磁流变阻尼器的两种力学模型和试验验证

本文根据我们设计制作出的磁流变阻尼器的阻尼特性试验结果，提出了描述阻尼器动态特性的两种新的力学模型。一种称之为修正的Bingham模型，它由Bingham单元（库仑摩擦单元与粘滞单元并联）与弹簧单元串联组成。该弹簧单元与磁流变液屈服前区的初始剪切模量和蓄能器的刚度等有关。另一种称为修正的Dahl模型，它采用Dahl模型来模拟库仑摩擦力，克服了常用的Bouc-Wen模型需要确定的参数过多的缺点。为了使模型在阻尼器的电流强度（磁场强度）改变的情况下仍然有效，引入一个内变量描述模型参数与电流强度（磁场强度）的关系。最后，通过理论分析与试验结果的比较，证明本文提出的两种力学模型能够较为精确地描述大多数的磁流变阻尼器在改变电流强度（磁场强度）情况下的动态特性。     

伪三维有限元地震活动模型及其在华北地区的应用

对伪三维地震活动模型做了进一步研究，主要是对无预设破裂方向的单元，引入应力摩尔圆方法来判定破裂发生的时间。该方法首先在一个简单的理论模型上加以应用，给出了一些计算结果，以检验所提方法的可行性。在此基础上，将这个模型应用到华北地区，得到了一些初步计算结果。这些研究结果为将地震活动的理论模型应用到实际地震活动中，提供了一种可能的研究途径。     

钢筋混凝土筒体的非线性有限元分析模型

本文提出了一种反复荷载下混凝土材料的本构模型，该模型采用平面应力状态下的弥散正交裂缝假设，钢筋采用弥散假设，并考虑了屈服、应变硬化、循环卸载与再加载规则等因素。该本构模型与其他模型相比，具有简便有效的优点。在此基础上，本文采用八结点平面应力单元建立了钢筋混凝土核心筒体非线性有限元分析模型，并对试验模型进行了非线性分析，计算结果与试验结果吻合较好。     

基于宏观模型的暗支撑短肢剪力墙非线性分析

建立了适合于带暗支撑短肢剪力墙非线性分析的宏观计算模型，分析推导了SAP程序中Link单元的刚度矩阵，明确了Link（单元中各弹簧的物理意义，给出了各单元等效刚度计算方法，选取了合适的单元力一位移关系。用由Link单元建立的宏观模型对3片普通短肢剪力墙和3片带暗支撑短肢剪力墙进行了静力弹塑性分析，试验和计算所得顶点力一位移骨架曲线符合良好，说明所建宏观模型合理，用由Link单元建立的宏观模型能较好的模拟带暗支撑短肢剪力墙的非线性行为。     

大陆地震的动力学模型研究

应用非线性动力学模型，以大陆构造构体为参照对象，对大陆地震的成组孕育和发生过程进行模拟研究，通过对６×８弹簧－滑块－阻尼器组合单元非线性动力学模型的理论计算及其结果的分析，得到了一系列与实际地震较类似的人工地震图像，如模型中的地震活动在时间上有轮回怀，在地点上有条带性，并在不同轮回中有条过移的现象。模型中应力变化十分复杂，但仍能为预测地震提供概略性的信息。     

大型渡槽有限条法动力建模研究

根据渡槽结构特点，采用有限条划分渡槽槽身，推导出渡槽槽身结构的单元刚度矩阵、相容质量矩阵的显式表达式；渡槽支架采用空间梁单元模拟；联接槽身和支架的盆式橡胶支座采用弹性元件单元模拟。编程程序具体计算了某大型渡槽的模态，并用ANSYS对大型渡槽进行模态分析，计算结果表明：该模型计算的渡槽结构的固有频率和ANSYS计算结果接近。模型可用于大型渡槽的动力分析。     

用一种墙体单元模型分析剪力墙结构

本文概括介绍了目前国内外分析剪力结构所采用的计算模型,并用虚拟原理推导了多垂直杆元模型的单元刚度矩阵,讨论了这一模型中相对转动中心高度的取值,接着提供了确定这一模型中的垂直杆元的轴向刚度和水平弹簧的抗剪刚度的计算方法,在计算抗剪刚度时,考虑了受弯和受剪之间的相互作用,使这一模型与实际结构更加符合,最后,提供了一个算例,并与试验结果比较,表明了该模型不仅力学概念清晰,计算简单,而且具有较好的计算精度     

