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。     

Response of stiffened and unstiffened plates subjected to blast loading

This paper describes the results of dynamic analyses carried out on both stiffened and unstiffened panels using both simplified and advanced analytical techniques. For unstiffened panels with inplane restraint along their edges, the dynamic response of an imperfect panel was predicted using a large displacement elastic analysis based on Lagrange's equation, with the panel being treated as a shallow shell. For stiffened panels, the finite element (FE) technique was used to establish the validity of using the simplified technique to predict the inter-stiffener panel displacements for a simply supported panel. A parametric study has been carried out to analyse the effects of in-plane boundary conditions, local stiffener buckling and initial imperfections on the overall response. The significant effect of boundary conditions is demonstrated by including the actual boundary conditions of a test frame in the finite element modelling of a large-scale stiffened floorplate panel used in an experimental test series.     

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.     

Behavior of beam web panel under opposite patch loading

Elastic buckling is studied for a panel with various boundary conditions including simple supports, fixed supports and elastic restraints. The panel is subjected to opposite patch loading. Following a review of existing work on the effects of localized compression, also known as patch loading, a study is conducted to take into account the restraints provided by the flanges of the I beam in a realistic manner. This study is based on a finite element model implemented in the CAST3M software. A new equation is proposed to calculate the buckling critical coefficient for a beam web panel considering the rotational stiffness provided by the flanges. The model is then applied to longitudinally stiffened web panels which are subjected to opposite patch loading.A parametric analysis is performed to determine the transition from a global buckling mode to a local buckling mode where the sub-panels on each side of the stiffener behave separately. The numerical results show that the flexural rigidity of the stiffener is the appropriate parameter that governs the buckling mode. From these results, a formula is proposed to calculate the buckling critical coefficient of stiffened web panels.     

The in-plane shear failure of transversely stiffened thin plates

This paper examines the response of stiffened plates with plain flat outstands when subjected to in-plane shear loading in the form of applied in-plane shear displacement. The buckling and post-buckling failure capabilities of thin plates subjected to in-plane shear, can, of course, be improved through the introduction of stiffening elements whose flexural and torsional rigidities can contribute significantly towards a more stabilised structural system. This paper details appropriate suitable finite element modelling strategies and procedures to enable the determination of the post-buckled failure response of the stiffened shear panels and to highlight the significant influence of the stiffeners. The modelling procedures are able to describe the complete loading history of the stiffened panel structures from the onset of initial buckling through the elastic post-buckling phase of behaviour involving the considerable interaction between plate and stiffener and then through initial material yielding and yield propagation to ultimate conditions and elasto-plastic unloading.     

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.     

Finite element buckling analysis of stiffened plates with filleted junctions

Modern aircraft wings are thin-walled structures composed of ribs, spars and stiffened panels, where the top skin is subject to compressive forces in flight that can cause buckling instability. If these panels are machined from a single billet of metal then the initial buckling performance can be significantly improved by increasing the fillet radius along the line junction between the stiffener webs and skin. Typically thin-walled structures are usually modelled with two dimensional elements. To model the stiffened panel with fillets three dimensional elements are required. For the stiffened panel selected for the analysis the paper shows that the three dimensional model shows a substantial increase in skin initiated buckling if the fillet is taken account of. A 5 mm radius leads to an increase of 34% increase in local buckling load performance for a skin portion of breath to thickness ratio of 100. The associated overall buckling load increases by 1.8%. The mass penalty for a 5 mm radius is 5.1%. To avoid local and overall buckling interaction an accurate measure of both buckling loads is very important and may have impact for designers. The three dimensional models with no fillets show very good agreement with the two dimensional models.     

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.     

Cold-formed steel lipped and plain angle columns with fixed ends

The objective of this study is to explore the significant post-buckling reserve in global buckling that has been observed in tests on cold-formed steel angle columns, and to provide design guidance for locally slender cold-formed steel lipped and plain angle columns with fixed end boundary conditions. Global buckling modes are generally regarded to have no post-buckling reserve, and indeed all column design curves, including those used in North America for cold-formed steel columns limit the strength to 0.877P_cre (where P_cre is the global buckling load) or lower. However, tests conducted on cold-formed steel angles by Young (2004,2005) [1], [2] demonstrate capacities significantly in excess of P_cre – an observation usually reserved for local-plate buckling modes, which due to transverse membrane resistance are known to have significant post-buckling reserve. In this work, specific attention is paid to the impact of end boundary conditions, with emphasis on warping (longitudinal) deformations. Utilizing nonlinear collapse analysis with shell finite element models, and existing testing, alternatives to current design methods are explored. New design procedures are recommended for strength prediction of cold-formed steel angle columns with fixed end boundary conditions.     

