【作者】 聂祺；

【导师】 李云贵；

【作者基本信息】 中国建筑科学研究院 ， 结构工程， 2009， 博士

【摘要】 建筑结构在罕遇地震作用下的动力响应长期以来一直是结构抗震研究的重点课题之一,但由于该问题影响因素较多,到目前为止该问题并没有得到很好解决。本文对建筑结构非线性动力时程分析的基本理论和数值方法展开研究,主要研究内容及研究成果如下:1在总结现有混凝土单轴滞回本构模型的基础上,考虑了地震作用下混凝土材料应力路径的复杂性,建立了一种能够考虑复杂应力路径及应力历史影响的混凝土单轴滞回本构模型。该模型分为骨架曲线和滞回规则两部分:对于受压骨架曲线,分别采用曲线型Mander公式和折线型Mander公式两种函数来描述;对于受拉骨架曲线采用两折线模型,对于受压区滞回曲线,采用曲线型Mander模型和直线型两种函数来描述,对于受拉区滞回曲线,采用朱伯龙模型公式和直线型两种函数来描述。从而使得该模型能够随着骨架曲线和滞回规则的调整,退化成为不同的模型,适用于不同计算精度和计算效率要求的建筑结构非线性时程反应分析。同时,该模型能够考虑箍筋约束效应的影响,需要标定的参数较少,能够较好的描述混凝土在反复荷载作用下的单轴非线性力学行为。在总结已有钢筋本构模型优、缺点和适用范围的基础上,本文选用了能考虑Baushinger效应的双线性强化单轴滞回本构模型作为建筑结构非线性时程分析所采用的钢筋本构模型。2以较有影响力的修正压场本构模型和应变强化塑性本构模型为基础,并加以改进,结合本文建立的混凝土单轴滞回本构模型,建立了两种适合模拟剪力墙和楼板的混凝土双轴滞回本构模型。这两种本构模型的优点在于模型参数较少且易于标定,能够在一定信置度水平上预测混凝土材料在复杂应力条件下的非线性力学行为,在一定的计算精度前提下可以满足工程使用要求。3对工程中常见的短肢剪力墙和细长连梁有限元计算模型中现有单元存在的计算精度较差的问题的原因进行了分析,提出了解决问题的具体对策。根据该对策,本文借鉴理性有限元的思想,结合解析试函数方法,利用广义协调元理论,构造了直接建立在直角坐标系内广义坐标型梁式壳元。该单元位移试函数的基函数采用弹性力学平面问题解析解并考虑了短肢剪力墙和连梁的变形模式,所以适合用来作为短肢剪力墙和连梁的单元模型。采用该方法构造的梁式壳元具备高阶位移场描述能力,列式简单、容易实现,当应用到非线性分析中时,能有效的预测短肢剪力墙和细长连梁的剪切破坏,符合高性能壳元的要求。算例表明:梁式壳元的抗畸变性能较好、计算精度较高,该单元的构造较好的解决了短肢剪力墙和细长连梁有限元计算模型这个待解决的工程问题。4采用本文建立的混凝土和钢筋本构模型,分别根据Allman膜元构造方法、龙驭球教授创建的厚薄通用板单元构造理论和本文构造的梁式壳元,建立了适用于不同类型钢筋混凝土剪力墙非线性有限元分析的整体式钢筋混凝土壳元微观模型。在整体式壳元模型中:采用纤维梁元模拟剪力墙中边缘构件;对一般剪力墙采用钢筋混凝土Allman膜元模拟剪力墙墙板的面内刚度,采用厚薄通用板单元模拟剪力墙墙板的面外刚度;对于短肢剪力墙和细长连梁,采用梁式壳元模拟其刚度。由于整体式壳元模型直接基于材料本构模型,所以能够给出剪力墙中混凝土及钢筋的整个非线性发展全过程。为验证该模型,将该模型的分析结果和两片钢筋混凝土剪力墙试件的试验结果进行对比。结果表明:整体式壳元模型能够对弯、剪、压共同作用下钢筋混凝土剪力墙的极限承载力和非线性弯曲、剪切耦合变形进行较为准确的预测,可为工程应用提供合适的数值解。与分层壳元模型、实体单元模型等微观模型相比,该模型自由度少,计算效率高,总计算量较小,在当前的计算机硬件资源的条件下适合作为建筑结构非线性动力时程分析的钢筋混凝土剪力墙单元模型。5建立了建筑结构非线性地震反应分析的三维空间模型,在空间模型中采用纤维梁元来描述梁、柱、支撑等构件的非线性力学行为,采用整体式壳元模型描述钢筋混凝土剪力墙的非线性力学行为。空间模型能够考虑多维地震动作用下建筑结构的多维地震反应,对结构简化假定较少,计算精度和计算效率都很高。6从算法稳定性、精度、效率和健壮性等性能指标出发,对各种不同的结构动力方程时间积分方法进行了分析,对显式算法、隐式算法的基本思想和特点及在建筑结构非线性动力分析中可能出现的问题进行了对比。在此基础上,提出了一个适合建筑结构在地震动作用下非线性动力响应求解的综合方案。该方案包括重力荷载作用下考虑施工模拟的建筑结构初始应力求解,地震动作用下建筑结构非线性动力响应的隐式求解(广义α法)和显式求解(中心差分法)。以上述模型及理论为基础,编制了建筑结构在地震动作用下非线性动力时程分析程序。通过不同算例对上述模型及算法的适用性和有效性给出了相应的定性结论,可供工程设计人员参考。7针对精细时程积分法对内存资源要求高、计算量较大的问题,将该算法加以改进,以该算法为基础建立了一种新的计算格式,通过矩阵分块算法和改变计算次序,有效的降低了对内存的需求,提高了计算效率。数值算例表明该改进方法的是有效的、适用的。更多还原

【Abstract】 The dynamic response of building structures subjected to rare severe earthquake loading has been one of the structural engineering’s important research topics for many years. Since many factors should be considered, there is still no perfect solution strategy to this subject. In this dissertation, the fundamental theories and numerical methods for the nonlinear dynamic analysis of building structures are discussed, and some new methods are successfully developed. The main content and contributions are listed as follows:1 Summarized on the existing models developed by other researchers, a new uniaxial hysteresis constitutive model for concrete which is able to consider the influence of complicated stress path and stress history, is proposed. This model consists of two parts: the skeleton curve and the hysteresis rule. The skeleton curve in compression is described by the curvilinear and the broken-line Mander formulae respectively, while the skeleton curve in tension is described by the bi-linear model. The hysteresis curve in compression is described by the linear and curvilinear Mander formulae, while the hysteresis curve in tension is described by the Zhu Bolong’s model and the linear models. The