基于蒙特卡罗的考虑随机初始缺陷的分析方法

现行规范采用的多种直接或间接考虑初始缺陷的取值方法均没有很好的考虑构件缺陷的随机分布,夸大了初始几何缺陷的影响。针对现有工程初始缺陷实测分布具有随机偶然性的问题,该文采用蒙特卡罗法模拟了结构构件的随机初始几何缺陷。为进一步提高抽样效率,同时采用了具有抽样记忆功能的拉丁超立方抽样技术,避免了在抽样空间内重复抽样,有效减少了模拟次数。结果表明:用自编程序实现的考虑钢框架结构随机初始几何缺陷的分析方法,可以在多高层钢框架结构高等分析中模拟初始缺陷的随机分布与遇合,为开展准确有效的高等分析与设计研究奠定基础。     

初始几何缺陷对非强支撑钢框架柱性能的影响

在钢框架二阶弹性分析中,结构整体初始几何缺陷和构件的初始几何缺陷是实际存在的,其影响不应忽略。基于由单根柱和梁组成的框架子结构模型,通过引入以上两种几何缺陷,得出了考虑初始几何缺陷影响的框架柱位移与内力的理论公式。利用该理论模型,可以较准确地分析框架结构整体几何缺陷与构件几何缺陷对二阶弹性弯矩的影响。参数分析结果表明:对于钢框架柱,结构的整体几何缺陷和构件几何缺陷对弯矩的影响均可以等效为作用于楼层处的假想水平力,而假想水平力的大小与作用于该楼层的竖向荷载有关。     

考虑随机缺陷的钢框架-支撑结构试验研究与有限元分析

该文对一榀单跨双层钢框架-支撑结构进行了静力试验,重点研究了初始几何缺陷对结构变形性能的影响,由试验结果与有限元分析结果对比吻合较好,证明了考虑随机初始缺陷有限元模型的正确性。采用有限元ANSYS软件对三跨三十二层钢框架-支撑结构的随机缺陷模型进行全过程高等分析,采用蒙特卡罗法拉丁超立方抽样的技术模拟了框架随机初始缺陷的分布情况,并对比多种国内外规范多种考虑初始缺陷的方法,重点研究了结构和构件的变形性能。结果表明:考虑随机初始几何缺陷的框架变形与无缺陷理想框架的柱顶侧移相差不大,在高层结构的高等分析中可不考虑。此外规范中假想力框架变形远远超出随机缺陷框架,可知假想力计算方法过分夸大了初始几何缺陷的不利作用。     

带有任意弹性支撑的大型有面外支撑杆X撑结构屈曲分析

X型支撑结构已广泛应用于大型海洋工程主要支撑结构设计中，如设计使用不当，将有可能发生由支撑杆的屈曲失稳而引发的结构坍塌变形。在极限荷载下，X撑杆的屈曲失稳本质上属于典型的多跨压杆稳定问题，其极限承载力与撑杆的结构组成、几何参数以及端部约束密切相关。该文主要研究有(无)面外支撑的非对称交叉支撑体系在任意弹性支撑下X撑结构屈曲特性，侧重于考察端部约束、受力形式、面外支撑刚度等因素的影响。首先基于线弹性理论框架，建立了双跨受压杆件平衡方程，利用牛顿迭代算法进行屈曲载荷计算，从而得到跨中连续的非对称交叉支撑杆的有效长度因子数值解，并对端点支撑刚度和跨中支撑刚度进行了敏感性分析。结合工程实践，给出了杆件屈曲长度系数和刚度约束条件关键设计参数。     

弯曲型支撑-框架的假想荷载法

为避免在钢结构设计中逐一去确定框架柱的计算长度,该文提出了一种应用于弯曲型支撑框架的假想荷载法。将假想荷载作用于框架楼层,配合二阶弹性分析,考虑材料非线性、残余应力和初始几何缺陷,研究了多种几何和荷载条件下的弯曲型支撑框架模型,分析了一系列模型的极限承载力,提出了统一的假想荷载系数以及假想荷载的近似公式,无论是有水平荷载或无水平荷载,无论是等截面还是变截面,其结果与有限元结果都符合较好。     

