Dynamic Buckling Analysis Research Articles

Stochastic Dynamic Buckling Analysis of Cylindrical Shell Structures Based on Isogeometric Analysis

In this paper, we extend our previous work on the dynamic buckling analysis of isogeometric shell structures to the stochastic situation where an isogeometric deterministic dynamic buckling analysis method is combined with spectral-based stochastic modeling of geometric imperfections. To be specific, a modified Generalized-α time integration scheme combined with a nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the buckling and post-buckling problems of cylindrical shell structures. Additionally, geometric imperfections are constructed based on NURBS surface fitting, which can be naturally incorporated into the isogeometric analysis framework due to its seamless CAD/CAE integration feature. For stochastic analysis, the method of separation is adopted to model the stochastic geometric imperfections of cylindrical shells based on a set of measurements. We tested the accuracy and convergence properties of the proposed method with a cylindrical shell example, where measured geometric imperfections were incorporated. The ABAQUS reference solutions are also presented to demonstrate the superiority of the inherited smooth and high-order continuous properties of the isogeometric approach. For stochastic dynamic buckling analysis, we evaluated the buckling load variability and reliability functions of the cylindrical shell with 500 samples generated based on seven nominally identical shells reported in the geometric imperfection data bank. It is noted that the buckling load variability in the cylindrical shell obtained with static nonlinear analysis is also presented to show the differences between dynamic and static buckling analysis.

Dynamic buckling analysis of doubly curved orthotropic shallow shells via the Kantorovich and Rosenbrock methods

Dynamic buckling analysis of doubly curved orthotropic shallow shells via the Kantorovich and Rosenbrock methods

Static and dynamic buckling analysis of two-layer shells include auxetic honeycomb core combined with laminated three-phase polymer/GNP/fiber surface resting on Kerr elastic medium in hygro-thermal environments

This article investigates the static and dynamic buckling behavior of a double-curved sandwich shell composed of two layers via improved first-order shear deformation theory without using the shear correction is utilized to model the sandwich shell. The sandwich two-layer shell are held together by elastic pins, each layer made from an ultra-light auxetic honeycomb core layer (negative Poisson’s ratio) and is reinforced by a layer of tri-phase polymer, graphene nanoplatelets (GNP), and fiber. The double-curved sandwich shell is supported by a Kerr elastic medium in hygro-thermal environment assuming that temperature and humidity only cause forces to be applied tangentially to the shell and do not change the mechanical properties of the shell material. The motion equations of sandwich two-layer shell are derived by Hamilton’s principle, then the finite element method and Bolotin method are used to derive the dynamic instability region of sandwich two-layer shell. The accuracy of these results is confirmed by a comparison with established statements within the specific conditions of the problem model. The influence of inputs on the static and dynamic stability of sandwich two-layer shell is fully explored and discussed. Additionally, this serves as a crucial foundation for the calculation and design of structures that can integrate a variety of materials with different properties with low cost and simplification.

Nonlinear dynamic buckling analysis of the FG-GPLRC cylindrical and sinusoid panels with porous core under time-dependent axial compression

The nonlinear dynamic buckling responses of functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and sinusoid panels with porous core are presented in this paper. The governing formulations are established by applying the nonlinear higher-order shear deformation theory (HSDT). an approximation technique is used to determine the stress function for complexly curved panels. Euler-Lagrange equations can be used to achieve the nonlinear motion equation. Numerical investigations are considered using the Runge-Kutta method for dynamic responses, and using the Budiansky-Roth criterion for critical dynamic buckling loads. Some discussions on the dynamic buckling responses of panels with porous core can be achieved from the numerical examples.

