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.     

非轴压下开裂的加劲钢板的极限状态和破坏状态的响应

开裂可能会导致加劲板极限强度的减小和破坏特点的改变。对此类问题,分析了不同形状及长度的裂缝对加劲板强度和破坏特点的影响。裂缝的位置为沿着轴向压力方向,而且不考虑裂缝的扩展。主要讨论了裂缝闭合对结构响应的影响。给出不同宽高比的加劲板的极限强度和破坏状态。最终,给出一个有限元建模方法,将有可能降低密肋板的分析成本。     

Ultimate shear strength of intact and cracked stiffened panels

The present paper focuses on the ultimate shear strength analysis of intact and cracked stiffened panels. Several potential parameters influencing the ultimate shear strength of intact panels are discussed, including the patterns and amplitudes of initial deflection, the slenderness and aspect ratios of the plates, and the boundary conditions defined by the torsional stiffness of support members. An empirical formula for the ultimate shear strength of intact stiffened panels is proposed based on parametric nonlinear finite element analyses in ANSYS. Furthermore, the ultimate shear strength characteristics of cracked stiffened panels are investigated in LS-DYNA with the implicit method. Three types of cracks are considered, namely vertical crack, horizontal crack and angular crack. A simplified method is put forward to calculate the equivalent crack length. And the formula for the ultimate shear strength of cracked stiffened panels is derived on the basis of the formula for intact stiffened panels.     

Ultimate strength of stiffened plates with a square opening under axial and out-of-plane loads

The high strength to weight ratio and high stiffness to weight ratio of stiffened plates find wide application in aircraft structures, ship structures, offshore oil platforms and lock gates. The strength and stability of stiffened plates is highly influenced by openings and initial imperfections. The main objective is to study the behaviour of stiffened steel plates with openings up to collapse and to trace the post-peak behaviour under axial and out-of-plane loads. Four stiffened steel plates with a square opening were fabricated for testing. Angle sections were used as stiffeners. Imperfections in the plate, stiffener and overall imperfection of the whole panel were measured. All fabricated panels were tested to failure. A finite element (FE) model was developed for the analysis of stiffened plates with initial imperfections and validated with the test results. Parametric studies were conducted using the developed FE model, and interaction curves and equations were developed for the design of stiffened plates with initial imperfections and openings. The interactive effect for stiffened panels with a square opening was found to be linear, with proportional reduction of the ultimate axial load carrying capacity due to the constant out-of-plane load.     

Validation of the equivalent plate thickness approach for ultimate strength analysis of stiffened panels with non-uniform plate thickness

The stiffened plate structures in ships and ship-shaped offshore installations often consist of non-uniform plate thicknesses. Nonlinear finite element methods are usually employed to predict structural strength for such panels. However, the introduction of non-uniform plate thicknesses renders such calculations difficult when analytical methods and design equations are used. The authors have suggested an equivalent plate thickness method that is based on the weighted average approach to analyse the strength of stiffened panels with non-uniform plate thicknesses. In the present paper, the validity of the equivalent plate thickness method to the ultimate strength analysis of stiffened panels with non-uniform plate thicknesses is checked through nonlinear finite element method computations. It is concluded that the equivalent plate thickness method is accurate for the panel ultimate strength analysis under combined biaxial compression and lateral pressure loads.     

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.     

Compressive tests on stiffened panels of intermediate slenderness

Test results are presented of eight stiffened panels subjected to axial compression until collapse and beyond. The specimens are three-bay stiffened panels with associated plate made of very high tensile steel S690. The use of this very high strength steel led to the unconventional solution of using U stiffeners and this paper aims at understanding the difference of performance of this stiffener type as compared with the conventional ones. Four different configurations are considered for the stiffeners, which are made of mild or high tensile steel for bar stiffeners and mild steel for ‘L’ and ‘U’ stiffeners. The influence of the stiffener's geometry on the ultimate strength of the stiffened panels under compression is analyzed.     

