Bending Buckling Research Articles

Application of discrete shear quadrilateral element for static bending, free vibration and buckling analysis of functionally graded material plate

This paper presents a discrete shear quadrilateral (DSQ) element to study the static bending, free vibration, and buckling analysis of functionally graded material (FGM) plate structures. The effective properties of the FGM plate are computed using the rule of mixtures. The plate kinematics is based on Resinner-Mindlin plate theory with discrete shear constraints introduced to relate the kinematical and the independent shear strains. The efficacy of the present element is demonstrated with a few examples for Static bending, free vibration, and mechanical and thermal buckling. The influence of various parameters such as the plate aspect ratio, material gradient index, and boundary conditions are systematically studied. From the study, it is obvious that the DSQ element yields accurate results and converges optimally.

Analysis of Flexural Buckling Capacity of Stainless Steel Columns under Axial Compression

In order to provide a basis for the compilation of the bending buckling stability part of axially compressed columns in the technical code for stainless steel structures, the design methods and experimental research data of similar components are collected and compared. The results showed that there are some deficiencies in the current European code for the design of stainless steel structures and the American code for the design of cold‐formed stainless steel structures. According to the collected test data of square tube, rectangular tube, circular tube, elliptical tube, welded H‐shaped steel, and cold‐formed C‐shaped steel for 199 section columns and according to the influence of cold‐formed effect and residual stress on the stability of axial compression members, the members are divided into three categories: A, B, and C according to the section form, in which the columns with cold‐formed square, rectangular hollow section, and lipped C‐section were included in A, columns with circular and oval hollow section were sorted into B, columns with welded H‐section were separated into C, and the three categories of axial compression stability curves are expressed in the form of Perry formula. The comparison with the test data shows that the three kinds of curves can well estimate the stability bearing capacity of members, and the discreteness is small. The reliability of the proposed formula is analyzed, and the results show that its reliability index β meets the requirements of the GB 50068 standard.

Research on overall stability of BS700 high-strength steel columns with box section

To study the overall stability of BS700 high-strength steel axially compressed columns with box section, the axial compression tests of 10 thin-walled box section columns were conducted in this paper, and the numerical calculation was completed using the finite element method. Moreover, the factor of initial geometric imperfections was considered during the processes of testing and analysis. The test results showed that the failure mode of BS700 high-strength steel columns with box sections was bending buckling. 1/1000 of the member length mentioned in the Code for Design of Steel structures (GB50017–2017) could be used as the maximum initial imperfection. Compared with the curves of the 3c type in the GB50017–2017 and Eurocode specifications, the long-column test results and finite element analysis results were evidently larger and close to those of 3b types in GB50017–2017 and Eurocode 3b (8% larger on average). Moreover, although the ANSI/AISC 360–10 specifications coincided well, this standard tended to be dangerous because it prescribed a relatively low slenderness ratio. Therefore, the curves of the 3b type stipulated in GB50017–2017 and Eurocode were recommended.

Testing, simulation and design of steel equal-leg angle section beams

The stability and design of steel equal-leg angle section members subjected to uniaxial bending are studied herein. An experimental investigation, comprising material testing, initial geometric imperfection measurements and physical tests on hot-rolled steel equal-leg angle section beams is first presented. The test results, in combination with existing experimental data on steel equal-leg angle section beams collected from the literature, are then used for the validation of numerical (shell finite element) models, developed within the commercial package ABAQUS. Next, a numerical parametric study is presented considering both hot-rolled and cold-formed steel angle section beams with a wide range of slenderness values. In major-axis bending, both lateral-torsional and local buckling were observed, with the former characterised by lateral deflection and twist of the cross-section along the member length but no cross-section deformation and the latter by relative twist and transverse bending of the outstands. In minor-axis bending, lateral-torsional buckling and Brazier flattening were observed, with the latter characterised by splaying of the outstands. Note that, for equal-leg angles under minor-axis bending, lateral-torsional buckling is dominant when the cross-section tips are in compression, while Brazier flattening is more influential when the cross-section tips are in tension. When designing for major-axis bending according to Eurocode 3, both local and lateral-torsional buckling are considered; it is shown herein that equal-leg angle section beams under major-axis bending can be designed using a normalised slenderness based on the minimum of the local and lateral-torsional elastic buckling moments, while also considering the ratio of the local to the lateral-torsional elastic buckling moments. For minor-axis bending, Eurocode 3 only requires cross-section checks; this is found to result in unsafe predictions in some cases. It is shown that both safer and more accurate resistance predictions can be achieved when lateral-torsional buckling and Brazier flattening are accounted for in the design of equal-leg angle section beams under minor-axis bending, using a normalised slenderness, based on the minimum of the lateral-torsional and Brazier flattening critical buckling moments. Finally, new design proposals for steel equal-leg angle section beams, covering both major- and minor-axis bending, are developed and verified against the experimental and numerical results. The proposed design rules are shown to offer substantially more accurate and consistent resistance predictions compared to existing codified design rules. The reliability of the new design provisions, with a recommended partial safety factor γM1=1.0, is verified following the EN 1990 procedure.