A novel isogeometric model for dynamic buckling analysis of doubly curved two-directional functionally graded porous shallow microshells in thermal environments via variable length-scale parameters

In this study, the thermo-mechanical dynamic buckling analysis of two-directional functionally graded porous (2D-FGP) shallow microshells resting on elastic foundations with arbitrary boundary conditions is performed using the isogeometric approach. The isogeometric approach takes advantage of non-uniform rational B-spline basic functions to exactly represent the structure geometry models and the attainment of higher order approximation conditions. The characteristics of the material vary in both the thickness and axial x orientation. Especially, a new point in this material length-scale parameter of microshell is analyzed as a function of spatial coordinates and as a function of the material gradient parameters. Using Hamilton’s principle, the modified couple stress theory, and Kirchhoff-Love’s shell theory, the governing equations of a 2D-FGP microshell lying on a Pasternak medium are obtained. A computer program that employs an isogeometric analysis method to analyze the static and dynamic buckling of a 2D-FGP doubly curved shallow microshell with various boundary conditions. The numerical results for thin cylindrical, spherical, and hyperbolic paraboloidal shallow microshells with various planforms, such as rectangular and circular, are presented. Several special cases are used to demonstrate the accuracy and efficacy of the developed model by comparing the numerical results obtained by the proposed formulations with other published data. In addition, the effects of certain parameters, such as the length scale parameters, the power-law indexes, the thickness-to-sides ratio, and the radius ratio, on the dynamic thermo-mechanical buckling response of the 2D-FGP shallow microshells with double curvature are explored in depth.

Isogeometric Dynamic Buckling Analysis of Trimmed and Multipatch Thin-Shell Structures

This paper extends our previous work on the isogeometric dynamic buckling analysis of thin-shell structures to the trimmed and multipatch situation where features such as cutouts and stiffeners can be easily incorporated. To be specific, a modified generalized- time integration scheme combined with a geometric nonlinear isogeometric Kirchhoff–Love shell element is used to simulate the complex buckling and postbuckling behaviors of thin-shell structures. The developed method can damp properly high-frequency contents while maintaining second-order accuracy in the dynamic buckling analysis. For the integration of arbitrary-shaped trimmed elements, a geometrically exact blending function method is developed to improve the efficiency of the dynamic shell buckling analysis. To deal with multipatch geometries, a penalty-based weak coupling approach is developed, where coupled patches with nonconforming trimmed interfaces or even with prescribed angles, such as stiffeners, can be analyzed. We demonstrate the accuracy, stability, and flexibility of the proposed framework with several numerical examples. In particular, the influences of “free” and “partially free” control points, penalty factor, trimming, as well as different modeling strategies on the dynamic solutions of shell structures are investigated.

Buckling, bending and dynamic analyses of laminated three-phase polymer/graphene/carbon fiber composite rectangular plates

The bending and dynamic buckling analysis of graphene reinforced with carbon fiber reinforced polymer (CFRP) composite plates was investigated in this study. The CFRP composites were fabricated using the hand layup method. The mechanical characteristics of CFRP composites with 0–1 wt% graphene reinforcement were evaluated using ASTM tests. The experimental dynamic analysis is carried out on graphene reinforced CFRP composites. A higher order finite element (FE) formulation is implemented to compute the characteristics of the CFRP plate using MATLAB software. The FE model's validity is compared to numerical data reported in the literature, and the results demonstrate excellent agreement. Furthermore, parametric analysis is performed to explore the influence of wt.% of graphene, aspect ratios, and end conditions on the bending and dynamic buckling properties of graphene reinforced with CFRP composite plates.

Dynamic buckling analysis of functionally graded shells

One of the most important parts of the structural calculation during their dimensioning is the study of static or even dynamic stability which can be treated in different manners as static buckling, parametric resonance, and dynamic buckling. In this work, we deal with dynamic stability by using the dynamic buckling criteria for functionally graded (FG) material shell structure. This paper aims to determine, in the dynamic case of FG structures composite type, the critical dynamic load using dynamic buckling criteria as phase plan and motion equation criterion. The different mechanical properties are taken as continuous functions through-thickness direction according to the volume fraction of the constituents by a simple power law distribution. The effect of variations of volume fractions and shell geometrical parameters is studied. Convergence tests and comparison studies have been carried out to establish the efficiency of the present model.