Empirical formulations for estimation of ultimate strength of continuous stiffened aluminium plates under combined in-plane compression and lateral pressure

The present research was undertaken based on the results obtained by the same authors in a sensitivity study on the buckling and ultimate strength of continuous stiffened aluminium plates. Empirical expressions are developed for predicting ultimate compressive strength of welded stiffened aluminium plates used in marine applications under combined in-plane axial compression and different levels of lateral pressure. Existing data of the ultimate compressive strength for stiffened aluminium plates numerically obtained by the authors through the previously performed sensitivity analysis are used for deriving formulations that are expressed as functions of two parameters, namely the plate slenderness ratio and the column (stiffener) slenderness ratio. Regression analysis is used in order to derive the empirical formulations. The formulae implicitly include effects of the weld on initial imperfections, and the heat-affected zone.     

Empirical formulations for predicting the ultimate compressive strength of welded aluminum stiffened panels

The present study was undertaken by the support from Ship Structure Committee (http://www.shipstructure.org), a North American-based interagency research and development committee, in association with SR-1446 project, and also from Alcan Marine, France. Empirical expressions are developed for predicting the ultimate compressive strength of welded aluminum stiffened panels used for marine applications. Existing data of the ultimate compressive strength for aluminum stiffened panels experimentally and numerically obtained by the SR-1446 project is used for deriving the formulations which are expressed as functions of two parameters, namely the plate slenderness ratio and the column (stiffener) slenderness ratio. The formulae implicitly include the effects of weld induced initial imperfections, and softening in the heat affected zone.     

平面内压力和侧向压力组合作用下预测连续加劲铝板极限强度的经验公式

在对连续加劲铝板屈曲和极限强度的敏感性研究基础之上,对压力作用下的铝板进行了深入研究。开发了一个经验公式,用于预测海洋工程中采用焊接加劲铝板在平面内轴压和各种侧向压力作用下的极限抗压强度。极限抗压强度的计算利用了一些的铝板敏感性分析的相关数据,推导出来的公式中含有两个参数,分别是板长细比和柱(加劲肋)长细比。推导过程中也用到了回归分析。公式考虑了焊接对初始缺陷和热影响区的影响。     

Assessment of the ultimate strength of narrow stiffened panel test specimens

The ultimate strength of five narrow stiffened panels tested with two stiffeners under axial compression until collapse and beyond is determined by finite element analysis, and is compared with experimental results. Models with two half bays plus one full bays in the longitudinal direction are used in the finite element analysis. The material properties used in the finite element analysis have been evaluated by tensile tests. The initial geometrical imperfections also affect significantly the collapse behavior of the stiffened panels. Hence, the initial imperfections of the stiffened plates were measured before the experiment. The results of the FE analysis with measured and with equivalent initial imperfections are compared and conclusions are derived about the possible bias of the results when the initial imperfections are not measured.     

Buckling and ultimate strength criteria of stiffened shells under combined loading for reliability analysis

The work presented in this paper forms part of a broader task in establishing a guide to serve as technical documentation for buckling and ultimate strength assessment of various types of marine structural components using the best state-of-the-art knowledge for extreme environmental loading. This paper concentrates on buckling and ultimate strength assessment of ring stiffened shells and ring and stringer stiffened shells involving various modes of buckling and under various loading like axial compression, radial pressure and combined loading. Comparisons are made with screened test data, which have realistic imperfections and various radius to thickness ratio values in the range generally used in offshore structures. The statistical data of model uncertainty factors in terms of bias and coefficient of variation (COV) are calculated and may be used in a further reliability study. Comparisons are also made with the codified rules, API BUL 2U and DNV buckling strength of shells.     

