各向同性和各向异性加劲板的局部屈曲和屈曲后的性能分析

研究了评估各向同性和各向异性加劲板的局部屈曲和屈曲后性能的方法。该方法考虑了2个加劲肋之间的加劲板块,用等效的各种不同刚度横向和转动弹簧代替其余的板块,作为所计算板块的弹性支座。在解决各向同性和具有任意边界条件的碾压对称组合板的局部屈曲问题时,采用二维里兹位移函数(pb-2Ritz)。通过板块的屈曲分析能准确地预测板的局部屈曲性能。最后,将此方法加以改进,用于预测表面已经局部屈曲的加劲板的屈曲后反应。选择适当的边界条件对所分析的构件在屈曲后性能的计算中是非常重要的。该方法计算的结果与相应的有限元结果符合较好。     

The computational post-buckling analysis of fuselage stiffened panels loaded in shear

Fuselage panels are commonly fabricated as skin-stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post-buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the Finite Element method and employing non-linear material and geometric analysis procedures it is possible to model the post-buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Previous work has demonstrated that using a commercial implicit code, the Finite Element method can be used successfully to model the post-buckling behaviour of flat riveted panels subjected to uniform axial compression. This paper expands the compression modelling procedures to flat riveted panels subjected to uniform shear loading, investigating element, mesh, idealisation and material modelling selection, with results validated against mechanical tests. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform shear loading, highlighting subtle but important differences between shear and compression modelling requirements.     

A semi-analytical model for local post-buckling analysis of stringer- and frame-stiffened cylindrical panels

A fast semi-analytical model for the post-buckling analysis of stiffened cylindrical panels is presented. The panel is comprised of a skin (shell) and stiffeners in both longitudinal (stringers) and circumferential direction (frames). Local buckling modes are considered where the skin may buckle within a bay and may induce rotation of the stiffeners. Stringers and frames are considered as structural elements and are thus not ‘smeared’ onto the skin. Large out-of-plane deflections and thus non-linear strain–displacement relations of skin and stiffeners are taken into account. The displacements of skin and stiffeners are approximated by trigonometric functions (Fourier series). First, a linear buckling eigenvalue analysis is carried out and some combination of buckling eigenmodes is chosen as imperfection. Then the load history is started and the Fourier coefficients are determined by minimizing the stiffened panel's energy at each load level. A curve-tracing algorithm, the Riks method, is used to solve the equations. The present model can be used to assess the post-buckling behavior of stiffened panels, for example, aircraft fuselage sections.     

A simplified method for elastic large deflection analysis of plates and stiffened panels due to local buckling

A computational model for analysis of local buckling and postbuckling of stiffened panels is derived. The model provides a tool that is more accurate than existing design codes, and more efficient than nonlinear finite element methods. Any combination of biaxial in-plane compression or tension, shear, and lateral pressure may be analysed. Deflections are assumed in the form of trigonometric function series. The deformations are coupled such that continuity of rotation between the plate and the stiffener web is ensured, as well as longitudinal continuity of displacement. The response history is traced using energy principles and perturbation theory. The procedure is semi-analytical in the sense that all energy formulations are derived analytically, while a numerical method is used for solving the resulting set of equations, and for incrementation of the solution. The stress in certain critical points are checked using the von Mises yield criterion, and the onset of yielding is taken as an estimate of ultimate strength for design purposes.     

The computational post buckling analysis of fuselage stiffened panels loaded in compression

Fuselage panels are commonly fabricated as skin–stringer constructions, which are permitted to locally buckle under normal flight loads. The current analysis methodologies used to determine the post buckling response behaviour of stiffened panels relies on applying simplifying assumptions with semi-empirical/empirical data. Using the finite element method and employing non-linear material and geometric analysis procedures, it is possible to model the post buckling behaviour of stiffened panels without having to place the same emphases on simplifying assumptions or empirical data. Investigation of element, mesh, idealisation, imperfection and solution procedure selection has been undertaken, with results validated against mechanical tests. The research undertaken has demonstrated that using a commercial implicit code, the finite element method can be used successfully to model the post buckling behaviour of flat riveted panels. The work has generated a series of guidelines for the non-linear computational analysis of flat riveted panels subjected to uniform axial compression.     

