abaqus分析热轧椭圆空心型钢的抗压强度（一）

   近年来，热轧椭圆空心型材因其美观和结构效率的互补性而受到工程师和建筑师的广泛关注。然而，目前缺乏椭圆空心型材的设计指导，阻碍了其在建筑中的更广泛应用。本文针对轴向压缩的基本载荷条件解决了这一缺点。本文介绍了实验室测试、数值建模和设计规则的制定。实验计划包括 25 个拉伸试样试验和 25 个短柱试验。所有测试的椭圆空心型材的长宽比均为 2，截面尺寸范围从 150 × 75 到 500 × 250 毫米。结果包括几何缺陷测量和满载端部缩短曲线。根据生成的测试数据开发并验证了非线性有限元模型。使用经过验证的数值模型进行参数研究，以研究不同细长和不同长宽比的椭圆空心型材。所得到的结构性能数据已用于建立横截面细长和横截面抗压强度之间的关系，这表明，根据所提出的横截面细长参数，欧洲规范 3 中圆形空心型材的 3 级细长极限 90 可以安全地用于椭圆形空心型材。BS 5950-1 中给出的等效半紧凑细长极限、AISC 360-05 中的非紧凑极限细长和 AS 4100 中给出的屈服细长极限也是有效的。BS 5950-1 中的改进有效面积公式也可以安全采用。目前正在进一步研究细长（4 级）椭圆形空心型材的有效面积公式。

   使用有限元（Fe）软件ABAQUS [9]的数值建模研究与实验程序并行进行。该程序的主要目的是复制实验压缩测试，并验证了模型，以进行参数研究。为Fe模型选择的元素是四个节点的，减少的集成壳元素，每个节点的自由度六个自由度，在Abaqus元素库中指定为S4R，适用于薄或厚的壳应用[9]。这些元素已被证明在类似的应用中表现良好[10-12]。通过基于弹性特征值预测进行网格收敛研究，仔细选择了均匀的网格密度，以实现准确的结果，同时最大程度地减少计算工作。发现合适的网格尺寸为2A/10（A/B）×2A/10（A/B）毫米，上限为20×20 mm。

    使用测量的试件尺寸和测量的材料应力-应变数据对短柱试验进行建模。几何缺陷的形式被认为是最低弹性特征模式模式，通常形状对称，图 15 显示了一个例子。除了测量的缺陷值外，缺陷幅度 w0 被认为是材料厚度 t 的三个固定分数（t/10、t/100 和 t/500）。没有测量残余应力数据，但在从椭圆形试件加工材料拉伸试样时观察到的可忽略不计的变形表明残余应力很低。因此，残余应力未纳入本研究中的数值模型。真实应力-应变关系是从拉伸试样试验获得的工程应力-应变曲线生成的，材料非线性通过分段线性应力-应变模型纳入数值模型，以模拟应变硬化区域。对固定端模型施加了边界条件，这是通过限制短柱底部的所有位移和旋转以及短柱受力端除垂直位移以外的所有自由度来实现的；在整个分析过程中，都对垂直位移进行了监测。采用改进的 Riks 方法 [9] 来求解几何和材料非线性短柱模型，从而可以追踪卸载行为。

图 16 显示了 EHS 150 × 75 × 4-SC2 的数值失效模式，并与相应的变形试件进行了比较。表 4 列出了数值模拟的结果，其中显示了不同缺陷水平下 FE 极限荷载与实验极限荷载之间的比率，并进行了比较。试验结果的复制令人满意，数值模型能够成功捕捉观察到的刚度、极限荷载、一般荷载端部缩短响应和失效模式。图 17 和 18 分别显示了 EHS 150 × 75 × 4-SC2 和 EHS 150×75×5-SC1 的测试结果与 FE 结果之间的比较。无论缺陷幅度如何，数值模型始终低估了三个截面尺寸为 300 × 150 × 8.0 的短柱的极限荷载。这种低估的可能解释包括横截面周围和短柱长度上的材料厚度变化以及材料屈服强度的变化（横截面周围或拉伸和压缩性能之间）。

对缺陷的敏感性通常相对较低，较粗的截面显示出最大的响应变化。例如，对于 EHS 150 × 75 × 8 模型，随着缺陷幅度从 t/100 增加到 t/10，极限荷载降低了 20%。这种敏感性是由于在发生局部屈曲之前组成元件所达到的应变硬化水平。较不粗壮的截面位于屈服平台之上或略低于屈服平台，因此对局部屈曲点的变化不太敏感（就极限载荷而言）。对于屈服载荷和弹性屈曲载荷值相近的细长椭圆形空心截面，预计敏感性会增加。