Optimal stiffener design of moderately thick plates under uniaxial and biaxial compression

In this paper, the optimal stiffener design of moderately thick plates under uniaxial and biaxial compression is investigated on the premise that the plate thickness and the required ultimate strength are given. As the theoretical basis of stiffener design, the ultimate strength formulations of weak stiffened thick panels under in-plane biaxial compression are first developed on the basis of large deflection orthotropic plate theory, in which the post-weld initial deflection is taken into account. The von Mises yield criterion is employed to determine the limit state of the panel, and the Nelder-Mead simplex algorithm is used to obtain the efficient solution of nonlinear differential equations. The optimization method presented is based on the stiffener design principles of the overall instability stress and of the working stress. In the optimization formulation, the numbers and geometric sizes of the stiffeners are defined as design variables; the weight ratio of stiffeners to plate is taken as a single objective function; requirements against overall buckling of the panel, local buckling of the plates between the stiffeners and local buckling of the stiffeners themselves are set as constraint functions. Results of both design examples and parameter studies show that, for moderately thick plates, the stiffener weight given by the proposed optimization method is much lower than the weight determined by the current stiffener design method on the premise of the same requirement of structural safety. Using the present optimization method to obtain the lightest and the most effective stiffener layout for moderately thick plates is proposed.     

Ultimate strength of stiffened aluminium panels with predominantly torsional failure modes

The aim of this paper is to investigate the ultimate strength of aluminium plates with flatbar stiffeners with a torsional buckling or tripping failure mode. The formulations for torsional buckling of stiffeners in steel plating are still debated. Compared with steel structures, the ultimate strength of aluminium structures is sensitive not only to residual stresses and initial deformations, but also to the deterioration of mechanical strength in heat-affected zones (HAZ). In the present paper, the ultimate strength of stiffened aluminium panels with predominantly torsional failure modes is investigated by experimental and theoretical analysis. Stiffened panels made of the aluminium alloy AA5083-H116 and AA6082-T6 are considered. Various height of flatbar and various thickness of plate and stiffener were studied. The test results are compared with numerical predictions by using the finite element code ABAQUS (ABAQUS Version 5.7 (1997)), considering the influence of initial deflections, welding residual stresses and HAZ. The influence of HAZ and residual stresses on the ultimate strength of stiffened aluminium panels with the actual failure mode is discussed in detail. The numerical predictions are also compared with strength of material formulations used in DNV Rules for Classification of High Speed and Light Craft (Rules for classification of high speed and light craft, Hull structural design (1996)), NORSOK (Design of steel structures (1998)) all for steel, using the relevant values of the modulus elasticity and yield strength of aluminium, as well as EUROCODE 9 (Eurocode 9, Part 1-1: General rules (1998)).     

A numerical and experimental investigation on composite stiffened panels into post-buckling

The structural behaviour of composite stiffened flat panels under axial compression is here investigated up to collapse. The panel configuration is designed to buckle once the limit load is reached and to work in post-buckling until the ultimate load. The design phase is based on the use of four different kinds of finite element analyses: eigenvalue, non-linear static with modified Riks’ method and both implicit and explicit dynamic analyses. Once the final configuration is identified, two specimens are manufactured. The initial geometrical imperfections are measured and analyzed, then axial compression tests are performed until collapse. As foreseen by the numerical analyses, experimental results prove the ability of the panels designed to work in the post-buckling field until collapse which takes place due to the failure of the stiffener blades. Finally, the measured initial imperfections are included in the model significantly increasing the numerical–experimental correlation.     

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.     