The buckling characteristics of some integrally formed bead stiffened composite panels

Composite panel stability can easily be improved by using vertical male beads. In this paper, new methods of stabilizing techniques used for the panels, webs and ribs of composite structures are studied. A parametric study is performed to assess the effects of important design considerations such as, bead length, number of beads, bead radius, bead depth and bead spacing on the initial buckling load of the panels. The results show that, there is an optimum bead spacing for each panel containing more than one bead which can be estimated using a simple equation. Integration of vertical beads with a length of less than 0.5 times the panel's length has no significant effect on the buckling load. There are no significant changes on the buckling loads of the beaded panels with bead depths greater than 0.6 times the bead radius. In this investigation, the instability of the nose and main ribs of a light airplane wing structure made of woven E-glass material and stiffened by P.V.C foam core and vertical male beads are also studied using experimental methods. The experimental results show that we can easily improve the buckling capability of the panels and webs by using vertical male beads instead of sandwiched construction. It is estimated that this would cause a weight reduction of about 50% and a manufacturing time reduction of about 50%.     

Improved prediction of simultaneous local and overall buckling of stiffened panels

In this paper, improved expressions for elastic local plate buckling and overall panel buckling of uniaxially compressed T-stiffened panels are developed and validated with 55 ABAQUS eigenvalue buckling analyses of a wide range of typical panel geometries. These two expressions are equated to derive a new expression for the rigidity ratio (EI_x/Db)_CO that uniquely identifies “crossover” panels—those for which local and overall buckling stresses are the same. The new expression for (EI_x/Db)_CO is also validated using the 55 FE models. Earlier work by Chen (Ultimate strength analysis of stiffened panels using a beam-column method. PhD Dissertation, Department of Aerospace and Ocean Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 2003) had produced a new step-by-step beam-column method for predicting stiffener-induced compressive collapse of stiffened panels. An alternative approach is to use orthotropic plate theory. As part of the validation of the new beam-column method, ABAQUS elasto-plastic Riks ultimate strength analyses were made for 107 stiffened panels—the 55 crossover panels and 52 others. The beam-column and orthotropic approaches were also used. A surprising result was that the orthotropic approach has a large error for crossover panels whereas the beam-column method does not. Some possible reasons for this are suggested.     

Compression tests of longitudinally stiffened plates undergoing distortional buckling

This paper describes a series of compression tests performed on longitudinally stiffened plates fabricated from a mild steel plate of thickness of 4.0 mm with nominal yield stress of 235.0 MPa. The stiffened plates with longitudinal stiffeners of a range of rigidities were tested to failure. The ultimate strengths and performances of the longitudinally stiffened plates in compression undergoing distortional buckling or interaction between local and distortional buckling were investigated experimentally and theoretically. The compression tests indicated that the critical buckling mode was dependent mainly on the rigidity of the longitudinal stiffeners and the width-to-thickness ratio of the sub-panels. A noticeable interaction between local and distortional buckling was also observed for some stiffened plates. A significant post-buckling strength reserve was shown for those sections with distortional buckling and for those sections showing interaction between local and distortional buckling. A limiting strength curve for distortional buckling of longitudinally stiffened plates was studied. Simple design strength formulas in the direct strength method are proposed to account for the distortional buckling and the interaction between local and distortional buckling of longitudinally stiffened plates. The strength curves were compared with the test and FE results conducted. The adequacy of the strength curve was confirmed. A set of conclusions on the buckling behavior of longitudinally stiffened plates was drawn from the experimental studies.     

