Buckling Mode Research Articles

The probabilistic dynamic stability analysis of fluid-filled porous cylindrical shells reinforced with graphene platelets

The aim of the current paper is the probabilistic dynamic stability analysis of graphene-reinforced functionally graded porous cylindrical shells under dynamic axial loads. For this purpose, various sources of uncertainty including the material and geometrical properties of the cylinder and loading are considered. By combining a Lagrangian solution method and a semi-analytical method, some formulations are developed for determining the dynamic buckling loads of the cylindrical shells. In order to model the fluid–reservoir interaction, a semi-analytical boundary solution is used. The functionally graded porous shells reinforced with graphene platelets (FGP-GPL) are modeled with three porosity distributions and three GPL dispersions in the shell thickness based on the Halpin–Tsai formulation. The kinetic equilibrium equations of the shells are derived based on Sanders’ nonlinear theory and the higher order shear theory. Moreover, in order to solve the nonlinear dynamic equations of motion, the Newton–Raphson and the Newmark methods are combined. Finally, the results are presented in terms of the probabilistic density functions (PDFs) and cumulative density functions (CDFs) of the buckling loads. In addition, a parametric study is conducted for the effects of the different material and physical conditions on the probabilistic dynamic buckling loads of the composite cylinders. As a result, in the probabilistic dynamic stability analysis of the composite shells, the distributions of the different buckling loads may have overlaps with each other. This phenomenon indicates that in probabilistic cases, the first buckling mode of a structure is not necessarily always the dominant failure mode.

Effects of process-induced residual stress and geometric characteristics on pressure-resisting capability of corrugation in primary barriers of liquefied natural gas carriers

The primary barrier of a liquefied natural gas (LNG) carrier generally has a corrugated shape, so as to withstand thermal shrinkage at cryogenic temperatures. Over the years, studies have been actively performed to improve the performance of the primary barrier through structural analysis. However, when analyzing the pressure-resisting capability of the corrugation, previous studies have not considered the residual stress generated during the forming process of the corrugation. This can lead to an overestimation of the pressure-resisting capability of the corrugation. In this work, the pressure-resisting capabilities of the corrugation were evaluated by considering the residual stress generated during the deep drawing process of the corrugation; the initial buckling mode was also considered through a linear buckle analysis based on a finite element analysis. Universal hydraulic test equipment was developed for measuring the pressure-resisting capabilities of corrugations of various sizes. By comparing the analytical results from the experiments, it was confirmed that the pressure-resisting capability of the corrugation decreased by 16% when the residual stress and initial buckling mode were considered simultaneously. We believe that this study can be used as a reference to present guidelines when setting design parameters to improve the pressure-resisting capability of a primary barrier.

Column Buckling of Corroded Steel Angles and Channels: Experiments and Failure Mode Analyses

Corrosion affects the sustainability of steel structures, especially those with improper maintenance and those exposed directly to the atmosphere and seashore environments. Corrosion-related accidents have been reported frequently recently; therefore, periodically assessing the structural health condition of steel structures is crucial. Clarifying the residual strengths of corroded steel structures with moderate to severe degrees of corrosion is important. Here, the uniaxial compressive strength of corroded steel angles and channels was investigated through experiments and nonlinear finite-element analyses. The behavior of these corroded specimens was found to depend strongly on the degree of corrosion, and had combined failure modes of global flexural buckling, local buckling, and cross-sectional yielding. The failure mode of the corroded steel specimens that largely behaved in a complex manner was examined. The relationship between the ultimate strength and degree of corrosion, and the applicability of a traditional global flexural buckling strength equation using the cross-sectional properties, were analyzed for strength evaluation. The strength equation provided relatively good strength estimates for lightly to moderately corroded specimens; however, it became less applicable for severely corroded specimens, possibly owing to the local buckling interaction. An empirical strength equation that reflects the trend of the experimental results was developed by modifying the traditional equation.