板肋加劲板整体稳定数值模拟与受力机理研究

分别采用梁单元与板壳单元建立同时考虑初始几何缺陷和焊接残余应力的受压板肋加劲板整体稳定分析有限元模型,并以相应试验结果进行验证,得到梁与板壳单元模拟受压板肋加劲板整体稳定的异同。采用经验证的数值模拟方法,对不同弯曲失稳方向板肋加劲板的受力机理进行了研究。结果表明:采用板壳单元可以较好还原板肋加劲板整体稳定受力性能,板壳有限元模型与试验试件的承载力最大相对误差为4.2%,平均相对误差为1.48%; 梁单元模型与长(中长)柱试验试件的承载力最大相对误差为5.4%,平均相对误差为1.92%,与短柱试件的承载力相对误差虽仅为0.7%,但由于不能考虑板件发生的塑性失稳,其应力-位移曲线拟合情况相对较差; 不同弯曲失稳方向板肋加劲板整体稳定构件的破坏特征不同,其中对于板肋侧弯曲的板肋加劲板整体稳定构件,被加劲板边缘部分受压达到材料屈服强度且板肋边缘受拉达到屈服强度时,构件整体达到其承载极限; 对于被加劲板侧弯曲的板肋加劲板整体稳定构件,当板肋边缘部分受压达到材料屈服强度时,构件整体达到其承载极限; 对于实际工程中组成钢箱梁顶板的板肋加劲板,制作时应避免朝向板肋侧的变形。     

A semi-analytical method for the elastic–plastic large deflection analysis of stiffened panels under combined biaxial compression/tension, biaxial in-plane bending, edge shear, and lateral pressure loads

In the earlier publications [Paik JK, Thayamballi AK, Lee SK, Kang SJ. A semi-analytical method for the elastic-plastic large deflection analysis of welded steel or aluminium plating under combined in-plane and lateral pressure loads. Thin-Walled Struct 2001;39;125–52; Paik JK, Thayamballi AK. Ultimate limit state design of steel-plated structures. Chichester: Wiley; January 2003], the author presented a semi-analytical method for the elastic–plastic large deflection analysis of unstiffened plates under biaxial loads, edge shear, biaxial in-plane bending and out-of-plane (lateral) pressure loads until the ultimate strength is reached. In the present paper, a similar method is applied to stiffened panels subjected to the same type of loading. The effect of initial imperfections in the form of initial deflection and welding residual stresses is accounted for in the calculations. The validity of the developed method is demonstrated by comparing with existing theoretical and numerical results where relevant. The present theory can be useful for ultimate strength analysis of plates and stiffened panels made of steel or aluminium alloys.     

Ultimate strength of compressed stiffened plates and minimum stiffness ratio of their stiffeners

A theoretical investigation into the effectiveness of a stiffener against the ultimate strength of a stiffened plate is carried out. Series of the buckling analyses, the elastic large deflection analyses and the elastic-plastic large deflection analyses are performed by the analytical method and the finite element method on the stiffened plate under thrust. Experiments are also carried out on the stiffened plate under thrust to confirm the theoretical results.On buckling of a stiffened plate, it is well known that ther exxists a minimum stiffness ratio of a stiffener to the plate, $\text{λ}{}^{\mathrm{B}}{}_{\min }$, which gives the maximum limiting value of the buckling strength. Concerning the ultimate strength it was confirmed that there exists a significant stiffness ratio of a st stiffener to the plate, $\text{λ}{}^{\mathrm{U}}{}_{\min }$ similar to $\text{λ}{}^{\mathrm{B}}{}_{\min }$ for the buckling strength.It was also found that there are three typical collapse modes for the stiffened plate under thrust, that is: (1) MODE OO, overall collapse after overall buckling; (2) MODE LO, overall collapse after local buckling; (3) MODE LL, local collapse after local buckling.Approximatelmethods are proposed to evaluate the ultimate strength and $\text{λ}{}^{\mathrm{U}}{}_{\min }$ of a multi-stiffened plate under thrust.The effects of initial imperfections such as welding residual stresses and initial deflection on ultimate strength and $\text{λ}{}^{\mathrm{U}}{}_{\min }$ of a stiffened plate under thrust are also discussed.     

主方支圆内隔板加劲T型节点破坏模式研究

根据箱型柱加劲隔板的构造,提出主方支圆T型管节点采用内隔板进行加劲的措施。通过T型节点静力加载试验,揭示合理的构造措施将使得加劲节点表现为内隔板首先塑性破坏、继而发展至主管上翼缘塑性破坏的模式,加劲节点的极限承载力提高明显,而且具有良好的延性。利用非线性有限元分析,探讨T型节点单内隔板和双内隔板加劲的构造措施、节点破坏...