Buckling Load Research Articles

Fractional-order structural stability: Formulation and application to the critical load of nonlocal slender structures

This study presents a framework to perform stability analysis of nonlocal solids whose behavior is described according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture the nonlocal response of the medium by means of nonlocal kinematic relations. We use the geometrically nonlinear fractional-order kinematic relations within an energy based approach to establish the Lagrange-Dirichlet stability criteria for nonlocal structures. This energy based approach to nonlocal structural stability is possible due to a positive-definite and thermodynamically consistent definition of the deformation energy enabled by the fractional-order kinematic formulation. The Rayleigh-Ritz coefficient for critical load is also derived for linear buckling conditions. The fractional-order formulation is finally used to determine critical loads for buckling of the slender nonlocal beams and plates using a dedicated fractional-order finite element solver. Results establish that, in contrast to existing studies, the effect of nonlocal interactions is observed on both the material and the geometric stiffness, when using the fractional-order kinematics approach. These observations are supported quantitatively via the solution of case studies that focus on the critical buckling response of fractional-order nonlocal slender structures, and a direct comparison of the fractional-order approach with classical nonlocal approaches.

Analysis of cold formed steel sheet pile for earth retaining wall

Failure loads of sheet pile having various profiles such as U, Z and Omega/Hat profiles under compression was carried out by using equations of strength of materials and compared the failure load under various modes such as Euler’s buckling, torsional buckling and failure load due to yielding. Compared the strength of various profiles under flexure by using finite element analysis. Sheet pile can be analyzed as a unit cell for the simplified finite element analysis. For selecting the unit cell sheet pile with omega/Hat section was analyzed for profile containing one to eight numbers and checked the convergence of bending stress and maximum lateral deflection. Interlocks were analyzed for three different conditions such as plane interlock, interlock filled with bitumen and welded interlock. Location of interlock and neutral axis of the wall will affect the stability of the structure. Sheet piles with various cross sections were analyzed and studied the shear stress and bending stress along the cross section. From the structural performance of various cross sections omega/hat section can be considered as the most efficient cross section for the cold formed steel sheet pile because of its more load carrying capacity under compression and high torsion resistance and less bending stress. Results from the finite element analysis for the selection of unit cell shows that the stress and deflection value was converge at the sheet pile having 6 numbers of profiles.
 Keywords: sheet piles, building, resistance.

Buckling analysis of axially compressed CFRR cylindrical shell with damaged porous microcapsule coating in hygrothermal environments

This paper shows an analytical approach to investigate buckling behavior of a carbon fiber reinforced resin (CFRR) cylindrical shell covered with a damaged porous microcapsule coating subjected to axial compressed loads under hygrothermal environment. The formulas are in view of the Donnell’s shell theory considering the von Kármán geometric nonlinearity. The material parameters of microcapsule coating are predicted with the self-consistent model and Mori-Tanaka model. By utilizing Galerkin approach, the buckling behavior for simple-support damaged double-layered cylindrical shell are determined. The influence of temperature and moisture, interface debonding damages, material properties, geometry parameters of microcapsules and porosity upon the buckling behavior of the double-layered cylindrical shell are investigated. Results show moisture and geometry size of microcapsules are propitious to the critical buckling and post-buckling compressive load. In addition, the micro-structure damage greatly affects temperature and moisture. The geometric parameters of microcapsules significantly affect the buckling and post-buckling behavior of double-layered cylindrical shell.

Buckling and vibration analysis of shape memory laminated composite beams under axially heterogeneous in-plane loads in the glass transition temperature region

Buckling and vibration study of the shape memory polymer composites (SMPC) across the glass transition temperature under heterogeneous loading conditions are presented. Finite element analysis based on C° continuity equation through the higher order shear deformation theory (HSDT) is employed considering non linear Von Karman approach to estimate critical buckling and vibration for the temperature span from 273 to 373 K. Extensive numerical investigations are presented to understand the effect of temperature, boundary conditions, aspect ratio, fiber orientations, laminate stacking and modes of phenomenon on the buckling and vibration behavior of SMPC beam along with the validation and convergence study. Effect of thermal conditions, particularly in the glass transition region of the shape memory polymer, is considerable and presents cohesive relation between dynamic modulus properties with magnitude of critical buckling and vibration. Moreover, it has also been inferred that type of axial loading condition along with the corresponding boundary conditions significantly affect the buckling and vibration load across the glass transition region.