暗支撑剪力墙非线性分析模型

建立了适合于带暗支撑剪力墙非线性分析的宏观单元模型,分别用带斜杆的多垂直杆单元模型和模拟框架单元模型对2个带暗支撑剪力墙进行了静力弹塑性分析,给出了模拟框架单元模型的刚度矩阵和杆件非线性力-变形关系,对两种不同单元模型的计算结果进行了对比,结果表明该两种模型能够较好反映带暗支撑剪力墙的弹性和塑性阶段的受力特点。     

钢筋砼磨擦耗能支撑框架结构的单元刚度和力学模型分析

为研究钢筋砼磨擦耗能支撑框架结构的动力反应性能，对其中的磨擦耗能器单元和框加杆单元的单元刚度和力学模型做了分析。钢筋砼磨擦耗能支撑单元由支撑杆单元和钢板－橡胶磨擦耗能器单元组成，支撑单元可取空间杆单元，磨擦耗能器单元为平面应力矩形单元。磨擦耗能器单元的剪切恢复力曲线为理想的弹塑性曲线，根据耗能器单元的力学模型，可确定其在每一时刻的刚度；框架结构空间杆单元的恢复力模型采用双线型模型，根据杆单元的力学模型，可确定其在每一时刻的刚度。并利用所编制的程序对十层单榀两跨空间普通框架和摩擦耗能支持框架在地震作用下进行了弹塑性反应时程分析，结果表明耗能支撑框架的顶层最大位移明显小于普通框架。     

一种考虑截面翘曲的剪力墙宏模型

提出了一种六自由度刚杆—弹簧单元，可以像有限元法那样根据精度和计算量的要求，以适当密度在水平和垂直方向拼装成剪力墙的宏模型。这一宏模型不仅可以反映中和轴的移动，而且不再受现有宏模型中平面假定的限制，可以反映初始平截面的剪切翘曲。这对于分析剪跨比较小的剪力墙是有一定必要性的。该模型竖向弹簧布置在Gauss积分点处，从而有效提高了计算精度和效率。利用该模型计算了五个剪力墙的弹塑性“推覆”过程，取得了与实验较为一致的结果。对一些有关宏模型中本构关系选取及变形假定的问题进行了讨论。     

Nonlinear earthquake response analysis and energy calculation for seismic slit shear wall structures

Based on the concept of structural passive control, a new type of slit shear wall, with improved seismic performance when compared to an ordinary solid shear wall, was proposed by the authors in 1996. The idea has been verified by a series of pseudo-static and dynamic tests. In this paper a macro numerical model is developed for the wall element and the energy dissipation device. Then, nonlinear time history analysis is carried out for a 10-story slit shear wall model tested on a shaking table. Furthermore, the seismic input energy and the individual energy dissipated by the components are calculated by a method based on Newmark-β assumptions for this shear wall model, and the advantages of this shear wall are further demonstrated by the calculation results from the viewpoint of energy. Finally, according to the seismic damage criterion on the basis of plastic accumulative energy and maximum response, the optimal analysis is carried out to select design parameters for the energy dissipation device.     

A distributed parameter model of a frame pin‐supported wall structure

Many reinforced‐concrete frames collapse via a soft‐story mechanism during severe earthquakes. Such collapses are mainly attributed to concentrated deformation in a soft story. Deformation control is thus important in preventing collapse. The frame pin‐supported wall structure is a type of rocking structure that releases constraints at the bottom of the wall. Previous research has obtained good results for the deformation control of this type of structure. However, the interior forces and strength demands of the pin‐supported wall have not been systematically explored. In this paper, a distributed parameter model is developed to investigate the strength demand of the wall in a frame pin‐supported wall structure. In the model, the pin‐supported wall is simplified as a bending beam and the frame is simplified as a shear beam. The two beams are joined by distributed shear connectors, so that the shear force can be transferred at any location on the interface. The model can be solved using differential equations based on equilibrium and compatibility. The accuracy of the model is verified using SAP2000 (Computers and Structures Inc., Berkeley, CA, USA). Displacement distribution of the structure and distributions of the moment and shear force within the pin‐supported wall are obtained for two typical external force profiles. It is found that the pin‐supported wall can effectively reduce the drift concentration factor. Distributions of the displacement, moment, and shear force are closely correlated with the relative stiffness of the wall and frame. Finally, recommendations on the stiffness and strength of a pin‐supported wall are made. Copyright © 2015 John Wiley & Sons, Ltd.     