Large deflection orthotropic plate approach to develop ultimate strength formulations for stiffened panels under combined biaxial compression/tension and lateral pressure

This paper uses the large deflection orthotropic plate approach to develop the ultimate strength formulations for steel stiffened panels under combined biaxial compression/tension and lateral pressure loads, considering the overall (grillage) buckling collapse mode. The object panel has a number of one-sided small stiffeners in either one or both orthogonal directions. The stiffened panel is then modeled as an equivalent orthotropic plate, for which the various elastic constants characterizing structural orthotropy are determined in a consistent systematic manner using classical theory of elasticity. The panel edges are considered to be simply supported. The influence of initial deflections is taken into account. The membrane stress distribution inside the panel under combined uniaxial loading (in either longitudinal or transverse direction) and lateral pressure is analyzed by solving the nonlinear governing differential equations of large deflection orthotropic plate theory. It is presumed that the panel collapses when the most highly stressed boundary location yields, resulting in closed-form expressions for the ultimate strength of the stiffened panel. Based on the insights previously developed through numerical studies, the panel ultimate strength interaction formulation between biaxial loads, with lateral pressure regarded as a secondary load component is then proposed as a relevant combination of the two sets of panel ultimate strength formulations, i.e. one for combined longitudinal axial load and lateral pressure and the other for combined transverse axial load and lateral pressure. The validity of the proposed ultimate strength formulations is verified by a comparison with nonlinear finite element and other numerical solutions.     

An investigation of lightly profiled sandwich panels subject to local buckling and flexural wrinkling effects

Sandwich panels exhibit various types of failure modes depending on the steel face used. For the flat and lightly profiled sandwich panels, flexural wrinkling is an extremely important design criterion as the behaviour of these panels is governed mainly by flexural wrinkling. However, in the lightly profiled panels, when the depth or spacing of the ribs increases, flat plate buckling between the ribs occurs leading to the failure of the entire panel due to the interaction between local buckling and flexural wrinkling modes. Current design formulae for sandwich panels do not consider such interactive buckling effects. To obtain a safe design solution, this interactive buckling behaviour should be taken into account in the design of lightly profiled sandwich panels. Therefore a research project was undertaken to investigate the interactive buckling behaviour of lightly profiled panels with varying depths and spacings of the ribs using a series of experiments and finite element analyses. A new improved design formula was developed for the safe and economical design of lightly profiled panels that takes into account the interaction between local buckling and flexural wrinkling. This paper presents the details of this investigation, the results and the new design formula.     

Tripping of thin-walled stiffeners in the axially compressed stiffened panel with lateral pressure and end moment

Tripping of stiffeners under combined loads of axial force, lateral pressure and end moment is studied. First, the neutral balance differential equation under the three combined loads is deduced. The equation is solved with Galerkin's method and a general eigenvalue problem is got. Second, the rotational restraint provided by the plate is studied. Based on the result of FEM, existing formula is modified and comparison of results according to different spring stiffness shows that the modified formula is more reasonable. A program based on the method is developed and its result has a very good coincidence with the result of FEM program MARC. Last, a series of calculation is conducted with above program to study the relation of the three kinds of loads. Regression of the results of the calculation gives out a correlativity formula of the three kinds of loads.     

两边连接交叉加劲钢板剪力墙弹性屈曲分析

采用ANSYS有限元软件对两边连接交叉加劲钢板剪力墙进行了弹性屈曲分析,重点研究了加劲肋与墙板的刚度比、墙板高厚比、边长比以及加劲肋宽厚比对弹性屈曲系数的影响,并将分析结果与十字加劲板进行了比较.研究表明,交叉加劲肋能够显著提高钢板剪力墙的弹性屈曲荷载,其远大于十字加劲肋;随着墙板边长比和高厚比的增大,屈曲系数趋于减小;而较小的加劲肋宽厚比能使墙板获得较大的屈曲系数;最后给出了两边连接交叉加劲板弹性屈曲系数的计算公式.     

