结构地震响应波动分析的被研究块体方法

发布时间：2018-04-09 18:01

本文选题：地震响应　切入点：波动方法　出处：《大连理工大学》2013年博士论文

【摘要】：结构振动的本质是波在结构中不断传播与反射,结构振动是结构中波动传播的外在表现形式,地震响应是结构中地震波传播所导致的结果。通过对结构中地震波传播与反射过程的研究,不但可以为结构地震响应提供波动求解方法,而且更有利于明确结构内部各处地震响应细节。结构在地震(特别是富含高频分量的近断层地震)作用下的瞬态反应问题,从波动角度出发给予求解会更为合理。另外,波传播理论能很好地解释建筑结构中存在的波动传播的时滞现象。因此,波动方法是研究结构地震响应的有效途径。本文针对结构地震响应问题,考虑了结构或构件的弯曲变形、剪切变形和轴向变形,分别提出高耸高层结构、二维框架结构以及三维框架结构地震响应波动分析的被研究块体方法,通过模拟结构中地震波传播过程来研究结构地震响应。该方法主要思想是在结构中建立被研究块体,然后求解每个被研究块体的动力平衡方程,得到结构的波动响应。该方法直接将地震加速度记录积分得到的位移时程施加到支座上,即可实现时间域内的递推计算,不需要求解结构动力学方程组,具有物理意义清晰,方法简单的特点。对于二维和三维框架结构的地震响应问题,该方法在各支座处可以自然地引入行波激励,不需要求解经典的多点激励动力学方程组。本文主要研究工作如下： (1)提出高耸、高层结构地震响应波动分析的被研究块体方法。针对弯剪型串联多自由度体系力学模型的高耸、高层结构,介绍了被研究块体的概念；由空间离散段的端部力与端部位移之间关系式,推导给出离散段的段中内力(轴力、剪力和弯矩)计算公式；考虑被研究块体质心与离散节点之间的纵向偏心,建立被研究块体的动力平衡方程。给出算法的稳定性条件；给出算法的实现过程,即在时间域上交替运用段中内力计算公式、被研究块体的动力平衡方程以及被研究块体质心与离散节点加速度之间关系式进行递推计算。通过弯曲波波速模拟、两端自由梁中弯曲波传播和自由端受静载作用下的悬臂梁内力分析,验证所提出被研究块体方法的正确性。通过圆环型变截面梁动力响应分析和等截面理想烟囱结构地震响应分析,验证被研究块体方法中考虑纵向偏心的正确性。由于考虑纵向偏心的影响,使得该方法具有补偿功能,即使空间离散段截面不同或离散网格不均匀也能得到精确的计算结果。对南京电视塔地震响应研究发现：在钢桅杆的危险截面处,考虑纵向偏心影响的应力值比常规有限元方法计算的应力值要大。按常规方法计算结果进行设计时,电视塔的钢桅杆可能会偏于危险,因此,高耸结构地震响应分析应考虑纵向偏心的影响。对24层框架结构地震响应研究表明：被研究块体方法可以为高层结构的弹塑性地震响应提供一种有效的波动分析方法。针对弯剪型串联多自由度体系的力学模型,利用被研究块体方法的控制方程,给出考虑纵向偏心项的矩阵形式结构动力学方程。该方程修正了传统弯剪型串联多自由度体系结构动力学方程中的质量阵和刚度阵。 (2)提出二维框架结构地震响应波动分析的被研究块体方法。将二维结构的梁或柱离散成空间段,取与节点相关联各空间离散段的一半及楼板构成被研究块体；推导给出二维局部坐标系中,空间离散段的段中内力计算公式；针对被研究块体质心建立了动力平衡方程；给出被研究块体方法的实现过程,即在时间域上交替运用段中内力计算公式、被研究块体动力平衡方程,并利用二维局部坐标与总体坐标之间位移关系式、被研究块体质心与节点加速度之间关系式进行递推计算。针对三跨六层钢筋混凝土框架结构,在一致激励和行波激励作用下,将被研究块体方法的计算结果分别与基于多点激励动力学方程的有限元法计算结果和MIDAS软件的计算结果进行对比,验证了被研究块体方法的正确性。通过对不同场地地震波作用下的四个二维框架结构(三跨六层钢筋混凝土框架结构、三跨三层、三跨六层现浇楼板钢筋混凝土框架结构和二跨十层钢-混凝土组合框架结构)的行波效应进行研究,结果表明：即使对于短跨结构,也不应一概忽略地震波的行波效应。行波效应可导致框架结构柱剪力和梁端弯矩出现增大现象,其中迎波方向的底层柱子剪力和一层梁端弯矩增加更为明显；底层柱子变形不一致,且结构的横向变形增大。 (3)提出三维框架结构地震响应波动分析的被研究块体方法。在三维结构中取与节点相关联各空间离散段的一半构成被研究块体；推导给出三维局部坐标系中离散段的段中内力计算公式；给出三维局部坐标系与总体坐标系之间的坐标转换矩阵；建立了被研究块体的动力平衡方程；给出被研究块体方法的实现过程,即在时间域上交替运用段中内力计算公式、被研究块体动力平衡方程,并利用三维局部坐标与总体坐标之间关系式进行递推计算。研究了六层三维钢框架结构的行波效应,结果表明：考虑行波效应时,框架结构柱剪力和梁端弯矩存在明显增大现象。研究结果进一步表明：不应一概忽略短跨结构的行波效应。
[Abstract]:The essence of vibration wave in the structure is in continuous transmission and reflection, is the external manifestation of structural vibration propagation in structures, the seismic response is caused by seismic wave propagation in structures. Through research on seismic wave propagation and reflection process structure, can not only provide for the wave method for seismic response of structures, and more details to the seismic response everywhere within the clear structures. Structures in the earthquake (especially rich in high frequency components of the seismic response under the action of transient), starting from the wave angle give the solution will be more reasonable. In addition, the wave propagation theory can well explain the phenomenon of wave propagation delays exist in the building structure. Therefore, the fluctuation method is an effective way to study seismic response of the structure.
According to the seismic response of structures, considering the bending deformation of the structure or component, shearing deformation and axial deformation were put forward, towering high-rise structure, two-dimensional frame structure and frame structure seismic response analysis of 3D wave of the block method, through the simulation of seismic wave propagation in structure to study the earthquake response of the structure. The main idea of this method is the study of block based on the structure, the dynamic equilibrium equations for each block is then obtained, the structural response fluctuation. This method directly to the seismic records of a time history integral is applied to the bearing, can realize the recursive calculation in time domain, do not need to solve the structural dynamic equations has a clear physical meaning and characteristics of simple method for 2D and 3D seismic response of frame, the method can naturally lead in each support The traveling wave excitation, does not need to solve the classical multi excitation dynamics equations. The main research work are as follows:
(1) proposed by high volatility analysis studies the block method of seismic response of high-rise structure. Aiming at the high shear bending type series system of multi degree of freedom mechanical model of high-rise structure, introduces the concept of block; from the relationship between the spatial discretization section of the end force and tip displacement, internal forces are derived in the discrete segment (axial force, shear force and bending moment) formula; longitudinal study by the eccentricity between the heart and the physical block discrete nodes into consideration, establish the dynamic equilibrium equation of block. The stability conditions are given; the algorithm realization process, namely in the time domain using the section internal force calculation in turn the formula, the dynamic equilibrium equation of block and study the relationship between the heart and the physical block discrete nodes are recursive acceleration calculation.
