane load and various boundary conditions on the instability regions are investigated.

A symplectic system is developed for dynamic buckling of cylindrical shells subjected to the combined action of axial impact load, torsion and pressure. By introducing the dual variables, higher-order stability governing equations are transformed into the lower-order Hamiltonian canonical equations. Critical loads and buckling modes are converted to solving for the symplectic eigenvalues and eigensolutions, respectively. Analytical solutions are presented under various combinations of the in-plane and transverse boundary conditions. The results indicated that in-plane boundary conditions have a significant influence on this problem, especially for the simply supported shells. For the shell with a free impact end, buckling loads should become much lower than others. And the corresponding buckling modes appear as a "bell" shape at the free end. In addition, it is much easier to lose stability for the external pressurized shell. The effect of the shell thickness on buckling results is also discussed in detail.

In this paper, nonlinear dynamic buckling of laminated composite cylindrical panels subjected to in-plane impulsive compressive load is studied along with the failure analysis. Balanced and symmetric angle-ply laminated composite curved panels are considered. Convergence study is performed, and results are validated with the results from the existing literature, and then the dynamic buckling loads are calculated. The failure index of laminated composite curved panel is also calculated to check the precedence of first ply failure load over nonlinear dynamic buckling load. The effect of aspect ratio, loading function, and radius of curvature is studied. The analysis is carried out using finite element method. It is observed that the first ply failure for balanced and symmetric angle-ply laminated composite curved panels occurs after the panel has buckled due to dynamic impulse loads.

Through the reconstructed kernel particle method (RKPM), the dynamic buckling characteristics of submarine pressure hull under hydrostatic pressure and impact load is investigated in this study. First, a large deformation buckling calculation model for stiffened shell structures was established using RKPM and elastic–plastic constitutive models. To study the influence of load asymmetry on the buckling strength of the structure and provide fundamental technical support for submarine structural design, the dynamic buckling phenomenon of the structure was studied under three conditions: hydrostatic pressure acting alone, hydrostatic pressure and impact load acting simultaneously, and hydrostatic pressure and uniformly distributed impact load acting simultaneously. The starting time of buckling was used as the criterion for determining the critical load of dynamic buckling. The results indicate that under the combined action of static and dynamic loads, asymmetric dynamic loads can seriously affect the buckling strength of the structure.

Considering first order shear deformation theory, the dynamic buckling governing equations of elastic bar with initial imperfections, transverse inertia and axial inertia are derived by Hamilton principle. The equations are converted into the form of non-dimension. Based on the finite difference method, the equations are solved approximately. The buckling mode of elastic bar under different axial impact velocities has been obtained. The influence of different axial impact velocity on the dynamic buckling of elastic bar is discussed.

Considering the effects of shear deformation and stress wave, the dynamic buckling governing equations of rectangular plates under axial step load are established. Based on the Rayleigh-Ritz method, the expression of the critical load is got. The relation curve between the critical load and critical length is described by using MATLAB software. In this paper, the influences of thickness, first-order shear deformation (FSD), and the number of modes are discussed.