Active Control of Thermo-mechanical Buckling of Composite Laminated Plates Using Piezoelectric Actuators

This paper is concerned with the active control of thermo-mechanical buckling of composite laminated plates using piezoelectric facesheets as actuators. The four-variable trigonometric shear deformation theory and Hamilton’s principle are applied to formulate the governing equation of structural system. The temperature feedback control strategy is proposed to conduct the active control of thermal-mechanical buckling. The simulation results show that the thermo-mechanical buckling of composite laminated plates can be effectively controlled by the presented control method. With a specific control gain, the critical mechanical buckling load can remain constant at different temperatures. The effects of geometric parameters, fiber angle, stacking sequence, position of piezoelectric layer and boundary conditions on the active control of thermo-mechanical buckling are also investigated.

Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique.

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

Parameter studies and evaluation principles of delamination damage in laminated composites

Delamination represents one of the most severe failure modes in composite laminates, especially when they are subjected to uniaxial compression loads. The evaluation of the delamination damage has always been an essential issue of composite laminates for durability and damage tolerance in engineering practice. Focusing on the most typical and representative elliptical delamination issue, an analytical model simultaneously considering the conservative buckling process and non-conservative delamination propagation process is implemented. Various computational cases considering different delamination depths, directions, aspect ratios, and areas are established, and the predicted results based on the analytical model are carefully compared. Effects of these geometrical delamination parameters on the buckling, delamination propagation, and failure behaviors of composite laminates are thoroughly analyzed, and innovative evaluation principles of the delamination damage have been concluded. It is found that the delamination area is the key factor that truly affecting the failure behaviors of delaminated composites, and the local / global buckling and failure loads show clear linearity with the delamination area, whilst the delamination depth and direction only have slight effects.

Determination of the 1st Buckling and Collapse Loads for Integrally Stiffened Panels by Artificial Neural Network and Design of Experiment Methodology

Buckling is a structural instability that load carrying capacity of a structural element may suddenly decrease. This sudden change in the load carrying capacity may cause catastrophic failures. Therefore, determination of the first buckling and collapse loads of structural elements is essential. FE analyses and structural testing are used to determine buckling characteristics of a structural element. However, in early design stages, FE analyses are time consuming and structural testing is costly. In this paper, artificial neural network tool is used to reduce computational effort to determine buckling loads of integrally stiffened structural panels in early design stages. Moreover, Latin Hypercube Sampling (LHS) methodology is used to reduce the number of required FE analyses to generate database that artificial neural network is based on. Mean errors and fit performance model results are compared to determine accuracy of the neural network results.

Nonlinear buckling analysis of FGP shallow spherical shells under thermomechanical condition

In this study, an analytical method is presented to investigate the nonlinear buckling analysis of functionally graded porous (FGP) shallow spherical shells exposed to external excitation in a thermal environment resting on elastic foundations. The elastic foundations of the FGP shell are consist of a two-term Winkler-Pasternak's model. Using the classical theory of shells and considering nonlinear von Karman-Donnell relations and Hook law, the governing equations of thin FG porous spherical shells are extracted. Galerkin's method is utilized to discretize the governing equation of shallow spherical shell. Regarding the discretized equations of motion, the explicit expressions for dynamic and static critical buckling loading are determined under thermomechanical effect. Two types of distributions for FG porous, including the uniform and symmetric porosity, are considered. To investigate the dynamic buckling exposed to external pressure and thermal effect, the equations of motion of FGP shallow spherical shells are examined via a numerical method named Runge-Kutta approach, and then with a procedure presented by Budiansky-Roth, the critical load for the nonlinear dynamic buckling is obtained. The influence of thermal environment changes, porosity coefficients, various porosity distributions, elastic foundations, and geometrical characteristics on the nonlinear static and dynamic buckling response of FGP shallow spherical shell is examined.