The bending wave simulation, free ends Liang Zhongwan Qu Bo spread and the free end of the cantilever beam under the action of static load, verify correctness of the study by block method. The ring type variable response analysis and uniform ideal chimney structure seismic dynamic response of the beam cross section, the authentication is considered in the method of blocks the correctness of the longitudinal eccentric. Because of considering the influence of the longitudinal eccentric, makes the method with compensation function, even if the space of discrete sections or different discrete nonuniform meshes can get accurate calculation results.
Study of seismic response of Nanjing TV Tower: the dangerous section steel mast, considering the longitudinal stress value calculation of eccentric effect than the conventional finite element method, the stress value should be large. According to conventional methods of calculation results of the design, the TV tower steel mast may tend to risk, therefore, the seismic response of high-rise structure the analysis should consider the effect of longitudinal eccentric. In response to the research shows that the 24 layer frame structure seismic: Study on block method can provide an effective response analysis method of the fluctuation of high-rise structure elastic-plastic earthquake.
According to the mechanics model of bending shear type series multi degree of freedom system, the control equation is of block method, are given in matrix form structure equations. The equations of longitudinal eccentric modified bending shear type tandem mass matrix dynamics of MDOF system equation and the stiffness matrix.
(2) proposed by fluctuation analysis study on block method of seismic response of frame structure. The two-dimensional Liang Huozhu discrete two-dimensional structure into space segment, by the study on block form taking is associated with a node the space of discrete segments and half floors; deduced two-dimensional local coordinate system, the calculation formula of internal force of discrete segment in space according to the study by heart block; constitution established the dynamic equilibrium equation is given; the realization process of block method, namely in the time domain using the section internal force calculation formula in turn, by research the block dynamic equilibrium equation, and the displacement relation between two-dimensional local coordinate and global style, is the relationship between the physical heart block with the acceleration of the node type recursive calculation.
For the three span six storey reinforced concrete frame structure under uniform excitation and traveling wave excitation, the calculation will be on the block method were compared with the finite element method multi excitation dynamics equation is calculated based on the comparison of the calculated results and the results of MIDAS software, to verify the correctness of the block method.
The four dimensional structure of the earthquake wave under different site (three span six storey reinforced concrete frame structure, three span three storey, three span six storey slab reinforced concrete frame and two span ten storey steel-concrete composite frame structure) were studied, the results show that the traveling wave effect even for short the cross structure, also should not ignore the traveling wave effect of earthquake wave. The traveling wave effect can lead to bending shear frame structure column and beam end become larger, the bottom column shear wave direction of attack and a layer of beam moment was increased; the bottom pillar deformation is not consistent, and the lateral deformation of the structure increases.
(3) proposed by fluctuation analysis study on block method of three-dimensional frame structure seismic response. Associated with each node takes half space discrete segments in the three-dimensional structure of the composition block; force formula is derived for 3D discrete segments in the local coordinate system in three dimensions is given; coordinate between local coordinate system and the general coordinate transformation matrix; dynamic equilibrium equation was established on the block; the implementation process was given on the block method, namely in the time domain using the section internal force calculation formula in turn, by research the block dynamic equilibrium equation, and recursive calculation using the relationship between the local three-dimensional coordinate and global type.
Study on the effect of traveling wave, the six layer of 3D steel frame structure. The results showed that: considering the traveling wave effect, bending shear frame structure column and beam are significantly increased. The results further showed that: should not ignore the effect of traveling wave short span structure.

【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：TU311.3

【参考文献】