钢筋混凝土剪力墙弹塑性分析方法

钢筋混凝土剪力墙弹塑性分析可以采用微观方法和宏观方法,本文对这些方法进行了介绍和比较,尤其是对于剪力墙的宏观有限元模型进行了较详细的论述,指出了各自的优缺点。认为如果对高层剪力墙结构进行分析,应尽可能采用宏观方法,而对于宏观剪力墙模型的选取是至关重要的。在此基础上提出了一些有益的建议。     

An elastic-plastic analysis of short-leg shear wall structures during earthquakes

Short-leg shear wall structures are a new form of building structure that combine the merits of both frame and shear wall structures. Its architectural features, structure bearing and engineering cost are reasonable. To analyze the elastic-plastic response of a short-leg shear wall structure during an earthquake, this study modified the multiple-vertical-rod element model of the shear wall, considered the shear lag effect and proposed a multiple-vertical-rod element coupling beam model with a new local stiffness domain. Based on the principle of minimum potential energy and the variational principle, the stiffness matrixes of a short-leg shear wall and a coupling beam are derived in this study. Furthermore, the bending shear correlation for the analysis of different parameters to describe the structure, such as the beam height to span ratio, short-leg shear wall height to thickness ratio, and steel ratio are introduced. The results show that the height to span ratio directly affects the structural integrity; and the short-leg shear wall height to thickness ratio should be limited to a range of approximately 6.0 to 7.0. The design of short-leg shear walls should be in accordance with the "strong wall and weak beam" principle.     

A mathematical model for the in-plane non-linear earthquake behaviour of unreinforced masonry walls. Part 2: Completion of the model

In this part, the parameter functions for clay brick masonry appearing in the non-linear model are established for the wall material used in the experiments by means of experimental data and a particular type of optimization. This special optimization makes use of the fact that the wall behaves linearly at the intensity level of each excitation, as described in Part 1, and involves matching in frequency space the experimental and theoretical complex frequency response functions relating the Fourier transforms of the top and base accelerations of the wall. It is found that the envelope curves for the parameter functions are bilinear and that the dynamic values of mechanical properties of masonry differ greatly from their static values. The completed model is appraised by comparing how the wall will respond to strong earthquake excitations when predicted using the model and how it actually responded on the shaking table. The predicted response is remarkably close to the experimental.     

强震环境下建筑复合节能墙体抗震性能评估模型

现阶段针对建筑复合节能墙体的抗震性能评估主要根据强震发生后墙体损毁程度实现,评估结果精确度低,因此构建强震环境下建筑复合节能墙体抗震性能评估模型,根据复合节能墙体构件的强度和刚度退化系数,描述强震环境下建筑复合节能墙体损伤情况;在此基础上,采用动态增量分析法(IDA)在不同强度地震动输入条件下,根据建筑复合节能墙体结构响应参数和地震动强度参数构建2种参数的关系曲线——IDA曲线,利用R-O单一函数曲线规则化IDA曲线,获取IDA概率分位曲线,并将50%概率分位曲线斜率用于描述墙体结构损伤的变化,该曲线斜率则为墙体结构损伤指数,依据该指数准确评估强震环境下建筑复合节能墙体抗震性能。实验结果表明,所构建模型可准确分析不同峰值地面加速度时建筑复合节能墙体结构的位移变化,且模型随地震等级不断提升,评估建筑复合节能墙体抗震性结果精度逐渐提高,是一种适合强震环境的建筑复合节能墙体抗震评估模型。     

A linear mathematical model for the seismic inplane behaviour of brick masonry walls part 1: Theoretical considerations