Dynamic buckling analysis of stiffened panels under in-plane uniaxial impact considering plate/web interaction

An analytical method is proposed by using the large-deflection theory to determine the axial dynamic buckling strength of stiffened panels with simply supported edges and isotropic linear-elastic materials. The buckling behavior of the attached plates and stiffener are separately expressed by various displacement functions. These displacement functions are expressed by trigonometric and hyperbolic series, which satisfy the boundary conditions and the motion governing equations for the stiffened panels. The method is validated by comparing its predictions with finite element results for a typical stiffened plate. Then, the influence of several critical parameters, including initial imperfection, impact load, and stiffener torsional rigidity, on the dynamic deflection and critical buckling load are studied. The results reveal that the local web behavior has a significant influence on the dynamic buckling behavior of stiffened panel.

Dynamic buckling analysis of reinforced composite plate subjected to harmonic loads

Composite plates are high-tech structures used in many areas of modern engineering, like building, space travel, ships, etc. In practice, these structures are often used in their thin form, typically a reinforced composite plate subjected to dynamic loads. Therefore, when subjected to loads, the plate may be instability. The article presents the element model, finite element algorithm, and buckling analysis results of reinforced composite plates subjected to dynamic loads in order to determine the buckling domain. Furthermore, the influence of some factors such as geometric parameters, reinforcing stiffeners, and material characteristics on the buckling domain of the plate is studied in detail.

Implicit dynamic buckling analysis of thin‐shell isogeometric structures considering geometric imperfections

AbstractIn continuation of our previous work on nonlinear stability analysis of trimmed isogeometric thin shells, this contribution is an extension to dynamic buckling analyses for predicting reliably complex snap‐through and mode‐jumping behavior. Specifically, a modified generalized‐ time integration scheme is used and combined with a nonlinear isogeometric Kirchhoff–Love shell element to provide second‐order accuracy while introducing controllable high‐frequency dissipation. In addition, a weak enforcement of essential boundary conditions based on a penalty approach is considered with a particular focus on the inhomogeneous case of imposed prescribed displacements. Moreover, we propose a least‐squares B‐spline surface fitting approach and corresponding error measures to model both eigenmode based and measured geometric imperfections. The imperfect geometries thus obtained can be naturally integrated into the framework of isogeometric nonlinear dynamic shell analysis. Based on this idea, the different modeling methods and the influence of the appropriately considered geometric imperfections on the dynamic buckling behavior can be investigated systematically. Both perfect and geometrically imperfect shell models are considered to assess the performance of the proposed method. We compare our method with established developments in this field and demonstrate superior achievements with regard to solution quality and robustness.

Some aspects of dynamic buckling and dynamic response of thin plate under in-plane compression

The paper is devoted to investigating the response of thin orthotropic square plates subjected to in-plane time-dependent compressive load related to static buckling load. Two types of loads have been considered: pulse load with a duration corresponding to a period of natural frequencies of a plate; harmonic load with a different mean value. It has allowed us to analyse the plate behaviour under dynamic load and present the application of phase portraits, Poincare maps and Lyapunov exponents for dynamic buckling analysis. The system’s response is analysed based on the FEM model and one degree of freedom oscillator derived from the full continuous model. The research has been performed to check the thesis that the methods used in the analysis of the stability of motions of a rigid body can be used in dynamic buckling determinations and dynamic response analysis of thin-walled deformable structures. The results show that both considered approaches give reliable outcomes, and derived stability conditions are matched.

Effect of Cutout on the Stability and Failure of Laminated Composite Cylindrical Panels Subjected to In-Plane Pulse Loads

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.