A refined quasi-3D logarithmic shear deformation theory-based effective meshfree method for analysis of functionally graded plates resting on the elastic foundation

In this paper, a new refined quasi-3-dimensional logarithmic shear deformation theory (RQ-3DLSDT) and an advanced moving Kriging interpolation (AMKI) based-meshless method is combined for the first time to study the static bending, free vibration, and compressive buckling analysis of isotropic and sandwich functionally graded plates laid on elastic foundations. The RQ-3DLSDT considering the effect of thickness stretching based only on four-unknown variables to determine the displacement field leading to reduce computational efforts. The weak forms of the equilibrium equation are discretized and numerically solved by the AMKI mesh-free method employed a proposed quadric correlation function for getting stable solutions.

Bending, axial buckling and shear buckling analyses of FG-porous plates based on a refined plate theory

ABSTRACT In this paper, numerical solutions are presented for static bending and mechanical buckling analyses of functionally graded porous (FGP) plates. The plate is modelled based on a refined plate theory and three porosity distributions with the same total mass density are considered. The set of the governing equations is derived using minimum potential energy and is solved numerically using the differential quadrature method (DQM). Convergence and accuracy of the solution are confirmed and the effects of porosity parameter, porosity distribution pattern, thickness and aspect ratio of the plate and boundary conditions on the deflection, intensity and distribution of stress and critical buckling load are investigated. It is shown by the numerical examples that an increment in the porosity parameter leads to a reduction in the critical buckling load and an increase in static deflection of the plate. Numerical results reveal that the effect of the porosity parameter on the distribution and intensity of the stress components strongly is dependent on the porosity distribution pattern.

Bending and Buckling Analysis of Functionally Graded Euler–Bernoulli Beam Using Stress-Driven Nonlocal Integral Model with Bi-Helmholtz Kernel

Static bending and elastic buckling of Euler–Bernoulli beam made of functionally graded (FG) materials along thickness direction is studied theoretically using stress-driven integral model with bi-Helmholtz kernel, where the relation between nonlocal stress and strain is expressed as Fredholm type integral equation of the first kind. The differential governing equation and corresponding boundary conditions are derived with the principle of minimum potential energy. Several nominal variables are introduced to simplify differential governing equation, integral constitutive equation and boundary conditions. Laplace transform technique is applied directly to solve integro-differential equations, and the nominal bending deflection and moment are expressed with six unknown constants. The explicit expression for nominal deflection for static bending and nonlinear characteristic equation for the bucking load can be determined with two constitutive constraints and four boundary conditions. The results from this study are validated with those from the existing literature when two nonlocal parameters have same value. The influence of nonlocal parameters on the bending deflection and buckling loads for Euler–Bernoulli beam is investigated numerically. A consistent toughening effect is obtained for stress-driven nonlocal integral model with bi-Helmholtz kernel.

A novel general higher-order shear deformation theory for static, vibration and thermal buckling analysis of the functionally graded plates

This paper proposes a new general framework of higher-order shear deformation theory (HSDT) and solves the structural responses of the functionally graded (FG) plates using novel exponential shape functions for the Ritz method. Based on the fundamental equations of the elasticity theory, the displacement field is expanded in a unified form which can recover to many different shear deformation plate theories such as zeroth-order shear deformation plate theory, third-order shear deformation plate theory, various HSDTs and refined four-unknown HSDTs. The characteristic equations of motion are derived from Lagrange’s equations. Ritz-type solutions are developed for bending, free vibration and thermal buckling analysis of the FG plates with various boundary conditions. Three types of temperature variation through the thickness are considered. Numerical results are compared with those from previous studies to verify the accuracy and validity of the present theory. In addition, a parametric study is also performed to investigate the effects of the material parameters, side-to-thickness ratio, temperature rise and boundary conditions on the structural responses of the FG plates.