In this study two mathematical models are presented for the linear dynamic behaviour of masonry walls. The study is completed in three stages: experimental observations, selection of a mathematical model and the determination of model parameters through optimization analysis. In the present paper (Part 1) the theoretical analysis used in the development of the mathematical models is presented. Part 2 is devoted to the optimization analysis. Evaluation of the experimental data, which is described in detail in Part 2, indicates that the first two modal frequencies of the wall specimen are close to each other. This may be attributed, on physical grounds, to strong interaction between the brick and mortar phases of the wall. Accordingly, a two-phase mathematical model, namely a mixture model (MM), is chosen to describe the wall behaviour because it can differentiate between the two phases of the wall and take into account the interaction between them. The equations of MM are put into a discrete form to simplify the optimization analysis. As a special case, MM contains a simple one-phase model called the effective modulus model (EMM). The equations of EMM are also established. Finally, the theoretical complex frequency response functions (CFRF) predicted by MM and EMM are obtained. CFRF relates the top acceleration of the wall to its base acceleration and is the response quantity chosen to be matched in the optimization analysis.     

Seismic analysis and design of rigid bridge abutments considering rotation and sliding incorporating non-linear soil behavior

A two-dimensional (2D) finite element analytical model is developed to analyze the seismic response of rigid highway bridge abutments, retaining and founded on dry sand. A well verified finite element code named FLEX is used for this purpose. The proposed model has the following characteristics: (1) The soil (dry sand in this study) is modeled by a 2D finite element grid; (2) The bridge abutment is molded as a rigid substructure; (3) The strength and deformation of the soil are modeled using the viscous cap constitutive model. This model consists of a failure surface and hardening cap together with an associated flow rule. The cap surface is activated for the soil under the wall to represent compaction during wall rocking. In addition, viscoelastic behavior is provided for representing the hysteretic-like damping of soil during dynamic loading; (4) Interface elements are used between the wall and the soil (at the backface of the wall and under its base) to allow for sliding and for debonding/recontact behavior; (5) The finite element grid is truncated by using an absorbing boundary approximation. Using this boundary at both sides of the grid simulates the horizontal radiation of energy scattered from the wall and the excavation. Shear beams are placed adjacent to the lateral boundaries from each side which give the far-field ground motion, for comparison with those computed adjacent to the boundaries. The analytical model is verified comparing predictions to results from dynamic centrifuge tests, with satisfactory agreement. The proposed model is used to study the dynamic response of an 8.0 m high and 3.0 m wide rigid bridge abutment (proportioned using the traditional approach to design) for different sinusoidal and earthquake acceleration input motions. The results from the analysis show that outward tilting of rigid bridge abutments is the dominant mode of response during dynamic shaking and that these abutments end up with a permanent outward tilt at the end of shaking. The results from all the analyzed cases of the 8.0 m high gravity retaining wall together with those from the analysis of the tilting wall centrifuge tests are discussed and used for proposing a practical method for evaluating the seismic response of rigid abutments during earthquakes.     

截面中部配置型钢的混凝土剪力墙抗震性能研究

本文通过试验研究了型钢混凝土(SRC)剪力墙的抗震性能,对16个试件进行了低周反复加载试验,得到了这些构件的延性比;研究了高宽比等参数对型钢混凝土剪力墙抗震性能的影响。在试验中,研究了在中部配置型钢的型钢混凝土剪力墙,结果表明这种新型的型钢混凝土剪力墙具有更好的抗震性能。在试验的基础上,本文建立了型钢混凝土剪力墙恢复力骨架曲线的数学模型,为分析高层结构的非线性地震反应分析提供了基础数据。     

Seismic Displacement of Gravity Walls by a Two-body Model

Gravity walls retaining dry soil are modeled as a system of two bodies: (a) the gravity wall that slides along the wall-foundation soil boundary and (b) the critical soil wedge in the soil behind the wall. The strength of the system is defined by both the frictional and the cohesional components of resistance. The angle of the prism of the critical soil wedge behind the wall is obtained using the limit equilibrium method. The model accounts for changes in the geometry of the backfill soil behind the wall by considering the displacements at the end of each time step under limit equilibrium. The model shows that the standard (single) block model is over-conservative for the extreme case of critical-to-applied-seismic acceleration ratios less than about 0.30, but works well for cases where this ratio ranges between 0.5 and 0.8. The model is applied to predict the seismic displacement of gravity walls (a) tested in the shaking-table and (b) studied numerically by elaborate elasto–plastic analyses.