Finite Element Analysis and Buckling Behaviour of I-shaped Beams with RHCFST Upper Flange

In order to analyse the buckling behaviour of I-shaped beams with rectangular high-strength concrete-filled steel tubular (RHCFST) upper flange, a total of 7 simply-supported beams are designed with height-width ratio of upper flange and span as the main parameters in this paper. Based on ANSYS software, the finite element models are established, and the eigenvalue buckling analysis of seven simply-supported beams are carried out. The buckling loads of the composite beams can be obtained and the influence of height-width ratio of upper flange and span on eigenvalue buckling loads of each order of the beams can be studied. The results show that the buckling loads of each order of the beams can be significantly improved with the decrease of the height-width ratio of upper flange and span. Height-width ratio of upper flange and span have greater influence on high-order buckling load of beams. When the first-order buckling mode of the beam is analysed, overall flexural-torsional buckling occurs and the overall linear displacement and angular displacement reach the maximum at the mid-span position of the beam. It can be concluded that the displacement of the beam is mainly out-of-plane displacement in Z direction, and the rotation of the beam is mainly in X direction. It lays a foundation for further nonlinear buckling analysis of such composite beams.

Tension-Compression and Shear of Plane Test Specimens from Laminated Composites with $$\boldsymbol{[90^{\circ}]}_{\boldsymbol{s}}$$ Structure: Numerical Method of Linearized Problem and Multiscale Buckling Modes

Tension-Compression and Shear of Plane Test Specimens from Laminated Composites with $$\boldsymbol{[90^{\circ}]}_{\boldsymbol{s}}$$ Structure: Numerical Method of Linearized Problem and Multiscale Buckling Modes

Finite element simulation for investigation on thermal post-buckling of geometrically imperfect GOP-reinforced beam

In this paper, a finite element (FE) simulation has been provided for investigation on thermal post-buckling of geometrically imperfect beams reinforced with graphene oxide powders (GOPs). To this end, a higher-order refined beam theory has been utilized to model the reinforced beam with uniform and non-uniform GOP content. Thus, the employed FE simulation contains a refined beam element in which shear deformations have been considered. Therefore, the degrees of freedom due to both bending and shear displacements have been included. It is also considered that the beam is in thermal environment leading to the thermal buckling at elevated temperatures. The first buckling mode shape of the beam has been considered as the geometrically imperfect configuration. The calculated post-buckling loads of a GOP-reinforced beam are shown to be dependent on several factors including graphene oxide volume, graphene oxide distribution, geometry imperfectness and also center deflection.

Control of kink-band formation in mille-feuille structured Al/Al2Cu eutectic alloys

Kink bands have recently received significant attention owing to their ability to increase the strength and ductility of some Mg alloys. In this study, we first demonstrated that it is also expected even in Al alloys, by controlling the morphology of the introduced kink bands. Several directionally solidified Al–Cu alloys, wherein an Al/Al2Cu eutectic lamellar microstructure developed, were focused, and the variations in deformation behavior with microstructure were examined. The alloys can be deformed at room temperature, and the yield stress exhibits strong anisotropy. A high yield stress appears when stress is applied parallel to the lamellar interface, accompanied by kink-band formation. The microstructure was found to play an important role in controlling kink-band formation and the resultant mechanical properties. Only a few large kink bands form in a eutectic alloy specimen with a full lamellar microstructure, which is accompanied by a lower yield stress. Thus, the kink band cannot be used positively in it. In hypoeutectic alloys in which primary Al grains coexist with the lamellar microstructure, however, significantly high yield stresses appear, which are accompanied by the homogeneous formation of small kink bands. The results demonstrate that microstructural control can vary the role of the deformation kink band from the fracture (buckling) mode to the deformation mode via the change in its morphology. This enables a large increase in yield stress while maintaining the ductility of the Al/Al2Cu eutectic alloy. The high yield stress is maintained at temperatures up to ~300 °C owing to the high thermal stability of the lamellar microstructure. These findings provide new ways to develop novel high-temperature high-strength Al alloys.

A Superconvergent Isogeometric Method with Refined Quadrature for Buckling Analysis of Thin Beams and Plates

A superconvergent isogeometric method is developed for the buckling analysis of thin beams and plates, in which the quadratic basis functions are particularly considered. This method is formulated through refining the quadrature rules used for the numerical integration of geometric and material stiffness matrices. The criterion for the quadrature refinement is the optimization of the buckling load accuracy under the assumption of harmonic buckling modes for thin beams and plates. The method development starts with the thin beam buckling analysis, where the material stiffness matrix with quadratic basis functions does not involve numerical integration and thus the refined quadrature rule for geometric stiffness matrix can be obtained in a relatively easy way. Subsequently, this refined quadrature rule for thin beam geometric stiffness matrix is conveniently generalized to the thin plate geometric stiffness matrix via the tensor product operation. Meanwhile, the refined quadrature rule for the thin plate material stiffness matrix is derived by minimizing the buckling load error. It turns out that the refined quadrature rule for the thin plate material stiffness matrix generally depends on the wave numbers of buckling modes. A theoretical error analysis for the buckling loads evinces that the isogeometric method with refined quadrature rules offers a fourth-order accurate superconvergent algorithm for buckling load computation, which is two orders higher than the standard isogeometric analysis approach. Numerical results well demonstrate the superconvergence of the proposed method for the buckling loads corresponding to harmonic buckling modes, and for those related with non-harmonic modes, the buckling loads given by the proposed method are also much more accurate than their counterparts produced by the conventional isogeometric analysis.