Experimental study on local buckling of fire-resisting steel columns under fire load

The structural behavior of stub columns using fire-resistant steel has been investigated experimentally under uniform fire load. The newly-developed fire-resistant steel is proven to have higher strength at elevated temperature than that of conventional steel. Also, the requirement of fire-protection in the fire-resisting steel can be released or relaxed as compared with conventional steel structures. However, the design criteria for the application of the fire-resisting steel in steel columns are still limited. To examine the structural behavior of this type of steel columns under fire load, a total of 24 stub column specimens, including both box columns and H columns, reached their limit states due to axial load under fire condition. The main purpose of these studies is to evaluate the variations of the ultimate strength of steel columns due to different width-to-thickness ratios under specified elevated temperature; in addition, to investigate the reduction effects on column strength resulting in the increasing temperature; and finally, to establish the design guidelines of steel columns using fire-resisting steel. From the experimental results, it is found that the ultimate loads of the stub columns decrease while the width-to-thickness ratios or the temperature increases. However, with the increase of temperature, the effect of the width-to-thickness ratio on ultimate strength decreases. It is also found that the effect of the width-to-thickness ratio on the ultimate strength of box column at elevated temperature is more significant than that of H column. Based on these studies, design guidelines are proposed for the requirement of the width-to-thickness ratios of both box column and H column fabricated from fire-resisting steel.     

Elastic local post-buckling of elliptical tubes

The elastic local post-buckling behaviour of elliptical tubes under compression is analysed in this paper. A brief outline of the local, distortional and global buckling behaviour of EHS tubes is firstly provided, where it is shown that local buckling modes govern the stability of short to intermediate length tubes while distortional modes control the stability of intermediate length to moderately long tubes and global buckling dominates the behaviour of longer tubes. Following this, an in-depth numerical study employing shell finite element modelling, of the elastic local post-buckling behaviour of compressed elliptical hollow section (EHS) tubes is presented. It is concluded that EHS tubes with a low to moderate aspect ratio can support loads up to their limit loads but are imperfection sensitive (shell-type behaviour), while EHS tubes with a moderate to high aspect ratio can carry loads higher than their limit loads (plate-type behaviour) and are imperfection insensitive. The slope of the ascending post-buckling path increases with the EHS aspect ratio and can reach values up to 40% of the slope of the linear primary path. The bound imperfection amplitude concept, separating the imperfection amplitude ranges where the EHS tube is sensitive and insensitive, is proposed. It is also found that, for increasing EHS aspect ratio, the compressive stresses grow and accumulate near the zones of minimum radius of curvature while the zones of maximum radius of curvature possess an approximately uniform and relatively low compressive stress level. Therefore, it is expected that an approach based on the effective width concept widely used for the evaluation of the strength of flat plates may be adapted to the design of EHS tubes with moderate to high aspect ratios.     

Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study

This paper develops advanced, yet design-oriented ultimate strength expressions for stiffened panels subject to combined axial load, in-plane bending and lateral pressure. The collapse patterns of a stiffened panel are classified into six groups. It is considered that the collapse of the stiffened panel occurs at the lowest value among the various ultimate loads calculated for each of the collapse patterns. The panel ultimate strengths for all potential collapse modes are calculated separately, and are then compared to find the minimum value which is then taken to correspond to the real panel ultimate strength. The post-weld initial imperfections (initial deflection and residual stress) are included in the developed panel ultimate strength formulations as parameters of influence. The validity of the developed formula is confirmed by comparing with the mechanical collapse tests and nonlinear FEA. A comparison of the present method is also made with theoretical solutions from the Det Norske Veritas classification society design guideline. Important insights developed are summarized.     

Retraining local and global buckling behavior of steel plastic hinges using CFRP

Carbon fiber-reinforced polymer (CFRP) composites have been shown to be particularly well suited for external strengthening of reinforced concrete members. However, there is limited information about how they can be used to strengthen steel structures that are susceptible to local and global instabilities. This paper discusses test results of full-scale steel flexural specimens subjected to reversed cyclic loading, some of which are wrapped with CFRP in the plastic hinge region. The main variables investigated are lateral bracing, to study the effect of CFRP wrapping on local buckling and lateral torsional buckling, wrapping scheme, and number of layers of fibers. The test results show that application of CFRP in the plastic hinge region of flexural members has substantial benefits. In particular, the CFRP wraps can increase the size of the yielded plastic hinge region, slow down the occurrence of local buckling, and delay lateral torsional buckling. These benefits reduce strain demands in the critical plastic hinge region and substantially improve energy dissipation capacity within the plastic hinge region.     

