Nonlinear Buckling Research Articles

Free bulging and nonlinear buckling of teardrop-shaped pressure hull

Free bulging and nonlinear buckling of teardrop-shaped pressure hull

Study on buckling characteristics of PC/PET spherical-cylindrical combined pressure cabin

The buckling characteristics of PC/PET spherical–cylindrical combined pressure cabins under uniform external pressure were studied via experimental and numerical methods. The material properties of the PC/PET plastic alloy were tested. Six spherical–cylindrical combined pressure cabins with different structures were designed and fabricated, and the thickness and geometry of each model were measured. The hydrostatic pressure experiment was carried out on all the pressure cabins, and the ultimate load of the pressure cabin was recorded. Linear buckling analysis and nonlinear buckling analysis of PC/PET spherical–cylindrical combined pressure cabins were carried out, and the numerical and experimental results were found to be consistent. Moreover, the effects of the spherical shell radius and the thicknesses of different combinations on the buckling load were studied.

Nonlinear buckling and free vibration analysis of auxetic graphene origami composite beams under nonuniform thermal environment

This study examines the thermo-mechanical behavior of auxetic metamaterial beams enhanced by graphene origami (GOri) under spatially varying nonuniform temperature distributions (SVTD). Utilizing Timoshenko beam theory considering von-Kármánn type nonlinear strain–displacement relationship, GOri beams are modeled as layered structures. The Ritz method is employed to solve equilibrium equations, analyzing the impact of GOri distribution patterns, content, and folding degree on post-buckling and vibration paths. The effects of five SVTDs, three end conditions, and three GOri distribution patterns on buckling, post-buckling behavior, and nonlinear free vibration characteristics are explored. Findings reveal that the parabolic temperature distribution with peak temperatures at beam ends (P-MAE) results in higher critical temperatures and nonlinear free vibration frequencies. This research provides crucial insights into the design and optimization of GOri-enabled metamaterial structures in complex thermal environments, highlighting the significant influence of nonuniform temperature distributions along the beam’s length.

Harnessing centrifugal and Euler forces for tunable buckling of a rotating elastica

We investigate the geometrically nonlinear deformation and buckling of a slender elastic beam subject to time-dependent ‘fictitious’ (non-inertial) forces arising from unsteady rotation. Using a rotary apparatus that accurately imposes an angular acceleration around a fixed axis, we demonstrate that dynamically coupled centrifugal and Euler forces can produce tunable structural deformations. Specifically, by systematically varying the acceleration ramp in a highly automated experimental setup, we show how the buckling onset of a cantilevered beam can be precisely tuned and its deformation direction selected. In a second configuration, we demonstrate that Euler forces can cause a pre-arched beam to snap-through, on demand, between its two stable states. We also formulate a theoretical model rooted in Euler’s elastica that rationalizes the problem and provides predictions in excellent quantitative agreement with the experimental data. Our findings demonstrate an innovative approach to the programmable actuation of slender rotating structures, where complex loading fields can be produced by controlling a single input parameter, the angular position of a rotating system. The ability to predict and control the buckling behaviors under such non-trivial loading conditions opens avenues for designing devices based on rotational fictitious forces.

Mechanical properties and failure analysis of ring-stiffened composite hulls under hydrostatic pressure

Ring stiffeners improve the buckling resistance of thin-walled hulls. In this study, theoretical models of buckling and strength failure of ring-stiffened composite hulls (RSCHs) were used to determine the design parameters. The hulls were prepared by filament winding on a mould composed of multi-petal-combined foams and steel shafts. The experimental results showed that the hydrostatic bearing performance of RSCHs was 1.79 times that of an unstiffened composite hull (USCH) with the same weight-to-displacement ratio (WDR). The crack in the damaged stiffened hulls penetrated the entire axis and expanded circumferentially, resulting in a stiffener fracture. Imperfections related to thickness deviations were introduced into a nonlinear buckling model by considering progressive damage. In contrast to the failure mechanism of USCH, the failure pressure of RSCHs was not at the peak of nonlinear buckling, and fibre compressive failure at 90° on the outermost layer of the skin was dominant. The error between simulated and experimental results was 4.64 %. The parameter analysis indicated that the stiffener height and width had different effects on the buckling load. However, when only the same type of strength failure occurred, both were independent of the load. This study demonstrated the load-bearing advantages of RSCHs for ocean engineering applications.