Interaction of Stiffened and Unstiffened Element Buckling Modes in CFS Plain Channel Compression Members

Plain channel compression members are composed of stiffened (web) and unstiffened (flanges) plate elements. Effective width method (EWM) for the design of cold-formed steel (CFS) compression members accounts for unstiffened and stiffened plate elements through plate buckling coefficient, k of 0.425 and 4.0, respectively in the elastic local buckling stress (fcrl) calculation. The more recent direct strength method (DSM) recommends the local buckling strength equations for the design of plain channel compression members. A lipped stub channel compression member undergoes interaction of local buckling initiated by the stiffened elements and distortional buckling initiated by the partially stiffened flange-lip assembly. Based on finite element analysis (FEA) results, it is demonstrated that such an interaction between buckling modes initiated by the stiffened web and unstiffened flanges is possible in plain channel compression members also. The behavior of plain channels can be represented as an interaction of buckling of the unstiffened flange and stiffened web elements, which is equivalent to local-distortional interaction in lip stiffened channels. The deformation plots are also provided to understand these mode interactions. The present study focuses on stub columns and does not consider the interaction of global buckling mode.

Buckling state analysis of compressed composite plates with cut-out

The subject of the research was a thin-walled plate weakened by a cut-out, made of carbon-epoxy laminate, subjected to compression. The study included an analysis of the critical and weakly post-critical behaviour using experimental and numerical methods. As a result of the research conducted on physical plates, a post-critical equilibrium paths, which were then used to determine the critical loads by approximation methods, were determined. Simultaneously, numerical calculations with finite element method were performed, using linear analysis of eigenvalue problems, which the results led to determination of the critical loads for the developed numerical model. The second step of the calculations included the performing of nonlinear analysis of the structure with initiated geometrically imperfection corresponding to the flexural–torsional buckling mode of the plate. The numerical results were compared with the experimental funding, revealing that the developed numerical model of the structure was correct. The numerical simulations were performed using the ABAQUS® software.

Buckling Pattern Transition Of Periodic Porous Elastomers Induced By Proportional Loading Conditions

This paper focuses on the buckling instabilities of periodic porous elastomers under combined multiaxial loading. A numerical model based on the periodic boundary condition (PBC) for the 2D representative volume element (RVE) is proposed, in which two proportional loading parameters are employed to control the complex stressing state applied to the RVE model. A homogenization-based orthogonal transformation matrix is established by satisfying the equality of the total work rate to realize a proportional multiaxial loading on the RVE. First, the transition behavior of buckling patterns of periodic porous structures is revealed through instability analysis for the RVE consisting of [Formula: see text] primitive cells with circular holes subjected to different proportional loading conditions. Simulation results show that the first-order buckling mode of RVE may change suddenly from a uniaxial shearing buckling pattern to a biaxial rotating buckling pattern at a critical loading proportion. Then the influences of the number of primitive cells in the enlarged RVE on the buckling behavior are discussed. When the number of primitive cells in any enlarging direction is odd, the points of buckling pattern transition of the enlarged RVEs vary significantly with the number of cells in RVE. When the number of primitive cells is even in both enlarging directions, there is no apparent difference for the critical buckling stresses of the enlarged RVEs.