Shape optimization of lattice sandwich panels for enhansing failure load using linear buckling load factor

Shape optimization of lattice sandwich panels for enhansing failure load using linear buckling load factor

Evaluation on compressive properties of composite laminates with a hole reinforced by metal plate

The in-plane compressive properties of carbon fibre reinforced polymer (CFRP) laminate with a hole is investigated. In order to compare the mechanical behavior, square or round metal plate as the reinforcement is placed near the hole of composite laminate on one side asymmetrically. Quasi-static compression experiment and Speckle approach are applied to the CFRP laminates before and after aluminum alloy reinforcement. Stress concentration, strain-load relation, fiber breakage are analyzed based on experimental results. We found that the static buckling and failure load and elastic modulus of the reinforced composite laminates are larger than the unreinforced composite laminate. The compression experimental result is consistent with the digital speckle experimental result. It is also found that the reinforcement of round metal plate is close to that of square metal plate in terms of the ratio of increased failure load to increased weight. Arch beam of the unreinforced composite laminate with open hole formed when bearing compression loading is analyzed and compared to that of the aluminum alloy plate reinforced composite laminates with open hole.

Design and Analysis of Composite Window Frame for a Regional Aircraft

This work presents the design and analysis of a thermoplastic composite window frame for integration into a regional aircraft. The main parameters which are investigated include buckling, damage and failure loads of a composite window frame subjected to shear loads repesentative of fuselage skin stress distribution due to flight loads. The attachment of such thermoplastic window frame to a thermoset fuselage skin was investigated including both adhesively bonded interface as well as riveting. Even though the bonded frame did meet the design criteria, its failure was very sudden, and the riveted assembly showed a considerably higher strength and structural integrity. The numerical simulation resulted in failure loads which matched very closely to experimental results.

Thermal-induced snap-through buckling of simply-supported functionally graded beams

The instability of functionally graded material (FGM) structures is one of major threats to their service safety in widely engineering applications. This paper aims to clarify a long-standing controversy on the type of thermal instability of simply-supported FGM beams. Firstbased on the Euler-Bernoulli beam theory and von Karman geometric nonlinearitya nonlinear governing equation of simply-supported FGM beams under uniform thermal loads by Zhang’s two-variable method is formulated. Secondan approximate analytic solution to the nonlinear integro-differential boundary value problem with a thermal-induced inhomogeneous force boundary condition is obtained by using a semi-inverse method when the coordinate axis is relocated to the bending axis (physical neutral plane), and then the analytical predictions are verified by the differential quadrature method (DQM). Finallybased on the free energy theoremit is revealed that the symmetry breaking caused by the material inhomogeneity can make the simply-supported FGM beam under uniform thermal loads occur snap-through postbuckling only in odd modes; furthermorethe nonlinear critical load of thermal buckling varies non-monotonically with the functional gradient index due to the stretching-bending coupling effect. These results are expected to provide new ideas and references for the design and regulation of FGM structures.

Modification of the Euler Load for the Stiffened Compressive Members and Determination of the Optimal Stiffening for the Maximum Buckling Load

The potential of buckling in compressive members has been considered as a disadvantage when using steel members in the construction industry. In spite of the progress made in this regard, buckling is still considered as a challenge in the analysis and design of compressive steel structural members. Such a challenging phenomenon can be controlled by strengthening of compressive members. Stiffened compressive members can control the weakness of steel members in the global buckling. In this paper, elastic buckling behavior of three-segment symmetric steel members with pinned ends is investigated. The differential stability equation for non-prismatic three-segment members is solved numerically. Critical load parameter for stiffened members is calculated considering different stiffened length and moment of inertia ratios. Based on a wide range of the calculated data, the buckling load could be accounted as a safe measure to be used in the design formulas. Evaluation of the effects of various parameters on the buckling load shows that the desired buckling load value can be achieved by a partially stiffened member. By constant increase of a member’s weight, the shorter the length of the variation in the cross-section, the higher moment of inertia is essential in the stiffened segment; and the maximum critical load parameter is achieved by a stiffened length ratio between 0.4 and 0.6.

Hyper-reduced arc-length algorithm for stability analysis in elastoplasticity

In this article an “hyper-reduced” scheme for the Crisfield’s algorithm (Crisfield, 1981) applied to buckling simulations and plastic instabilities is presented. The two linear systems and the ellipse equation entering the algorithm are projected on a reduced space and solved in a reduced integration domain, resulting in a system of “hyper-reduced” equations. Use is made of the Gappy proper orthogonal decomposition to recover stresses outside the reduced integration domain. Various methods are proposed to construct a reduced bases, making use of simulation data obtained with standard finite element method and a stress-based error criterion for the hyper reduced calculations is proposed. A “greedy” algorithm coupled with this error criterion is used to generate intelligently full standard finite element simulations and enrich the reduced base, demonstrating the adequacy of the error criterion. Finally, numerical results pertaining to elastoplastic structures undergoing finite strains, with emphasis on buckling and limit load predictions are presented. A parametric study on the geometry of the structure is carried out in order to determine the domain of validity of the proposed hyper-reduced modeling approach.