随机缺陷模态法在弦支穹顶稳定性计算中的应用

初始几何缺陷对弦支穹顶的稳定性能有较大的影响。在结构整体稳定性计算中,利用随机缺陷模态法为结构施加合理的初始几何缺陷是该文的主要研究目的。首先采用一致缺陷模态法,在不同初始几何缺陷下,对肋环2型弦支穹顶结构进行稳定性能分析,然后讨论随机缺陷模态中方差的取值方法,并利用该方法对肋环2型弦支穹顶结构进行了210种不同初始几何缺陷下的稳定性能分析,两种分析方法所施加缺陷的最大值均为结构跨度的1/300。分析结果表明:结构的初始几何缺陷对结构的稳定性能影响较大,考虑初始几何缺陷后结构稳定性能为完善结构的50%左右,且采用一致缺陷模态法时也需通过考虑不同缺陷分布形式的多次计算才能合理评估结构的稳定性能,建议在跨度较大、较为复杂的结构中采用随机模态法来考虑初始几何缺陷对结构稳定性能的影响。     

初始缺陷对耐压结构承载性能影响

目的基于有限元方法,通过分析研究深海耐压圆筒结构在不同初始缺陷下的屈曲压力,研究初始缺陷对厚壁圆筒承载极限的影响。方法建立了三维厚壁筒模型,分别研究了圆筒在初始几何缺陷、初始应力缺陷和两种缺陷复合的状态下,结构的承载性能,并将得到的结果与理想状态下的结构作对比。结论结果表明,无论是初始几何缺陷,还是初始应力缺陷,都会降低结构的承载极限。     

框架弹塑性失稳的层稳定系数

对传统计算长度系数法和考虑柱间相互作用修正的计算长度系数法的分析研究,指出了修正方法在应用过程中可能出现的问题;根据层稳定理论,定义了层通用长细比。利用ANSYS,考虑材料非线性、残余应力、初始几何缺陷,分析了不同抗侧刚度的单跨和多跨刚架,在各柱参数不相等的情况下的极限承载力,得到了极限承载力和层通用长细比的关系曲线。ANSYS分析表明,在层通用长细比的某个范围内存在明显的整层有侧移失稳和薄弱柱无侧移失稳的相互作用。为了考虑这种相互作用,对层通用长细比和层稳定系数重新进行了定义,参照现行规范柱子曲线,提出了可以考虑框架有侧移失稳和无侧移失稳相互作用的层稳定系数公式;与有限元结果进行对比验证,发现两者符合很好。     

基于反演推定的空间结构随机缺陷传播法

在空间结构施工过程监测和检测评估等工作中,需依据部分已测节点几何位形推断结构全部节点几何位形。该文提出随机缺陷传播算法,建立几何位置偏差在节点之间的传播法则,利用有限已知节点几何位形偏差反演推定空间结构整体几何缺陷,进而确定结构整体几何位形,并用随机偏差理论证明所生成的结构随机缺陷服从正态分布。对一个缩尺K6单层网壳模型进行实测和稳定分析,结果表明:相对于随机缺陷法和一致缺陷模态法,采用随机缺陷传播法生成的结构几何缺陷与实测几何缺陷接近,据此计算得到的极限承载力更接近结构承载力理论值。基于随机缺陷传播法得到的空间结构整体稳定极限荷载因子中位数,可作为结构的实际极限承载能力代表值。     

考虑随机几何初始缺陷的储油罐抗震可靠度分析

采用屈曲模态的线性组合形成初始缺陷构型,假定缺陷幅值服从零均值正态分布,通过拉丁超立方抽样法生成几何初始缺陷样本。进而,采用增量动力分析法获得加速度峰值与罐壁径向位移最大值的关系,并根据Budiansky-Roth准则确定出地震作用下罐壁失稳临界应力值。基于ABAQUS用户单元子程序实现了基于附加质量法的缺陷储油罐地震反应分析。据此,求解出随机地震作用下考虑和未考虑初始几何缺陷的储油罐可靠度。对比分析表明,随着地震作用的增大,罐壁最大压应力离散程度也增大,其概率分布呈现出非正态性,随机初始几何缺陷显著降低了储油罐的抗震可靠度。     

初始几何缺陷对仓壁柱承钢筒仓稳定性能的影响

仓筒壁直接支承于支柱是小型钢筒仓的一种简单、经济的支承方式。薄壳结构通常对初始几何缺陷十分敏感。引入周向轴对称焊缝凹陷和特征值屈曲模态两种缺陷形式,通过几何非线性分析,研究初始缺陷对轴压下仓壁柱承筒仓稳定性能的影响。研究表明,周向焊缝凹陷会显著降低结构的屈曲荷载,且与焊缝位置密切相关,而特征值模态缺陷只有在支柱接近仓顶时才会显著影响其屈曲强度。     

A stochastic approach to the problem of stability of a spherical shell with initial imperfections

A probabilistic method is applied to the problem of stability of a spherical shell with initial imperfections, subjected to uniform external pressure. The distribution law of the normal deflections of the shell is obtained following the Smoluchovsky equation, at a given density of the initial deflections. On this basis the probability for the deflections to be in a given interval is found. A relation for the probability for a jump transition to a new stability form is obtained for a spherical shell with a given probability distribution of the initial imperfections. The relations obtained can be used for solving different kinds of reliability problems, as well as problems for prediction of the shell stability forms together with the probability for their realization.     