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

Nonlinear thermo-mechanical dynamic buckling and vibration of FG-GPLRC circular plates and shallow spherical shells resting on the nonlinear viscoelastic foundation

NURBS-based isogeometric formulation for linear and nonlinear buckling analysis of laminated composite plates using constrained and unconstrained TSDTs

Two isogeometric plate models employing Reddy's third-order shear deformation theory (TSDT) and unconstrained third-order shear deformation theory (UTSDT) are presented and compared for linear and nonlinear buckling analysis of laminated composite plates with and without imperfection and subjected to different inplane loads. Cubic non-uniform rational B-spline (NURBS) basis functions that easily satisfy C1 continuity of the IGA-TSDT model are employed. The total Lagrangian approach in conjunction with the principle of virtual work is used to derive the governing equations. The primary and secondary solutions are traced using a tangent based arc-length method with a simple branch switching technique. The performance of the models is evaluated by validation and comparison with solutions obtained using ANSYS, Navier method (for linear analysis only), and those in the literature. The buckling response is significantly affected by pre-buckling boundary conditions and strain-displacement relations. The nonlinear buckling approach, among other approaches, is observed to be the most accurate methodology for an arbitrarily laminated composite plate. Further, IGA-UTSDT with nine DOF gives marginal improvement over IGA-TSDT with five DOF at the cost of computation. The IGA-TSDT is observed to be superior to FEM-TSDT in terms of computation demand and performance.

Prediction of sectional collapse of thin-walled structure under pure bending by nonlinear composite beam theory

Brazier (1927) found that when one dimension of the beam cross-section was relatively smaller than the others, large in-plane displacements over the cross-section might occur, even though the strains could remain very small. Under this circumstance, the so-called Brazier effect refers to the cross-sectional ovalization, which leads to nonlinear bending buckling and collapses. This paper studies the Brazier effect by the nonlinear Variational Asymptotic Beam Sectional Analysis (VABS) theory which considers finite cross-sectional deformations. Nonlinear VABS reduces three-dimensional (3D) continuum to a one-dimensional (1D) beam analysis and a two-dimensional (2D) cross-sectional analysis featuring both geometric and material nonlinearities without unnecessary kinematic assumptions. The present theory is implemented using the finite element method (FEM) in the VABS code, a general-purpose beam cross-sectional analysis tool. An iterative method is applied to solve the finite warping field for the classical-type model using the Euler–Bernoulli beam theory. The deformation gradient tensor is directly used to deal with finite deformation, various strain definitions, and several types of material laws. Numerical examples demonstrate the capabilities of VABS to predict the sectional collapse of thin-walled structures under pure bending.

Nonlinear Buckling of Flexible Pipe Carcass Considering Residual Stress Due to Deformation

Nonlinear Buckling of Flexible Pipe Carcass Considering Residual Stress Due to Deformation

Global Stability Behavior of Pre-Cast Cable-Stiffened Steel Columns

Cable-stiffened steel columns (CSSC) have a high load-carrying capacity and strong stability compared to ordinary steel columns. In practical engineering, the connection between the crossarm and main column of a CSSC is usually welded. However, the welding-residual stress adversely affects the steel column. In this study, pre-cast CSSCs, with a pinned connection between the crossarm and main column, are presented. The new type of pre-cast CSSCs avoid the welding-residual and are easy to disassemble. A model test and numerical analysis of its global stability behavior under eccentric compression is conducted. Based on the analysis, the buckling modes of these columns are defined and a method for determining the governing imperfection in a nonlinear buckling analysis is proposed. The effects of slenderness ratio, cross-arm length, cable diameter, and other parameters on the load-carrying capacities of the columns are investigated using the proposed method. The results of this study can be used as a reference for the engineering designs and specifications of pre-cast CSSCs.