Finite element investigation on plate buckling coefficients of tapered steel members web plates

An extensive finite element analysis study was conducted to estimate the critical buckling coefficients for tapered steel webs. Three boundary conditions for the web plate were included: simply supported edges, flange restrained edges and fixed edges. The studied parameters are: the tapering ratio of the panel, the panel’s normalized length and the flange-to-web thickness ratio. Three loading conditions were considered: uniform compression, pure bending and pure shear. New formulas are proposed for the axial, bending and shear buckling coefficients for tapered plates. The plate tapering increases its resistance to buckle due to the stiffness provided by the smaller plate width zone to the larger width zone. The presence of the beam’s flanges increases the web resistance to buckle and the web plate tends to behave more like a fixed edges plate as the flanges thickness increases. The existing procedure for the combined compression and bending interaction is validated against the proposed formulas. The proposed formulas were found to be valid for singly tapered members by introducing newly proposed reduction factors.

Shear deformation characteristics and defect evolution of the biaxial ±45° and 0/90° glass non-crimp fabrics

Currently, the shear pre-tension coupling behavior and evolution of various mesoscopic defects for the biaxial non-crimp fabric (NCF) are not revealed. Here, this work systematically conducted the picture frame shear with applied pre-tension and hemisphere forming for the ±45° and 0/90° glass NCF. In the picture frame shearing, it is identified that the effective shear response of the biaxial NCF in the positive shear mode should be characterized in the cycle 1 due to the irreversible destruction of the NCF architecture. Besides, the applying pre-tension is originally demonstrated to be capable of effectively suppressing the wrinkle defect and delaying the triggering shear angle of the wrinkle. Moreover, for the ±45° NCF, the stitching thread suffers tension in positive shear mode, and the wrinkle is the main defect. In the negative shear mode, due to the non-pure shearing at high shear angle and compression of stitching thread, the mesoscopic defects, including bending and unit cell buckling of the stitching thread, are generated. In the hemisphere forming, it is revealed that the shear deformation is certainly arose in the tensile region of the ±45° NCF due to the asymmetrical yarn shrink. The same fabric wrinkle and mesoscopic stitching thread defects are also originally identified, demonstrating the hemisphere forming is highly correlated to the large shear deformation. The results here provide a basic reference to suppress the defects in the performing process of the biaxial NCF.

Seismic behavior of steel tube confined reinforced concrete double-column bridge bents

A novel type of composite bridge bent consisting of slender steel tube confined reinforced concrete (STCRC) double-column connected by binding steel plates is proposed. Its main advantage is the convenient construction process that eliminates the embedment of a steel tube into the concrete foundation. Four STCRC double-column bent specimens were tested under the pseudo-static loading considering the key parameters of the axial load ratio and the disconnection mode of circular steel tube. All test specimens showed the mixed failure mode of column bending and binding steel plate buckling. As the axial load ratio increased from 0.12 to 0.24, the lateral load capacity and flexural stiffness of the specimens were improved. Although the disconnection mode of the steel tube changed the layout of plastic hinges, it had a limited influence on the seismic behavior of STCRC double-column bents. The ultimate limit state of the double-column STCRC bridge bent could be simplified as a frame model with plastic hinges, by which the lateral resistances were well predicted.

Size-dependent static and dynamic analysis of Reddy-type micro-beams by strain gradient differential quadrature finite element method

Abstract This paper proposes a strain gradient differential quadrature finite element method to analyze the size-dependent static and dynamic behaviour of Reddy-type micro-beams. This element has 6 of freedom per node and avoids the exploitation of shape functions. A sixth-order differential quadrature-based geometric mapping scheme is constructed to realize the higher-order continuity requirements of kinematic variables. And then, it is combined with the minimum total potential energy principle to derive the motion equation of a generic element. Afterwards, several numerical examples are provided to establish the validity of the developed element. Finally, we utilize this method to analyze the static bending, free vibration, and linear buckling characteristics of uniform and stepped micro-beams. Numerical results show that the current element has prominent convergence and adaptability advantages over the classical shape function-based element. Besides, the size-dependence of vibration and critical buckling mode shapes of micro-beams is demonstrated in the graphical form for the first time.