Post-buckling strength of rectangular concrete-filled steel tube panels

为研究矩形钢管混凝土壁板的屈曲后强度，根据平板的弹塑性屈曲理论并考虑残余应力的影响，确定了板件发生塑性屈曲、弹塑性屈曲和弹性屈曲的正则化界限宽厚比。采用试验验证的有限元模型进行了宽厚比为20~150、钢材屈服强度为275~960 MPa的矩形钢管混凝土壁板局部屈曲分析，以界限宽厚比为控制点，根据有限元结果拟合出了矩形钢管混凝土壁板的有效宽度计算式。研究结果表明：弹性屈曲板件的屈曲后强度提高程度显著高于弹塑性屈曲板件；屈曲后强度的提高程度与钢材屈服强度无明显相关性；与无面外约束钢板相比，混凝土的单侧约束作用可使板件的屈曲后强度普遍提高约50%；提出的矩形钢管混凝土壁板的正则化界限宽厚比和有效宽度计算式与试验结果吻合较好，有效宽度试验值比所提公式计算值平均增大7.2%，标准差为0.091。     

Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method

Differential quadrature element method (DQEM) for buckling analysis of stiffened circular cylindrical panels subjected to axial uniform compressive stresses is presented for the first time. The methodology and procedures are worked out in detail. The circular cylindrical panel and the stiffeners are treated separately. Governing differential equations are derived based on the equilibrium of the panel and the stiffener, and on compatibility conditions along the interface of panel elements and stiffeners. Torsional stiffness of the stiffener is ignored. Circular cylindrical panels with a stringer stiffener or a chordwise stiffener are analyzed by the DQEM, and the results are compared with previously published data to verify the established methodology and procedures. Some new results are presented for the circular cylindrical panels with two orthogonal stiffeners.     

An experimental study of ultimate compressive strength of transversely stiffened aluminium panels

An experimental investigation was carried out to determine the ultimate strength of welded stiffened aluminium panels in alloy 6082 T6 subjected to in-plane compressive loads normal to the directions of the stiffeners. This load case is not treated in the European standard for aluminium structures, Eurocode 9. A total of 21 panel specimens with various side aspect ratios and both open and closed stiffener sections were tested in a purpose made test rig. Great care was taken to ensure the rig gave very precise boundary conditions. The panels were manufactured by metal inert gas arc welding and friction stir welding. An extensive measurement program was carried out to determine the distribution of material strength and initial geometric imperfections. Small imperfection amplitudes were found. Tensile tests revealed variation in material properties, but the strength values were on average higher than the values stated in Eurocode 9. The panels failed by two different deformation modes; global flexural buckling and local buckling of the plate elements between the stiffeners.     

矩形钢管混凝土壁板的屈曲后强度

为研究矩形钢管混凝土壁板的屈曲后强度,根据平板的弹塑性屈曲理论并考虑残余应力的影响,确定了板件发生塑性屈曲、弹塑性屈曲和弹性屈曲的正则化界限宽厚比。采用试验验证的有限元模型进行了宽厚比为20～150、钢材屈服强度为275～960 MPa的矩形钢管混凝土壁板局部屈曲分析,以界限宽厚比为控制点,根据有限元结果拟合出了矩形钢管混凝土壁板的有效宽度计算式。研究结果表明：弹性屈曲板件的屈曲后强度提高程度显著高于弹塑性屈曲板件;屈曲后强度的提高程度与钢材屈服强度无明显相关性;与无面外约束钢板相比,混凝土的单侧约束作用可使板件的屈曲后强度普遍提高约50%;提出的矩形钢管混凝土壁板的正则化界限宽厚比和有效宽度计算式与试验结果吻合较好,有效宽度试验值比所提公式计算值平均增大7.2%,标准差为0.091。     

Behavior of framed modular building system with double skin steel panels

A new type of lateral force-resisting system, a framed modular building with double skin steel panels of slender thin steel plates is presented. Modular construction leads to faster construction, improved quality and reduced resources and waste. A steel panel strengthened framed modular system is developed for the lateral load resisting system instead of in situ concrete core walls. The proposed double skin steel panel systems showed moderate ductility and energy dissipation due to their post-buckling strength. Full-scale experiments on a framed modular system with double skin steel panels were conducted. The test of the frame with steel panel systems showed that all steel panel systems reached a yielding point before the frame structure started to yield, so that severe damage to the frame as a primary structure was controlled. Also, the steel panel systems increased the initial lateral stiffness of the total system and maintained the elastic range of the panels up to near the yielding point of plates without local buckling driven from its shear behavior. By rigid-plastic analysis, the post-buckling strength of thin plates under in-plane bending was predicted and compared with experimental results. Based on the experimental data of the panels, the analytic model of these panel systems was constructed and compared with the experimental results of frames with double skin steel panel systems.     

Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method

This paper presents the Ritz method for the elastic buckling analysis of shells with ring-stiffeners under general pressure loading. The stiffeners may be of any cross-sectional shape and arbitrarily distributed along the shell length. Using polynomial functions multiplied by boundary equations raised to appropriate powers as the Ritz functions, the method can accommodate any combination of end conditions. As far as it is known, the Ritz method has not been automated in this way for the buckling of ring-stiffened shells. By formulating in a nondimensional form, generic buckling solutions for shells with various end conditions, stiffener distributions and under various pressure distributions, were presented. These new buckling solutions should serve as useful reference sources for checking the validity and accuracy of other numerical methods and software for buckling of cylindrical shells. This paper also shows that the appropriate distribution of ring stiffeners can lead to a significant increase in the buckling capacity over that of a stiffened shell with evenly spaced and identical ring stiffeners.     

Buckling and dynamic instability analysis of stiffened shell panels

The static and dynamic instability characteristics of stiffened shell panels subjected to uniform in-plane harmonic edge loading are investigated in this paper. The eight-noded isoparametric degenerated shell element and a compatible three-noded curved beam element are used to model the shell panels and the stiffeners, respectively. As the usual formulation of degenerated beam element is found to overestimate the torsional rigidity, an attempt has been made to reformulate it in an efficient manner. Moreover, the new formulation for the beam element requires five degrees of freedom per node as that of shell element. The method of Hill's infinite determinant is applied to analyze the dynamic instability regions. Numerical results are presented through convergence and comparison with the published results from the literature. The effect of various parameters like shell geometry, stiffening scheme, static and dynamic load factors, stiffener size and position, and boundary conditions are considered in buckling and dynamic instability analysis of stiffened panels subjected to uniform in-plane harmonic loads along the boundaries.     

Local buckling and post-local buckling redistribution of stress in slender plates and sections

Cold-formed open steel sections are comprised of component plates termed stiffened elements (webs) and unstiffened elements (flanges). The local buckling and post-local buckling behaviour of sections may be determined from the behaviour of the component plates. Much research effort has documented the theoretical elastic local buckling of plates and sections, however until recently few experimental studies have been reported on the local buckling and post-local buckling behaviour of unstiffened plates. This paper presents experimental and numerical studies of unstiffened plates and sections that contain them in both compression and bending, and in particular analyses the mechanism that provides post-buckling strength. It is shown that, as with stiffened elements, the mechanism is the post-local buckling redistribution of stress, however unlike stiffened elements this redistribution can occur to such an extent that tensile stresses commonly form in axially compressed slender elements. The stress distributions at ultimate are compared with current international cold-formed steel specifications.     

边界裂纹导致的剪力墙板性能退化时的屈曲和后屈曲强度分析

目前有很多关于反复荷载作用下细长墙板所出现的疲劳裂纹的报告。裂纹可能最初是由焊接、腐蚀或错误使用造成的。板边裂纹一般会发展到靠近翼缘、加劲肋和其他边界构件。这些裂纹会导致薄壁墙板的承载能力下降。本文主要研究具有板边裂纹的剪力墙板的屈曲和后屈曲性能。假定裂纹与边界平行或者呈常态分布。通过有限元线性和非线性分析,确定裂纹和板的各种几何与力学特性的影响(如裂纹的长度和位置,边界条件,表面比和板材的长细比,材料的泊松比和弹性模量)。结果显示:当张力场区域内产生裂纹时,结构构件的性能会发生退化。     

Study on the influence of the initial deflection and load combination on the collapse behaviour of continuous stiffened panels

Using the finite element analysis, a series stiffened panels under combined normal loads and biaxial compressions are conducted to investigate the effect of several influential factors on the ultimate limit states. Two spans/bays FE model with periodical boundary condition is adopted to consider the interaction between adjacent structural members. The initial deflections assumed as Fourier components including symmetric and asymmetric modes are used to identify the half-wave number of collapse of the local plate, which is compared with half-wave number of buckling calculated by formula. Based on the numerical results, the influences of half-wave number assumed in the equivalent initial imperfection and loads combination on the collapse behaviours of stiffened panels are discussed. It is found that lateral pressure might increase the ultimate strength of stiffened panels for the stiffener-induced failure modes. The one half-wave region of local plate influences significantly the load carrying capacity of stiffened panels.     

Torsional buckling behaviour of stiffened cylinders under combined loading

In this study cylindrical boundary conditions for finite element analysis are formulated that allow torsional displacement and buckling of a sector of a cylinder of half axial height, and of a circumferential arc angle that will divide into 360°. Finite element tests are carried out on un-stiffened elastic cylinders to verify the method of analysis against classical elastic torsional buckling theory.Elastic–plastic limit point finite element tests are carried out on ring and stringer stiffened and stringer stiffened cylinders to investigate the effects of stiffeners on post-buckling behaviour in torsion.A stringer stiffened cylinder is subjected to many combinations of axial force and surface pressure in the elastic range of response and then tested to failure in torsion to investigate the effects of axial and surface pressure loads on the resistance to plastic collapse in torsion.