Non-linear static and dynamic buckling analysis of laminated composite cylindrical shell embedded in non-linear elastic foundation using the swarm-based metaheuristic algorithms

In this paper, by determining the optimal fiber's angles for maximum critical buckling load, the non-linear static and dynamic buckling analyses of laminated composite cylindrical shells resting on non-linear elastic foundation subjected to external loading are investigated. The laminated composite cylindrical with three, four, and five layers is considered. In the present study, first, the optimal fiber's angles are found using the swarm-based metaheuristic algorithms, then, the non-linear static and dynamic buckling analyses are carried out at optimum fiber directions. According to classical shell theory, von-Kármán equation, and Hooke's law, the stress-strain relations are derived for the laminated composite cylindrical shell. Then, based on the Galerkin's method, the discretized motion equation is obtained. For the optimization problem, the design variables are ply angles, and the objective function is maximizing the critical buckling load. Four recently developed swarm-based metaheuristic algorithms including, grey wolf optimizer (GWO), whale optimization algorithm (WOA), grasshopper optimization algorithm (GOA), and salp swarm algorithm (SSA), are utilized to solve these optimization problems. Based on the results, the optimization algorithms have improved the value of the critical buckling load significantly. Also, the WOA algorithm had better results than the others, while the GOA was the weakest.

Nonlinear Static and Dynamic Buckling Analysis of Imperfect Stiffened Double-Layer FGP Shallow Spherical Shells Embedded Within Elastic Foundations

In this work, an analytical method is presented to analyze the nonlinear static and dynamic buckling of imperfect stiffened double-layer functionally graded porous (FGP) shallow shells subjected to external pressure. The shallow spherical shell consists of two layers, where upper layer of shell is nonporous functionally graded (FG) material and the lower layer of shell is FG porous. This spherical shell is resting on elastic foundations, which consist of two-term Winkler–Pasternak’s model. Two FG porous distributions types consisting of symmetric porosity distribution (SPD) and nonsymmetric porosity distribution (NSPD) are investigated. The porous materials are assumed to vary through the thickness direction based on the assumption of a common mechanical feature of the open-cell foam. Utilizing the classical theory of shells considering geometrical nonlinearity based on von Kármán–Donnell relations and Hooke’s law, the governing equations of stiffened double-layer FG porous spherical shells are extracted. To discretize the partial differential equation of shell and obtaining the system equations of motion, the Galerkin method is applied. Regarding the discretized equation of motion, the explicit expressions for dynamic and static critical buckling load are determined. To investigate the dynamic behavior, the equation of motion is solved via a numerical method named Runge–Kutta approach, and then a presented approach by Budiansky–Roth is employed to obtain a critical load for the nonlinear dynamic buckling. The influence of various porosity distributions and coefficients of the shallow shell, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling analysis of imperfect stiffened double-layer FG porous shallow shells is examined.

Dynamic buckling of rotationally restrained FG porous arches reinforced with graphene nanoplatelets under a uniform step load

This paper presents a dynamic buckling analysis for a rotationally restrained functionally graded (FG) graphene nanoplatelets (GPLs) reinforced composite (FG-GPLRC) porous arch under a uniform step load where GPL nanofillers are uniformly dispersed while the porosity coefficient varies along the thickness direction of the arch. The effective material properties of the FG-GPLRC porous arch are determined by the volume fraction distribution of materials. Analytical solutions for the symmetric limit point dynamic buckling and anti-symmetric bifurcation dynamic buckling loads of rotationally restrained FG-GPLRC porous arches are derived by using an energy-based approach. Critical geometric parameters that determine the dynamic buckling mode switching behavior are also identified and discussed. Depending on the geometric parameters and the rotational restraint stiffness, the FG-GPLRC porous arch can buckle in either a symmetric limit point mode or an anti-symmetric bifurcation mode dynamically. It is also found that the dynamic buckling load of the arch can be considerably improved by adding a small amount of GPLs as reinforcing nanofillers. The influences of the porosity coefficients, GPL weight fractions, arch dimensions and geometries on the dynamic buckling behavior of rotationally restrained FG-GPLRC porous arches are comprehensively investigated through extensive parametric studies.