Research on local buckling capacity of lipped C-section stainless steel beams under weak axis bending

In order to obtain the local buckling capacity of lipped C-section stainless steel beams under weak axis bending, local buckling tests were carried out on 6 stainless steel beams under weak axis bending made of Austenitic stainless steel S30408 (AISI304), revealing the mechanical properties and failure mechanism when local buckling occurred, and the failure phenomenon, load–displacement curves, load–strain curves and local buckling capacity of the specimens were obtained. The test results showed that the failure mode of the specimen was local buckling located in the mid-span web, showing a convex or concave mode. The wave peak was near the mid-span section, and the local buckling of the web along the longitudinal direction occurred in multi-wave buckling mode. The refined finite element model of lipped C-section stainless steel beam specimens under weak axis bending was established. The mechanical properties and local buckling bearing capacity of each specimen were simulated and analysed. The accuracy of the refined model was verified by comparing the finite element results with the test results. In order to simplify the finite element simulation analysis, the refined finite element simulation was simplified. Then 4 kinds of imperfection simplification models were established considering different initial imperfections, and 8 kinds of length simplification models were built based on different lengths and support constraints. Detailed comparison and analysis were performed on results of simplified model refined finite element model and tests to verify the accuracy of the simplified model.

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.

A Numerical Approach Based on Finite Element Method for the Wrinkling Analysis of Dielectric Elastomer Membranes

Abstract Dielectric elastomer (DE) actuators are deformable capacitors capable of a muscle-like actuation when charged. When subjected to voltage, DE membranes coated with compliant electrodes may form wrinkles due to the Maxwell stress. Here, we develop a numerical approach based on the finite element method (FEM) to predict the morphology of wrinkled DE membranes mounted on a rigid frame. The approach includes two steps: (I) pre-buckling and (II) post-buckling. In step I, the first buckling mode of the DE membrane is investigated by substituting the Maxwell stress with thermal stress in the built-in function of the FEM platform simulia abaqus. In step II, we use this first buckling mode as an artificial geometric imperfection to conduct the post-buckling analysis. For this purpose, we develop an equivalent model to simulate the mechanical behavior of DEs. Based on our approach, the thickness distribution and the thinnest site of the wrinkled DE membranes subjected to voltage are investigated. The simulations reveal that the crests/troughs of the wrinkles are the thinnest sites around the center of the membrane and corroborate these findings experimentally. Finally, we successfully predict the wrinkles of DE membranes mounted on an isosceles right triangle frame with various sizes of wrinkles generated simultaneously. These results shed light on the fundamental understanding of wrinkled dielectric elastomers but may also trigger new applications such as programmable wrinkles for optical devices or their prevention in DE actuators.

Flexural properties and failure mechanisms of infusible thermoplastic- and thermosetting based composite materials for marine applications

This study aims to evaluate the flexural properties and associated failure mechanisms of a reactive thermoplastic relative to traditional thermosetting resin systems (polyester, vinylester, epoxy) for potential application in marine vessels over 50 m in length, as part of the H2020 FIBRESHIP project. All resin systems are compatible with the vacuum assisted liquid resin infusion manufacturing technique commonly used in small/medium size shipyards. Glass fibre reinforced polymer (GFRP) laminates were manufactured, test samples extracted, immersed in deionised water or an organic liquid (diesel) and mechanically tested to evaluate the flexural strength and modulus. Failure mechanisms are analysed by scanning electron microscope (SEM). In terms of flexural strength, the reactive thermoplastic based laminate performed similar to the epoxy in terms of retained strength in both deionised water and diesel. The governing failure mode of fibre buckling and kink band formation coupled with interlaminar cracking was identified for both the epoxy and the thermoplastic. The vinylester laminate retained equivalent strength in all three environments while polyester showed the greatest reduction in water due to extensive interlaminar cracking. Overall, the flexural properties of the reactive thermoplastic are shown to be competitive with traditional candidate resin systems for marine structures. The strength reduction and failure modes in the dry, wet and diesel condition were similar to the epoxy while the reduction of modulus was negligible in water and less than 10% in diesel.

An application of the direct strength method to the design of castellated beams subject to flexure

The aim of this research is to investigate the instability of castellated beams and the interaction between lateral-torsional and compression tee local buckling modes. Firstly, a comprehensive study of 197 simply supported Litzka castellated beams under pure bending is carried out. The study involves eigenvalue and fully nonlinear finite element analyses, e.g. including both material nonlinearity and geometric imperfections. After computing the critical moments associated to local and global modes and the ultimate moments, an approach based on the Direct Strength Method is proposed using regression techniques to derive strength prediction equations. The developed method is then compared with current standards procedures. The results show that the proposed equation predicts better strength values in all cases, especially those in which local and/or interaction failure modes dominate the behavior of the beam. The results also show that some of the procedures suggested in standards and guides for the design of castellated beams under flexure, either underestimate or overestimate the failure moment when considering the interaction between global buckling mode and plastification.