Imperfection sensitive variation of critical loads at hilltop bifurcation point

Variation of critical loads due to initial imperfections at the hilltop bifurcation point is described by elastic stability theory. We derive a system of bifurcation equations for a potential system expressing local behavior at this bifurcation point, which is a double critical point occurring as a coincidence of a simple pitchfork bifurcation point and a limit point. The piecewise linear law of imperfection sensitivity of critical loads in Thompson and Schorrock [J. Mech. Phys. Solids 23 (1975) 21] is revised by extending initial imperfections to be considered in the bifurcation equations. Based on this sensitivity law, a procedure to determine the most influential (worst or optimum) initial imperfection is formulated. As the most essential development of this paper, under the assumption that initial imperfections are subject to a multi-variate normal distribution, we derive the probability density function of critical loads that follows a Weibull-like distribution. The validity of theoretical developments is assessed through its application to elastic truss structures.     

初始缺陷对板钢结构极限承载力的影响分析

从含初始弯曲的大挠度方程出发,以薄板厚度的折减量为摄动参数,将残余应力考虑成等效荷载,并通过参数分析的方法修正残余应力等效荷载,根据实用板与理想板的比拟,得出板的厚度折减量和板的极限承载力方程。非线性有限元分析和试验数据的对比表明:该文提出的方法实用、精度高,是分析板钢结构极限承载力的通用方法,可作为非线性有限元分析方法的补充,大大简化了结构极限承载力分析的复杂性。     

局部缺陷对旋转壳内力分布的影响

本文应用有初始几何缺陷的壳体非线性应变分量公式及内时本构理论，对冷却塔在重力作用下的内力进行了弹塑性大变形计算，分析了常见的几种缺陷对冷却塔内力分布的影响。对于工程实际中有缺陷的冷却塔的整体性能分析具有重要意义，可以为工程设计提供理论基础。     

On the complete extinction of selected imperfection wavelengths in dynamically expanded ductile rings

In this work the inception and development of multiple necks in dynamically expanded ductile rings with ab initio geometric imperfections has been addressed. Finite element simulations and linear perturbation analysis have been applied for that task. In the numerical calculations a selected wavelength is included into the model defining along the circumference of the ring an array of periodic geometric imperfections of predefined amplitude. In the stability analysis a perturbation of a given mode is added to the background solution and the growth rate of the perturbation is evaluated. The attention has been focused on the extinction of both long and short wavelength imperfections and the appearance of a dominant necking pattern which emerges when the geometric imperfections are vanished. The role played by the loading rate on the extinction of imperfections is also addressed. Moreover, the necking strain is found to be dependent on the imperfection pattern and the loading rate. Its maximum value is registered for the loading cases in which the initial imperfections distribution is completely extinguished.     

Investigation on the Geometric Imperfections driven Local Buckling Onset in Composite Conical Shells

Buckling is a critical failure phenomenon for structures, and represents a threat for thin shells subjected to compressive forces. The global buckling load, for a conical structure, depends on the geometry and material properties of the shell, on the stacking sequence, on the type of applied load and on the initial geometric imperfections. Geometric imperfections, occurring inevitably during manufacturing and assembly of thin-walled composite structures, produce a reduction in the carrying load capability with respect to the design value. This is the reason why investigating these defects is of major concern in order to avoid over-conservative design structures. In this paper, the buckling behavior a conical structure with 45° semi-vertical angle is numerically investigated. The initial imperfections are taken into account by using different strategies. At first, the Single Perturbation Load Approach (SPLA), which accounts for defects in the form of a lateral load, normal to the surface, has been adopted. Then, the actual measured defects have been applied to the structure by using the Real Measured Mid-Surface Imperfections (MSI) approach. Investigations on cylindrical shells using the first strategy have already shown the occurrence of a particular phenomenon called “local snap-through”, which represents a preliminary loss of stiffness. In order to better understand this phenomenon for conical shells, both the aforementioned techniques have been used to provide an exhaustive overview of the imperfections sensitiveness in conical composite shells. This study is related to part of the work performed in the frame of the European Union (EU) project DESICOS.