Thermal buckling of ballasted tangent track

Euler type analysis usually used for compression members in structural engineering does not work for railroad track. Euler type analytical formulas for horizontal and vertical buckling endorsed in a recent literature is reviewed to demonstrate its weakness. Using definition of moment and curvature as well as principle of equilibrium, the author suggests formula for horizontal buckling load of railroad track and demonstrates validation in context with currently accepted values, published results, and past field tests. The buckling load from suggested formula agrees with the recent buckling load formula based on total energy theorem. A formula is suggested to study the effect of misalignment on critical temperature differential or critical load. A vertical buckling load formula is derived from horizontal buckling load formula. A buckling process is narrated through step by step computation. Formulas are suggested to compute the effect of track misalignment on critical buckling load and threshold radius of a vertical curve.

Improvement in Critical Load for Buckling of Structural Steel I-Section Column in Fixed-Free Condition by Modifying the Cross-Section

Improvement in Critical Load for Buckling of Structural Steel I-Section Column in Fixed-Free Condition by Modifying the Cross-Section

On the peak quasi-static load of axisymmetric buckling of circular tubes

The axial crushing of thin-walled metal circular tubes was addressed in this work for its importance in many engineering applications especially when failed in concertina mode. Theoretical estimates of the peak load were formulated for lower and upper bounds based on Rankine-Gordon principle and the elastic-plastic criterion of buckling, respectively. Numerical simulations were also made to validate these estimates using ABAQUS 14-2 finite element software. Previous findings were compared with both the theoretical and numerical results of the present work. It is found that the peak load is unique for a particular specimen, while the lower bound stress can be equal for different values of D, t and L, as long as the D/t ratio is the same. Moreover, the upper bound stress requires both D/t and L/D ratios. It was also found that all numerical results agree favorably with the theoretical predictions, but not with all of the experimental findings. This partial disagreement was proved to be attributed to the questionable data extracted from one of the cited work. Empirical relations for the available experimental findings were established to confirm the source of disagreement as well as to afford a unified relation which might represent data of different materials, and finally to offer an alternative prediction of experimental peak load.

Buckling and free vibration analyses of pultruded GFRP laminated composites: Experimental, numerical and analytical investigations

Two of the most important of the loads exposed to the structures whose construction material is pultruded GFRP are buckling and vibration loads. Therefore, it is crucial to determine the behavior of this material against buckling and vibration loads considering the fiber and layer configurations. Pursuant to this goal, comprehensive experimental, numerical and analytical studies have been undertaken. An exact analytical solution based on first order shear deformation plate theory was used for the solution of stability and vibration problems. The virtual displacement principle was utilized herein to derive governing differential equations. Effective material properties of pultruded GFRP composites were obtained by using the mixture rule model. The laminated plate was assumed to be a plate strip in cylindrical bending. The solutions were obtained with an infinite series. On the other hand, a numerical study was conducted by a finite element software, ABAQUS. Burn-out and mechanical tests were performed to determine the mechanical properties of the obtained pultruded GFRP composite specimens. The buckling and modal analysis for natural frequencies tests were utilized to investigate the performance of pultruded GFRP specimens. The experimental findings were compared with the calculated analytical and numerical results, and good conformance was obtained. Macro and micro mechanical damage analyzes were performed to better understand the behavior of the pultruded GFRP composite specimens.

Postbuckling response of functionally graded hybrid plates with cutouts under in-plane shear load

The present study deals with the investigation of buckling and postbuckling responses of functionally graded hybrid square plates which are symmetric about its mid plane. The cutouts of various sizes and shapes located at the center of the plate are considered. The plate is subjected to positive and negative in-plane shear loads. The boundary conditions used are simply supported on all the four edges of the plate. Three stacking sequences are considered to investigate the optimum stacking sequence at which the critical buckling and first failure loads are highest. Functionally graded hybrid plates (FH) subjected to negative in-plane shear load is more effective compared to plates subjected to positive in-plane shear load. Diamond shaped cutout with small sized perforation has the highest critical buckling and first ply failure loads amongst the FH plates with cutouts. It is observed that the direction of applied in-plane shear load, fiber stacking sequence; cutout shape and size substantially influence the strength and failure characteristics of functionally graded hybrid composite plates.