A Data-Driven DNN Model to Predict the Ultimate Strength of a Ship’s Bottom Structure

Plates and curved plates are essential components in ship construction. In the design stage, the methods used to evaluate the ultimate strength required to confirm the structural safety of plates include prediction through analytical methods, finite-element analysis (FEA), and empirical formulas. However, with nonlinear buckling, the results of the empirical formula and the FEA differ for small flank angles (1~9). As a result, the prediction of the nonlinear ultimate strength of flank angle (1~9) plates still requires significant computation time and cost. To compensate for this, this study performed an ultimate strength prediction method utilizing a deep neural network together with the 4050 curved plate analysis. In addition, this paper presents the analysis results of the nonlinear finite-element method and the geometric shape and ratio of curved plates as training data. Based on the results of this study, designers can more efficiently design appropriate curved plate members by considering the ultimate strength.

Koiter–Newton Reduced-Order Method Using Mixed Kinematics for Nonlinear Buckling Analysis

The Koiter–Newton method improves the computational efficiency of nonlinear buckling analysis; however, the construction of reduced-order models using fully nonlinear kinematics is still a tedious and time-consuming work. In this paper, the Koiter–Newton reduced-order method using mixed nonlinear kinematics is presented for the geometrically nonlinear buckling analysis of thin-walled structures. Strain energy variations up to the fourth order were achieved using mixed kinematics for the improved Koiter theory. Corotational kinematics, which is inconvenient for high-order variations, was applied to calculate the first- and second-order variations for the internal force and tangent stiffness, respectively, whereas the third- and fourth-order strain energy variations were facilitated by explicit algebraic formulations using updated von Kármán kinematics. A reduced-order model with 1+m degrees of freedom was established, of which m perturbation loads were considered to make the method applicable for buckling problems. The geometrically nonlinear response was traced using a predictor–corrector strategy by combining the nonlinear prediction solved by the reduced-order model and the correction using Newton iterations. Numerical examples of structures with various buckling behaviors demonstrate that the performance of the proposed method is not obviously affected by using simplified kinematics, and sometimes it even exhibits a superior capability for path-following analysis.

Wind buckling analysis of cylindrical shells with various geometric imperfections

This study addresses the complexity of buckling behavior in cylindrical shells subjected to non-uniform wind loading, emphasizing the significant impact of geometric parameters on buckling patterns. Cylinders with varying aspect ratios exhibit distinct linear and nonlinear buckling behaviors, complicating the determination of the most detrimental structural imperfections across different geometries. Notably, imperfections affecting stocky cylinders may be less impactful for slender ones. This paper introduced equations for calculating linear critical pressures under wind loading, followed by an extensive numerical analysis assessing the imperfection sensitivity in anchored cylindrical shells of uniform thickness with diverse aspect ratios. Two types of geometric imperfections were employed to assess their influence on the nonlinear buckling strength of cylinders with varying geometries. Results demonstrate that eigenmode imperfections predominantly compromise the buckling strength of stocky cylinders, whereas nonlinear incremental mode imperfections significantly influence the nonlinear critical pressures of intermediate-length and slender cylinders. Consequently, empirical expressions have been formulated to calculate the imperfection reduction factor, offering a precise evaluation of nonlinear buckling pressures in imperfect cylinders under wind loading.

Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

This research proposes a computationally efficient methodology using a Constrained Variational Asymptotic Method (C-VAM) for non-linear buckling analysis on a hat-stringer panel with delamination defects. Starting with the geometrically non-linear kinematics, the VAM procedure reduces the three-dimensional (3-D) strain energy functional to an analogous 2-D plate model and evaluates the closed form warping solutions. Utilising the resulting warping solutions and recovery relations for the skin and the stringer, displacement continuity at the three-dimensional level is enforced between the stringer and the skin based on the pristine and delaminated interface regions. Consequently, the constrained matrices obtained from C-VAM is incorporated into an in-house developed non-linear finite element framework. Using the developed formulation, a stiffened panel with delamination of 40 mm between the stringer and the skin is analysed under compression. The results have been validated locally and globally, employing experimental data and 3-D finite element analysis (FEA). Experiments are carried out on the co-cured panel by applying quasi-static loading with displacement-controlled conditions, and 3-D FEA is carried out in Abaqus. Load-response plots have been obtained to validate the results at the global level, and they are in excellent agreement with experiments and 3-D FEA. Subsequently, out-of-plane displacement contour plots are obtained; the number of half waves and wave intensity in 3-D FEA and C-VAM are comparable, although there are minor differences compared to the experimental findings. The proposed framework is shown to be computationally efficient by over 55% as compared to 3-D FEA for performing non-linear buckling analysis on the stiffened composite structure considered in the current work.

On the nonlinear buckling and postbuckling responses of sandwich FG‐GRC toroidal shell segments with corrugated core under axial tension and compression in the thermal environment

AbstractThis paper presents an analytical approach for buckling and postbuckling analysis for functionally graded graphene‐reinforced composite (FG‐GRC) toroidal shell segments with the trapezoidal or round corrugated core under the axial tension and compression. The considered shells are placed in a thermal environment and surrounded by an elastic foundation. Based on the von Kármán‐Donnell shell theory with geometrical nonlinearities, Stein and McElman approximation, and a homogenization technique for corrugated shells, the basic equations of shells are established. The previous homogenization technique is improved by adding the thermal forces in the internal force expressions. The shell‐foundation interaction is expressed using the model of the Pasternak assumption. The Ritz energy method is used to obtain the pre‐buckling and postbuckling behaviors of the shells, from which the critical buckling tensions and compressions can be investigated. The influences of FG‐GRC face sheets, corrugated core, and foundation on the buckling behavior of sandwich shells can be shown in the numerical analysis.Highlights Postbuckling of toroidal shell segments with the corrugated core is analyzed. A homogenization technique is improved for the thermal forces in the core. The shells are made of functionally graded graphene‐reinforced composite. The nonlinear Kármán‐Donnell shell theory and Ritz energy method are applied. Special effects of input parameters on the buckling behavior are investigated.

Stability of Prestressed Stayed Steel Columns Under Eccentric Compression

Prestressed stayed steel columns (PSSCs) are structural components notable for their exceptional stability and load capacity. However, their behavior under eccentric compression remains poorly understood compared to their performance under axial compression. This study conducted tests and finite element analysis (FEA) to investigate the stability of PSSCs under eccentric compression loading. The study focused on examining the overall stability, buckling modes, and ultimate load capacity of PSSCs under various scenarios. The findings revealed that PSSCs exhibit significantly higher stability and load capacity than conventional columns. However, when subjected to eccentric compression, they experience a substantial decrease in stability. The results of the linear and nonlinear buckling analyses suggest that interactive buckling may occur under certain conditions, thereby influencing the buckling load. These findings clarify the correlation between stability and eccentric compression, offering valuable insights for future research and practical engineering applications.