在验证了 FE 模型能够复制长宽比为 2 的 EHS 测试行为的一般能力后，进行了一系列参数研究。参数研究的主要目的是调查横截面细长和长宽比对极限承载能力的影响。根据对 150 × 75 × 6.3 截面进行的拉伸试样试验，开发了一个分段线性材料应力-应变模型，如图 19 所示。非线性参数分析中的初始几何缺陷采用最低弹性特征模态的形式，振幅 w0 为 t/100，这与测试结果最一致（表 4）。参数研究中考虑的截面尺寸为 150 × 150、150 × 100、150 × 75 和 150 × 50，厚度各不相同，以覆盖横截面细长范围。该结果已用于验证椭圆形空心截面所提出的细长参数和横截面分类极限，并将在下一节中详细讨论。

A numerical modelling study, using the finite element (FE) package ABAQUS [9], was carried out in parallel with the experimental programme. The primary aims of the programme were to replicate the experimental compression tests and, having validated the models, to perform parametric studies. The elements chosen for the FE models were four-noded, reduced integration shell elements with six degrees of freedom per node, designated as S4R in the ABAQUS element library, and suitable for thin or thick shell applications [9]. These elements have been shown to perform well in similar applications [10–12]. A uniform mesh density was carefully chosen by carrying out a mesh convergence study based on elastic eigenvalue predictions with the aim of achieving accurate results whilst minimising computational effort. A suitable mesh size was found to be 2a/10(a/b) × 2a/10(a/b) mm with the upper bound of 20 × 20 mm.

The stub column tests were modelled using the measured dimensions of the test specimens and measured material stress–strain data. The form of geometric imperfections was taken to be the lowest elastic eigenmode pattern, typically symmetrical in shape, an example of which is shown in Fig. 15. The imperfection amplitude w0 was considered as three fixed fractions of the material thickness t (t/10, t/100 and t/500) in addition to the measured imperfection values. No residual stress data were measured, but the negligible deformation observed when the material tensile coupons were machined from the elliptical specimens indicated that the residual stresses were low. Therefore, residual stresses were not incorporated into the numerical models in this study. The true stress–strain relations were generated from the engineering stress–strain curves obtained from the tensile coupon tests and material non-linearity was incorporated into the numerical models by means of a piecewise linear stress–strain model to mimic, in particular, the strain-hardening region. Boundary conditions were applied to model fixed ends and this was achieved by restraining all displacements and rotations at the base of the stub columns, and all degrees of freedom except vertical displacement at the loaded end of the stub columns; this vertical displacement was monitored throughout the analysis. The modified Riks method [9] was employed to solve the geometrically and materially non-linear stub column models, which enabled the unloading behaviour to be traced. The numerical failure mode of EHS 150 × 75 × 4-SC2 is illustrated in Fig. 16 and compared with the corresponding deformed test specimen. Results of the numerical simulations are tabulated in Table 4, in which, the ratios between the FE ultimate load and the experimental ultimate load are shown and compared for different imperfection levels.

Replication of test results has been found to be satisfactory with the numerical models able to successfully capture the observed stiffness, ultimate load, general load–end shortening response and failure patterns. Comparison between test and FE results are shown for EHS 150 × 75 × 4-SC2 and EHS 150×75×5-SC1 in Figs. 17 and 18, respectively. The ultimate loads of the three stub columns of section size 300 × 150 × 8.0 are consistently under-predicted by the numerical models, regardless of the imperfection amplitude. Possible explanations for this under-prediction include variation of the material thickness around the cross-section and along the length of the stub columns and variation in material yield strength (either around the cross-section or between tensile and compressive properties).

Sensitivity to imperfections is generally relatively low, with the stockier sections showing the greatest variation in response. For example, in the case of the EHS 150 × 75 × 8 models, the ultimate load reduces by 20% with an increase of imperfection amplitude from t/100 to t/10. This sensitivity is due to the level of strain hardening achieved by the constituent elements before local buckling occurs. The less stocky sections lie on or marginally below the yield plateau and are therefore less sensitive (in terms of ultimate load) to variation in the point of local buckling. Increased sensitivity would be anticipated for slender elliptical hollow sections where the yield load and elastic buckling load were of similar value.

Having verified the general ability of the FE models to replicate test behaviour for EHS with aspect ratio of 2, a series of parametric studies were conducted. The primary aim of the parametric studies was to investigate the influence of cross-section slenderness and aspect ratio on the ultimate loadcarrying capacity. A piecewise linear material stress–strain model was developed from the tensile coupon tests conducted on the 150 × 75 × 6.3 sections, and is shown in Fig. 19. Initial geometric imperfections in the non-linear parametric analyses adopted the form of the lowest elastic eigenmode with an amplitude w0 of t/100, which has demonstrated the best agreement with the test results (Table 4). The section sizes considered in the parametric studies were 150 × 150, 150 × 100, 150 × 75 and 150 × 50 with varying thickness to cover a spectrum of cross-section slenderness. The results have been utilised for the validation of proposed slenderness parameters and cross-section classification limits for elliptical hollow sections and are discussed in detail in the following section.