new model can be adjusted by the variation of the skeleton curve and the hysteresis rule and even degenerated into different models, to accommodate the various nonlinear dynamic analyses of building structures with different requirements on computational precision and efficiency. Furthermore, this new model can reflect the confinement effects of the hoop reinforcement; fewer parameters required to be calibrated; and can well describe the uniaxial nonlinear behaviors of the concrete under cyclic loading.After studying the existing constitutive models of the steel bar, the bilinear hardening model with the Baushinger effect is selected for the nonlinear dynamic analyses of building structures.2 By combination of the proposed uniaxial constitutive model of concrete, two biaxial hysteretic constitutive models of concrete suitable for simulating the shear-walls and the slabs are established based on the well-known MCFT model and the strain hardening plastic model. These two new models contain fewer easily calibrated parameters only, and can predict the nonlinear behaviors of concrete materials under complicated stress conditions based on the engineering’s computational precision requirements.3 The low precision problem of using the traditional shell elements to compute the short-leg shear wall and the slender coupling beam like structures is discussed. Then, a countermeasure is proposed as follows. According to the essence of rational finite element method, a new generalized coordinate beam-shell element is constructed by the generalized conforming theory and the analytical trial function method. All formulations are established in the Cartesian coordinate system directly. Since the analytical solutions of the plane stress problem are taken as the basis functions of the element trial functions for the displacement fields, and the deformation modes of the short-leg shear walls and the slender coupling beams are fully considered, the new element is quite suitable for related finite element analyses. The formulations of the new element are relatively simple, and possess the capacity of describing higher-order displacement fields. When the element is used in a nonlinear analysis, it can effectively predict the shear failure of the short-leg shear wall and the slender coupling beam. Numerical examples show that the new beam-shell element exhibits good performance and is insensitive to mesh distortion. It provides an effective tool for engineering computations of the short-leg shear wall and the slender coupling beam.4 Using the constitutive models of concrete and steel bar proposed in this dissertation, a new RC integral shell element model for nonlinear finite element analyses of various RC shear walls is developed. The new shell element is based on the combination of the ideas of the Altaian’s membrane element, thin-thick plate element proposed by Prof. Long Yu-Qiu, and beam-shell element proposed in this dissertation. In the computational model of the distributed RC integral shell element, the boundary elements of the shear walls are simulated by the fiber beam element model; the reinforced concrete Allman’s membrane element and the thin-thick plate element are used to simulate in-plane and out-of-plane stiffness of normal shear walls, respectively; and the short-leg shear walls and slender coupling