Assessment of non-linear critical pressure of MWCNT reinforced hybrid sandwich semi-ellipsoidal dome under hydrostatic pressure: A numerical and experimental study

The present study involves the numerical and experimental buckling response of MWCNT reinforced composite sandwich semi-ellipsoidal dome subjected to uniform hydrostatic external pressure. The skin of the composite sandwich dome is made up of MWCNT-GFRP composite layers and the PLA honeycomb core, which is reinforced with and without strips. Various honeycomb core configurations, such as SRHC-1 to SRHC-3, are formulated in such a way that the strips are reinforced between the regular honeycomb core in longitudinal and transverse directions to enhance the stiffness characteristics of the structure. The nonlinear buckling analysis of the MWCNT reinforced composite sandwich dome is formulated and solved through the commercially available software ANSYS®. The geometry and material non-linearity of the MWCNT reinforced sandwich dome structures are incorporated in the numerical model while solving the non-linear differential equations and identifying the critical pressure of the sandwich structures using arc length method. The testings were performed to obtain the various mechanical properties, the non-linear behavior of yield stress with a plastic strain of the MWCNT-reinforced GFRP skin and the transverse shear modulus of the various honeycomb core patterns. The efficiency of the present numerical modeling and buckling analysis is confirmed by comparing the critical pressure obtained through the experimental buckling analysis performed on the MWCNT-reinforced prototype sandwich dome and the results available in the literature. Various parametric studies are performed on the MWCNT-reinforced composite sandwich dome to examine the influence of MWCNT reinforcement on the skin, honeycomb core patterns, stacking sequence of skins, aspect ratio and slenderness of the shells and geometric imperfections on the critical pressure.

Nonlinear Buckling and Postbuckling Response of Porous FGM Shallow Spherical Caps and Circular Plates with Nonlinear Elastic Foundation Effects Using the Ritz Energy Method

Nonlinear Buckling and Postbuckling Response of Porous FGM Shallow Spherical Caps and Circular Plates with Nonlinear Elastic Foundation Effects Using the Ritz Energy Method

On the Role of Nonlocal Strain Gradient Elasticity in Nonlinear Buckling of FG Porous Reinforced Curved Nanobeams Having Different Degrees of Curvature

Curved nanobeams are one of the essential components in manufacturing nano-electromechanical systems needing nonlinear stability design. In the current investigation, the nonlinear buckling characteristics of functionally graded porous reinforced curved (FGPRC) nanobeams having different degrees of curvature are analyzed by counting the higher-order gradients of the classical strain tensor as well as nonlocal-type interatomic interactions. In this regard, two independent length-scale constants within the framework of the nonlocal strain gradient theory (NSGT) of continuum elasticity are taken into account. Via employing the promising low computational cost and geometrically adaptable method of isogeometric collocation, various branches of NSGT-based equilibrium graphs of FGPRC nanobeams are plotted relevant to each considered degree of curvature. It is extrapolated that the quantity of graphene platelet (GPL) weight fraction has a negligible influence on the significance of nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect in the value of the maximum deflections or lateral loads at the detected limit points, especially attributed to a higher degree of curvature. Besides, it can be remarked that, in the FGPRC nanobeam owning a small degree of curvature, lessening the quantity of porosity index results in an increment in the significance of the nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect on the maximum deflection at both upper and lower limit points. However, in the FGPRC nanobeams owning medium and large degrees of curvature, it gets lesser at the upper limit point, but becomes higher at the lower limit one.

Nonlinear buckling and postbuckling behaviors of porous FG-GPLRC cylindrical shells with stiffeners subjected to external pressure

Buckling and postbuckling behaviors of porous functionally graded graphene platelets-reinforced composite (porous FG-GPLRC) cylindrical shells with stiffeners subjected to external pressures are presented in this paper. Three distribution types of porosity in the shells are considered. The smeared technique for stiffeners is employed to model the mechanical behaviors of the stiffened shells. The mechanical formulations are established by the thin shell theory considering large deflection assumption, and the Ritz method is applied for three deflection amplitudes. The postbuckling formula of the pressure-deflection and the explicit critical buckling pressures can be achieved. The numerical investigations indicate the outstanding effects of stiffeners, porosity distribution, porosity coefficient, and graphene platelet (GPL) mass fraction on the nonlinear buckling responses of the stiffened shells.