Micro and meso‑scale modelling of the response of transversely isotropic foam to impact — a structural cell-assembly approach

Foam materials can exhibit transverse isotropy in their mechanical behaviour if their cells are elongated in the foam-rise direction during the fabrication process. Such transversely isotropic foam displays different deformation patterns depending on the loading direction. Since the deformation of foam cells is extremely difficult to observe experimentally due to their small size, a structural cell-assembly model is established via Finite Element (FE) modelling to examine all-level deformation details. A representative volume element (RVE) comprising an appropriate number of cells is established via convergence analysis, and the simulation results are analysed and compared with experimental data [1]. The cell-assembly model is able to capture the mechanical response of PU foam for compression at various strain rates and loading angles to the foam-rise direction, in terms of both the overall stress-strain response and deformation mode. Analysis of the deformation modes of cells via FE simulation indicates that loading in the foam-rise (0°) direction induces: (i) unstable buckling of cells for quasi-static compression; (ii) cell rotation+buckling in addition to cell buckling for quasi-dynamic and dynamic compression. Loading in the transverse (90°) direction generates uniform deformation via stable bending of cell struts for quasi-static, quasi-dynamic and dynamic compression. Loading at angles between 0° and 90° induces a combination of stable cell bending and cell buckling; the ratio of the amount of cell bending to that of cell buckling increases with both loading angle and strain rate. Rate-dependence of the mechanical behaviour of PU foam can also be captured by incorporating rate-sensitivity into the mechanical properties of the cell strut material.

An experimental study on intraply fiber hybridization of filament wound composite pipes subjected to quasi-static compression loading

Abstract This paper aimed to explore the failure modes and crashworthiness characteristics of intraply hybridized fiber reinforced pipes (FRP) made of basalt and glass fiber reinforcements subjected to quasi-static compression loading. Experimental investigations were performed on various fiber orientation angles (±40°, ±55°, and ±70°) of the basalt FRP, glass FRP and hybridized basalt/glass FRP, fabricated by filament winding technique. Fracture mechanisms of pipe samples were discussed to understand failure modes. Three distinct failure modes as transverse shearing, lamina bending, and local buckling were observed in crushing tests. Hybridized samples proved to fix instability deficiency of pipes by exhibiting the progressive failure as combination of transverse shear and lamina bending crushing modes. Also, experimental results belong them within the range of pipes made of glass and basalt fiber data's as expected. In the view of fiber orientation aspect, decrease in winding angle resulted with the significant increase of energy absorption capability of all pipes. The pipes made of glass fiber showed the best specific energy absorption characteristics with the lowest crushing load efficiency.

Structural similitude design for a scaled composite wing box based on optimised stacking sequence

Testing appropriately-designed scaled-down structures instead of the full-size prototype structure is beneficial for quickly understanding the prototype structural behaviour in a cost-effective way. In this study, a novel approach is proposed to design scaled composite structures that can be used to predict the structural responses (e.g. static bending, modal behaviour, and compressive buckling) of the prototype. The objective is to overcome the main drawback of the conventional design method, which tends to result in low accuracy of the prototype prediction when certain variables cannot be appropriately scaled due to manufacturing constraints (e.g. ply thickness). In the present work, a set of scaling laws being independent of boundary conditions were firstly derived for plates and beams respectively based on their governing equations. The genetic algorithm (GA) was then applied to help design the stacking sequence of the scaled models, accommodating the mismatch in similarity conditions resulting from the manufacturing constraint in ply thickness. This GA-based design method was demonstrated to be effective in designing scaled plate, I-beam, and stiffened plate models, with improved accuracy in predicting the prototype structural behaviour compared with the conventional method. The application of this new design method was also extended to an A320 size wing box structure, validating its robustness for complex structures.

Numerical investigations on bending and shear buckling interaction of I-Girders with slender WEB

Steel I-girders with slender web are commonly used in the engineering practice. Previous research results proved that the current bending and shear interaction (M-V) check of the EN1993-1-5 does not always provide safe side resistance. The current research work focuses on the analysis of the M-V interaction behavior of longitudinally unstiffened and stiffened I-girders with slender web. Applicability interval of the current EN1993-1-5 based M-V interaction resistance model is determined and based on the executed numerical investigation a refined M-V interaction equation is proposed to ensure safe and economic design. The results of the numerical parametric study also proved that the flange contribution in the shear buckling resistance does not match the current design rules of the EN 1993-1-5. In a specific parameter range (girders with light flanges) the current design rule underestimates the flange contribution to the shear buckling resistance leading to conservative resistances. However, for I-girders with heavy flanges the current design method gives unsafe results. Therefore, the current paper presents an improved formula to the flange contribution ensuring better approximation of the computed resistances.