beams are modeled by the beam-shell elements. Since the distributed RC integral shell element is directly based on material model, it can describe the whole elastic-plastic development process of the concrete and the steel bar in the shear walls.The new RC integral shell element model is verified by a comparison between the calculated results and the experimental data of two RC shear wall specimens. The results demonstrate that, for RC shear walls subjected to the combined loadings of bending, shear and compression, the RC integral shell element model can evaluate ultimate loading, coupling effects for nonlinear bending and shear deformations with satisfied accuracy. Compared with other microscopic models such as multi-layered shell element model and solid element model, it is obvious that the present model has the fewest degrees-of-freedom and the highest computational efficiency. It can be concluded that the present model is suitable for the RC shear walls in the time history analysis of building structures under the current computer hardware conditions.5 A 3-D spatial model for the nonlinear time-history analyses of the building structures subjected to earthquake loading is proposed. In this model, the beams, the columns and the braces are simulated by the fiber beam element model, while the RC shear walls are simulated by the distributed RC integral shell element model. Such a spatial model, which is imposed on fewer simplification hypotheses, not only can consider the multi-dimensional responses of building structures subjected to multi-dimensional earthquake loading, but also possesses high computational precision and efficiency.6 The stability, precision, efficiency and robustness of different time integration algorithms for equations of structural dynamics are discussed. A comparison of the characters and the problems which may happen in the nonlinear time-history analyses of building structures between the explicit and the implicit algorithms is also given. Then, a comprehensive solution scheme for the nonlinear dynamic response of the building structures subjected to the earthquake loading is proposed. This scheme includes the solution strategy of the initial stresses when the construction simulation of building structures under gravity load is considered, the implicit solution strategy (generalizedαmethod), and the explicit solution strategy (central difference method) for the nonlinear dynamic response of the building structures under the earthquake loading. Based on the above models and theories, a computer program of the nonlinear dynamic time-history analysis for the buildings structures subjected to earthquake loading is developed. The validity and availability of this program and its related algorithms are demonstrated by various numerical examples. All the results can be references by engineering designers.7 The traditional precise time integration algorithms usually occupy many memory resources, and their computation costs are also relatively high. In order to overcome these disadvantages, an enhanced algorithm is successfully developed. By partitioning of the matrix and exchanging computational sequence, the memory demand can be reduced effectively, and the computational efficiency is also improved. Numerical examples demonstrate the validity of the new algorithm.更多还原