Geometrically Nonlinear Dynamic Response of Perforated Plates by Modified Differential Quadrature Method

The paper presents a modified differential quadrature (MDQ) method to investigate the dynamic response of perforated plates with elastically restrained edges under uniaxial impact compressive load. The perforated plate is divided into several separate plate elements that can be connected by using penalty function method (PFM) to ensure continuity along the shared edges. The in-plane stress distribution of the plate under the mechanical edge loading is determined by the pre-buckling analysis. To analyze the effect of elastically restrained edges on the dynamic response of perforated plates, artificial springs imposed for the edges are considered in the governing equilibrium equations. Verification analysis is carried out to demonstrate the efficiency and accuracy of the proposed method by comparing the results obtained with those available in the literature. Finally, the various effects of initial imperfection, rotational restrained stiffness, hole size and location, and shear load, on the dynamic response of perforated plates are investigated. The results show that the dynamic buckling load of perforated plates is significantly influenced by the rotational restraint stiffness, hole size and shear load as well as the initial geometric imperfection, whereas the effect of hole location can be neglected in the analysis of dynamic buckling of plates. Additionally, the results predicted by the proposed method can correlate well with the available numerical results.

Dynamic electromagnetic buckling analysis of pulsed magnets

The dynamic electromagnetic buckling behaviors of pulsed magnets are investigated by both theoretical analysis and experiments for the first time in this paper. The electromagnetic dynamic buckling models of pulsed magnets, which include the dynamic effects of inertia, stress wave propagation, etc., are developed to analyze the effect of the practical operating conditions. Representative coils have been developed and tested by the discharge experiments of high voltage and current, and the theoretical results are highly consistent with experimental results, which shows that the models proposed in this paper are accurate, effective and reliable. Moreover, the experimental results are the direct and solid evidence for the existence of buckling in pulsed magnets. It is found that the windings in different locations of pulsed magnets exhibit a variety of buckling behaviors from Euler buckling to asymmetric collapse, which reflect the complexity of the buckling analysis of pulsed magnets. Lastly, the influences of Lorentz force distribution, inertia effect, stress wave propagation, material properties and geometry to the buckling behaviors are also discussed based on the proposed models, and a laminated laying method of fiber reinforcement is proposed to improve the buckling strength of pulsed magnets.

Study of modal properties and crashworthiness performance of crash box numerical model with different joining modelling strategies

It is important to understand the natural frequencies and the mode shapes for automotive structure such as crash box as it will be subjected to the dynamic loading in its real application. In addition, it is also important to study other dynamic behaviour such as crash and buckling as crash box is one of energy absorbing member that is intended for car safety during collision. In this study, modal properties of three different crash box models joint by three different joint modelling strategies and also their crash and buckling behaviour was analysed and investigated. Computational frequency analysis, dynamic crash analysis and nonlinear buckling analysis was performed on all of crash box models. the crash box modelled with node equivalent method to represent the welded joint shows higher stiffness at the joining area and therefore shows higher value of natural frequencies that the model with CBEAM and CBAR elements as their joining elements. In term of crash behaviour, the model with CBEAM element shows higher reaction force compared to the CBEAM. This proves that different type of joint modelling strategies behaves differently.

Nonlinear dynamic buckling analysis of imperfect viscoelastic composite laminated plates

The aim of this paper is to study the effects of linear viscoelastic behavior on dynamic buckling response of imperfect composite laminated plates subjected to in-plane dynamic loads by implementing semi-analytical finite strip method (FSM). The semi-analytical FSM converges with a comparatively small number of strips and correspondingly small number of degrees of freedom. Thus, it is usually implemented more easily and faster than many other computational methods. The governing equations are derived by using classical laminated plate theory (CLPT) and the behavior of plate is assumed to be geometrically nonlinear through Von-Karman assumptions. The Newmark's implicit time integration method in conjunction with the Newton-Raphson iteration are employed to solve the nonlinear governing equation. A Kelvin-Voigt viscoelastic model is considered, and the effects of viscosity coefficient, thickness of the layers of the composite plate and boundary conditions on the nonlinear dynamic buckling response are discussed. In order to justify the accuracy of the results, some of them are verified against those available in other sources. It is also shown that the nonlinear dynamic buckling response of an imperfect viscoelastic composite laminated plate is significantly different from the elastic one by considering different viscosity coefficients.