Bending and thermal buckling of unsymmetric functionally graded sandwich beams in high-temperature environment based on a new third-order shear deformation theory

This paper presents new results of static bending in high temperature and thermal buckling of sandwich functionally graded beam based on new third-order shear deformation theory (TSDT) and finite element formulations. We assume that the sandwich beam placed in a high-temperature environment for a long time, and so that the temperature distributions uniformly across the beam thickness and material properties are temperature-dependent. Using this TSDT, the analysis does not need any shear correction factors and has no shear-locking. The results show that not all functionally graded structures could process similar to mechanical behaviors and have the ability to perform in high temperature.

Study on the behavior of multi-cell composite T-shaped concrete-filled steel tubular columns subjected to compression under biaxial eccentricity

This paper investigates the behavior of multi-cell composite T-shaped concrete-filled steel tubular (MT-CFST) columns subjected to compression under biaxial eccentricity. Nineteen specimens were tested and presented. The main variables were the position and angle of eccentric loading. The experiment showed that the main failure modes of the specimens were overall bending and local buckling. The position and angle of eccentric loading were two important factors that affected the ultimate load of MT-CFST columns. Finite element software was used to analyze MT-CFST columns subjected to compression under biaxial eccentricity. The simulated results were in good agreement with the experimental data. By modifying the relevant parameters, the effect of the strength of concrete, the thickness of steel tubes, and the section dimension on the ultimate load of specimens were investigated. Based on fiber element analysis, the N–M curves and failure surface of the specimens were obtained. According to the fiber element analysis results, a simplified formula was proposed to predict Mx/M0x–My/M0y curves for specimens subjected to compression under biaxial eccentricity. It can be used to check the bearing capability of MT-CFST columns subjected to compression under biaxial eccentricity. The results predicted by the simplified formula coincide with both the results of experimental testing and finite element analysis.

The differences in the mechanical performance of prismatic and non-prismatic beams with corrugated steel webs: A comparative research

The differences in the mechanical performance of prismatic and non-prismatic beams with concrete flanges and corrugated steel webs (CSWs) are numerically investigated in this paper with respect to their behaviour in bending, shear and shear buckling. With regard to the bending behaviour, it is found that the quasi-plane assumption is still valid for the non-prismatic beams with CSWs, similar to the prismatic beams with CSWs, at their elastic stage and their bending stiffness are mainly provided by the concrete flanges. This is attributed to the accordion effect of such webs. In terms of the shear behaviour, it is found that the inclined bottom flange shares a significant portion of the shear force in the non-prismatic beam with CSW, while the effective shear force carried by the CSW is greatly reduced; this phenomenon is called the Resal effect which is the most important reason leading to the shear performance difference between the prismatic and non-prismatic beams with CSWs. Thus, the traditional calculation assumption that the CSWs bear all the vertical shear force in the prismatic beams with CSWs is no longer applicable in calculating the shear stress in the non-prismatic cases. Additionally, it is noticed from two numerical cases, simulating the prismatic and non-prismatic beams with CSWs under end loading, that the average shear stress in the CSW of the non-prismatic beam decreases gradually from the free-end to the fixed-end with the increase of the hogging bending moment, while the shear stress in the CSW remains nearly constant in the prismatic beam. The numerical results, as well, show that the root cross-section, although it bears the maximum bending moment and shear force, is not the critical shear section of the CSW of the non-prismatic beam. Finally, considering the shear buckling behaviour, it is found that the shear buckling stress of the non-prismatic with CSW is much greater than that of an equal-weight prismatic beam with CSW through eigenvalue buckling analyses.

A New Hyperbolic Two-Unknown Beam Model for Bending and Buckling Analysis of a Nonlocal Strain Gradient Nanobeams

In present paper, a novel two variable shear deformation beam theories are developed and applied to investigate the combined effects of nonlocal stress and strain gradient on the bending and buckling behaviors of nanobeams by using the nonlocal strain gradient theory. The advantage of this theory relies on its two-unknown displacement field as the Euler-Bernoulli beam theory, and it is capable of accurately capturing shear deformation effects, instead of three as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton’s principle. Analytical solutions for the bending and buckling analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending buckling of nanobeams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory. The results obtained are found to be accurate. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and buckling behaviour of nanobeams, but also comparable with the other shear deformation theories which contain more number of unknowns