地基动力相互作用的时域数值分析

在水坝、桥梁等大型建筑物的地震响应分析中,结构与半无限地基间的动力相互作用始终是一个重要的研究领域。但由于问题的复杂性,在其数值模拟过程中存在诸多困难,使得动力相互作用分析目前仍多限于频域或时频联合的求解模式,存在许多不尽人意之处。其实,从理论发展的角度比较来看:首先,时域数值分析适宜考虑结果破坏阶段的系统非线性力学特征,并能提供结构与地基的瞬时响应,较频域算法结果更具信息完备的特点;其次,子结构分析模式便于单独分析结构与地基两组成因素的动力特征,分别建立相应的动力计算模型,与直接法需要将结构与地基一体化并建立形式复杂的系统运动方程相比,大大简化了建立系统动力计算模型的复杂度和求解难度。因此可以说,时域子结构数值求解算法是动力相互作用分析研究的一个重要发展方向。进而,以动力相互作用时域数值分析的具体实现为目的,本文基于阻尼溶剂抽取时域算法(DSEM),在有限元法框架内,从无限地基动力计算模型的建立,输入地震波计算模型的建立,到散射场波动问题求解,相互作用系统动力响应分析,结果数据场的图形分析与处理等方面,开展了一系列研究工作:1. 从结构-地基交界面节点的力平衡与运动协调条件出发,推导了动力相互作用时域子结构分析的基本动力方程;从结构的一般动力平衡方程出发,推导了动力相互作用时域直接法分析的基本动力方程。两者经简化后,可获得目前常用的各类结构地震响应分析计算模型。这些为文中后续工作的开展提供了理论依据。2. 从模拟无限域辐射阻尼效应的基本原理出发,推导了逐步积分格式的表述地基在交界面位置力与变位关系的阻尼溶剂抽取时域实现算法。该地基时域计算模型避免了其他地基模型在时程分析中普遍存在的复杂卷积求解问题,从而为动力相互作用的时域数值分析带来极大的便利。3. 动力相互作用时域分析中,通常需要同时输入地震波的加速度、速度及位移时程。然而,基于加速度记录做数值积分获得的地震位移曲线往往存在明显的基线漂移现象。为此,文中提出了加速度长周期校正的时频联合两步算法。首先是时域预校正,即基于最小二乘拟合技术,从加速度记录中扣除二次曲线形式的微弱的非零基线;然后,针对预校正后积分位移时程仍可能存在的基线长周期摆动现象,在低频区间内对加速度记录再次进行傅立叶窗函数部分滤波操作。4. 为反映不规则场地条件(如基坑散射场)对相互作用输入地震动产生的影响,文中以动力相互作用时域分析为手段,并利用2) 中建立的地基无限域时域计算模型,提出了散射场波动问题的时域逐步求解算法。新算法适应散射场表面形状复杂多变的情况,并可直接求取散射场波动的时程响应。5. 将2) 中基于阻尼溶剂抽取时域算法建立的地基动力计算模型,引入到1) 中推导的时域子结构分析基本动力方程中,提出了动力相互作用分析的时域分区逐步积分算法(SS-DSEM)。算法完全在有限元法框架内实现,体现了时域数值算法信息完备的优势,且逐步积分形式的实现更利于在大规模结构抗震分析中采用。6. 针对有限元数据场的图形分析与处理,基于单元本身的插值性质,完善与发展了母单元绘制技术,克服了计算机图形学经典绘制技术中容易造成有限元模型拓扑结构被大连理工大学博士学位论文破坏、单元有用信息丢失等缺陷。提出了高效的三维实体有限元图形处理的整套母单元可视化绘制算法,包括变位云图、高斯应力云图、三维场切片云图,层片/表面云图,等值线/等值面绘制等,可以使整个数据场后处理过程达到有限元分析的精度,尤其适合高阶插值数据场的图形分析与处理。 在以上基本原理阐述与公式推导的同时,文中详细地给出了各步骤的具体实现算法,并开发了相应的数值分析程序。算例试验表明,本文算法完全在有限元法框架内实现,在应用方面具有良好的适宜性和可扩展性,为结构一无限地基动力相互作用大规模空间问题的解决提供了可靠的数值处理手段。关键词:结构一地基动力相互作用,时域数值算法,子结构,有限单元法,阻尼溶剂抽 取法,无限地基,动刚度,地震波,波动散射,可视化,前后处理一11-
逆变焊机
Numerical analysis of structure-soil dynamic interaction has been recognized as an important part in the structural earthquake-resistant design, especially for long-span bridges and large hydraulic dams. However, due to the complexity of dynamic interaction mechanics, the structure-soil dynamic interaction is usually confined to solve in the frequency domain, which is unsuitable for nonlinear problems and makes the numerical analysis method hard to be further developed in the theory.Recently, many researches of dynamic soil-structure interaction analysis are concentrated in the time domain, because not only the problem of nonlinearity can be better simulated in the time domain than in the frequency domain, but also the typical structural responses analysis is not accustomed to working in the frequency domain. Compared with the direct method, the substructure method is more practical in the formula derivations of general dynamic equations of the system. Moreover, the substructure method is convenient to analyze the dynamic properties of the structure and unbounded soil separately. Therefore, the research with the time-domain substructure method is an important developing direction for the dynamic interaction numerical analysis.Within the framework of the Finite Element Method (FEM), by applying the Damping Solvent Extraction Method (DSE Method), the purpose of this dissertation is to develop a new practical solving procedure for the time-domain numerical analysis of the dynamic interaction, especially for some large-scale civil engineering projects. And then, many related researches are evolved in this paper, mainly including: dynamic numerical models for the infinite soil, numerical models of the seismic input waves, solution of the wave scattering problems, numerical analysis of dynamic interaction, and post-processing for the results data field, etc.1. For time-domain numerical analysis of dynamic interaction, the basic governing dynamic equations in direct method are fully derived from the usual basic dynamic equations of structure, and also the ones in the substructure method are strictly formulated according to the dynamic force equilibrium and deformation compatibility on the structure-soil interfaces. Various time-domain numerical methods applied in practical analyses can be generalized from the simplified forms of the above two governing equations, which provides theoretical basis for the subsequent works in the dissertation.2. DSE Method is an effective simple procedure for the numerical simulation of the dynamic radiation properties of infinite medium through the following two steps: first, applying artificial damping into bounded soil region, and then extracting it by shifting the frequency along the frequency axis. Based on DSE Method, it is convenient to calculate the dynamic interaction forces acting on the interface between unbounded rock and structure. A robust time-domain damping-extraction procedure is proposed in this dissertation, and the corresponding Finite Element implementation of the procedure is also described with a step-by-step numerical integration scheme, in which the convolution integrals, as required inother time-domain algorithms can be avoided. The new algorithm is very convenient to combine with the existent FEM analysis programs for the structure dynamic responses.3. As seismic excitations adopted in the time-domain numerical evaluation, the seismic velocity and displacement histories are usually also essential, other than in the traditional frequency-domain interaction analysis, which usually requires to only input the seismic acceleration records. However, due to the effects of little long-period signal noises, it is a common problem for the evidently shifted baseline existed in the corresponding displacement history by double numerically integrating the acceleration records. So, this dissertation examines the problem in detail and proposes a new simple time-frequency domain correction method to eliminate long-period errors of seismograms. Firstly, the non-zero parabola mean-c