Seventh-Order Polynomial Constituting the Exact Buckling Mode of a Functionally Graded Column

In this paper, a functionally graded material column that is simply supported at one end and clamped at the other is considered. The buckling mode is postulated as a high-order polynomial. Six novel closed-form solutions are found by the semi-inverse technique. These solutions can be used as benchmark problems with which numerous approximate solution techniques can be tested. Technical novelty consists in searching solutions via semi-inverse method, namely, by postulating the mode shape and searching for the variable flexural rigidity that matches the mode shape. The method is not universal in the sense that it does not develop method of finding the buckling loads for any, arbitrarily, axially graded columns; rather it furnishes closed-form solutions for flexural rigidity grading for columns that might possess the seventh-order polynomial mode shape. Still, this finding appears to be remarkable because it delivers the closed-form solution for the buckling loads.

An adaptive XIGA with locally refined NURBS for modeling cracked composite FG Mindlin–Reissner plates

This paper is devoted to numerical investigations on mechanical behavior of cracked composite functionally graded (FG) plates. We thus develop an efficient adaptive approach in terms of the extended isogeometric analysis (XIGA) enhanced by locally refined non-uniform rational B-spline (LR NURBS) for natural frequency and buckling analysis of cracked FG Mindlin–Reissner plates. In this setting, the crack geometries, which are described by the level sets, are independent of the computational mesh; and the LR NURBS basis functions, which have the abilities of local refinement and modeling the complex shape, are used as the shape functions of XIGA. According to the recovered stresses of the first buckling or free vibration mode, a posteriori error estimator for driving the adaptive process is defined. The accuracy can be effectively improved through adaptive local refinements, demonstrated through numerical experiments with complex geometries. Compared with uniform global refinement, XIGA based on adaptive local refinement has the characteristics of high precision at low cost and fast convergence rate. The effects of some factors such as crack length and location, plate thickness, gradient index, boundary condition, loading type, etc. on critical buckling loads and natural frequencies are investigated.

Research on the dynamic buckling of a typical deck grillage structure subjected to in-plane impact Load

The dynamic buckling of the main deck grillage would result in the total collapse of the ship hull subjected to a far-filed underwater explosion. This dynamic buckling is mainly due to the dynamic moment of the ship hull when the ship hull experiences a sudden movement under impact load from the explosion. In order to investigate the ultimate strength of a typical deck grillage under quasi-static and dynamic in-plane compressive load, a structure model, in which the real constrained condition of the deck grillage was taken into consideration, was designed and manufactured. The quasi-static ultimate strength and damage mode of the deck grillage under in-plane compressive load was experimentally investigated. The Finite Element Method (FEM) was employed to predict the ultimate strength of the deck grillage subjected to quasi-static in-plane compressive load, and was validated by comparing the results from experimental tests and numerical simulations. In addition, the numerical simulations of dynamic buckling of the same model under in-plane impact load was performed, in which the influences of the load amplitude and the frequency of dynamic impact load, as well as the initial stress and deflection induced by wave load on the ultimate strength and failure mode were investigated. The results show that the dynamic buckling mode is quite different from the failure mode of the structure subjected to quasi-static in-plane compressive load. The displacements of deck edge in the vertical direction and the axial displacements are getting larger with the decrease of impact frequency. Besides, it is found that the dynamic buckling strength roughly linearly decreased with the increase of initial proportion of the static ultimate strength P0. The conclusions drawn from the researches of this paper would help better designing of the ship structure under impact loads.

Experimental research on four-point-bending loading of composite fuselage frame

A four-point-bending loading test device was designed for the pure bending loading of the composite fuselage curved frame. The reinforcing subplates, reinforcing frames, wedge-shaped blocks and other parts were installed in the load segment of test pieces to enhance the local stiffness, strength and torsional stiffness. Four-point-bending loading tests and nonlinear finite element calculation of C-frame and Z-frame pieces under the condition of positive bending was carried out. The calculated buckling mode was in good agreement with the test result, which provides a certain theoretical basis for the instability mode analysis of curved frames. The test and analysis results show that under the condition of positive bending and the middle section of C-frame has lateral instability and the end inner edge of the frame has the local buckling and damage. While the middle section of inner edge of the Z-frame has only local buckling and damage. The test results of two kinds of frame show that the stability and structural strength of Z-frame are better than that of C-frame.