A numerical study on local buckling and energy dissipation of CHS seismic bracing

Seismic provisions for steel buildings present limiting width-thickness and slenderness ratios for bracing members, most of which were established based on experimental observations. A finite element study has been undertaken to evaluate these limits for pin-ended circular hollow section (CHS) steel braces. Uncertainties in modeling and quantification arise in the simulation of cyclic brace buckling. A finite element modeling procedure was developed and calibrated using existing experimental data. Sensitivity of the finite element analysis results to the uncertainties in modeling and quantification methods were studied in detail. A parametric study was conducted utilizing the calibrated modeling technique. Fifty four CHS brace models possessing different diameter-to-thickness ratios varying from 5 to 30 and slenderness ratios varying from 40 to 200 were analyzed. The effect of cyclic hardening modulus on the response of braces was explored. In all analysis, the models were subjected to reversed cyclic displacements up to ten times the yield displacement. In this paper, the results are presented in terms of the ductility level attained by the member at the onset of local buckling. It is shown that local buckling of the section is not only a function of the diameter-to-thickness ratio but is also influenced by the slenderness ratio of the member. Moreover, the amount of hardening modulus was found to affect the local buckling response significantly. The need to include this material property into seismic provisions is demonstrated. Finally, the hysteretic energy dissipated by the member was quantified for each displacement excursion.     

Finite element analysis and design of sandwich panels subject to local buckling effects

Past research into the local buckling behaviour of fully profiled sandwich panels has been based on polyurethane foams and thicker lower grade steels. The Australian sandwich panels use polystyrene foam and thinner and high strength steels, which are bonded together using separate adhesives. Therefore a research project on Australian sandwich panels was undertaken using experimental and finite element analyses. The experimental study on 50 foam-supported steel plate elements and associated finite element analyses produced a large database for sandwich panels subject to local buckling effects, but revealed the inadequacy of conventional effective width formulae for panels with slender plates. It confirmed that these design rules could not be extended to slender plates in their present form. In this research, experimental and numerical results were used to improve the design rules. This paper presents the details of experimental and finite element analyses, their results and the improved design rules.     

Application of direct strength method to axially loaded perforated cold-formed steel studs: Distortional and local buckling

A study to develop methods of analyzing perforated, axially loaded, cold-formed steel studs using the provisions of the Direct Strength Method [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004] was undertaken using the Finite Strip Method as the method for determining the elastic buckling stresses. Several different models were developed to represent the effect of the web perforations. The capacities predicted using the Direct Strength Method for the limit states of distortional and local buckling were compared to capacities calculated using the equations contained in the AISI Specification [American Iron and Steel Institute (AISI). North American Specification for the Design of Cold-Formed Steel Structural Members 2001 Edition with Supplement 2004 (AISI/COFS/NASPEC 2004) and Commentary (AISI/COFS/NASPEC 2004), Washington, DC; 2004]. The limit state of longwave buckling is considered in a companion paper [Sputo T, Tovar J. Application of direct strength method to axially loaded perforated cold-formed steel studs: Part 1. Longwave buckling. Thin Walled Struct, submitted for publication]. The validity of the results is discussed and recommendations are made for the use of the Direct Strength Method for these members.     

Monotonic and cyclic behavior of concrete-filled steel-tube beam-columns considering local buckling effect

A mathematical model is developed to evaluate the monotonic and cyclic behavior of concrete-filled steel tube (CFST) beam-columns with rectangular cross section. The model includes the reduction in the steel compressive strength due the local buckling effect. The degradations in unloading and reloading stiffness of steel tube due to local buckling are also included. The model is based on fiber element method in which uniaxial stress–strain material laws are used for cross section components. The results obtained from the mathematical model were compared with experimental results for columns under monotonic as well as cyclic loads. It is observed that the proposed model predicts well the columns and beams nonlinear behavior compared with the experimental results.