串联隔震体系屈曲后屈曲及大变形力学行为
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摘要
在已有的建筑结构控制技术中,基础隔震技术在最近的几次地震中被证明是一种减轻地震灾害有效的方法。在实际工程中大多数隔震结构采取了由地下室悬臂柱和叠层橡胶隔震支座组成串联隔震体系的隔震方案,维持叠层橡胶支座的稳定性是确保隔震支座实现其隔震功能的重要环节。由于悬臂柱柱身变形及串联系统的二阶效应对隔震支座的承载力和复位性能会产生一定的不利影响,有关悬臂柱与橡胶隔震支座串联系统的安全性问题,成为工程设计和研究人员目前关注的焦点之一。本文针对这一问题,系统研究了串联隔震体系的屈曲、后屈曲和大变形等力学行为。主要内容包括以下几个方面:
(1)针对串联隔震系统的稳定性问题,建立临界荷载的控制方程,探讨参数变化对临界荷载的影响。首先建立单个叠层橡胶支座稳定性分析的场矩阵;其次根据传递矩阵法建立了串联隔震系统稳定性分析的场矩阵,并根据所得的场矩阵建立了其临界荷载的控制方程,避免了繁琐的力学推导过程;最后计算了两种不同型号的串联隔震系统的稳定性,着重探讨了叠层橡胶支座和地下室柱参数变化对串联隔震系统临界荷载的影响。
(2)针对串联隔震系统的水平刚度问题,建立水平刚度计算公式,探讨了压应力对水平刚度及结构地震响应的影响。首先建立了单个叠层橡胶支座的场矩阵;其次根据传递矩阵法建立了串联隔震系统的场矩阵,推导出串联隔震系统的水平刚度计算公式;最后探讨了压应力对水平刚度及结构地震响应的影响。
(3)为了解决带连梁串联隔震系统的稳定性问题,建立了基于传递矩阵法的临界荷载求解公式。首先建立稳定性分析单个支座的场矩阵和连梁等效成抗弯弹簧的点矩阵;其次根据传递矩阵法建立串联隔震系统稳定性分析的特征矩阵,并根据所得特征矩阵建立其临界荷载的控制方程;最后通过计算两种不同型号的串联隔震系统的临界荷载和探讨连梁参数变化对串联隔震系统临界荷载的影响。
(4)利用微分求积法计算分析了基于考虑剪切变形和不考虑剪切变形两种模型梁柱的大变形和后屈曲力学行为。首先以不考虑剪切变形及考虑轴线伸长的模型,建立了大挠度非线性几何方程,利用微分求积法求解了梁柱的后屈曲和大变形力学行为;其次以考虑剪切变形和轴线伸长的模型,建立了精确大挠度非线性几何方程,并利用微分求积法对比分析了基于两种不同模型梁柱的后屈曲和大变形行为。
(5)探讨了叠层橡胶隔震支座和串联隔震体系的后屈曲和大变形力学行为。把叠层橡胶隔震等效成均质弹性体,考虑轴线伸长和剪切变形,建立了大挠度非线性几何控制方程,利用微分求积法求解叠层橡胶隔震支座的后屈曲和大变形力学行为;对串联隔震体系,建立考虑轴向伸长和剪切变形的大挠度非线性几何控制方程,因为串联隔震体系在连接位置材料和几何不连续,不能利用微分求积法求解,采用微分求积单元法把串联隔震体系分解为橡胶隔震支座和地下室悬臂柱两个单元,在连接位置考虑力的平衡和变形协调,把控制方程组装成整体微分求积格式,求解串联隔震体系后屈曲和大变形行为。所得结果与串联隔震体系拟静力试验进行比较,结果表明计算结果和试验结果规律吻合。
The base isolation technology among existing building structure control technology shows excellent performance in effectively reducing the damage resulted from the recent ground motion. In engineering practice, most isolated structures are taken up by serial seismic isolation system which is composed of multilayer electrometric bearings and cantilever column of basement. To ensure the stability of serial seismic isolation system becomes very important. The deformation of the basement cantilever column and second-order effect has negative effect on bearing capacity and reduction capacity of isolation components. The security problem of serial seismic isolation system has become focus of attention by engineers and researchers. To solve such the problem, in this paper the buckling, post buckling and large deformation of serial seismic isolation system have been studied systematically. The main work and conclusions gained are listed as follows:
(1) According to the stability of laminated rubber bearing serially connected with column, which concerned engineering field, the critical load governing equation is established and investigated the influences on the stability. First, field matrix of stability of single laminated rubber bearing is established; Secondly, field matrix of the stability of laminated rubber bearing serially connected with column and the stability governing equation based on transfer matrix method are established , respectively, which avoids tedious mechanical derivation; Finally, calculated the stability of two kinds of series seismic isolation system using numerical calculation method, and investigate parameter variation of multilayer electrometric bearings influence on the stability of series seismic isolation system., some of the conclusions drawn useful for practical engineering applications.
(2) According to horizontal stiffness of laminated rubber bearing serially connected with column, which concerned engineering field, the horizontal stiffness formula was established and compressive stress influence on horizontal stiffness and dynamic response of isolated structure were investigated. First, field matrix of single laminated rubber bearing was established. Secondly, field matrix of the laminated rubber bearing serially connected with column, the relation between internal force and displacement at arbitrary cross sections and state variable at end of laminated rubber bearing serially connected with column, the horizontal stiffness formula based on transfer matrix method were derived, avoiding tedious mechanical derivation. Finally, compressive stress influence on horizontal stiffness and seismic response of isolated structure were investigated. The results shows that the horizontal stiffness decrease with the rise of the compressive stress, laminated rubber bearings fixed in foundation should be adopted in near fault area.
(3) To solve the stability of series seismic isolation system connected with column and coupling beam, which concerned engineering field, the critical load governing equation based on transfer matrix method was established. First, field matrix of stability on single laminated rubber bearing and point matrix of stability on coupling beam were established; Secondly, characteristic matrix of the stability on series seismic isolation system and the stability governing equation based on the characteristic matrix were established , which avoided tedious mechanical derivation; Finally, calculated the stability of two kinds of series seismic isolation system using semi-analytic method, and investigated parameters variation influence on the stability of series seismic isolation system, some of the conclusions drawn useful for practical engineering applications.
(4) By using differential quadrature method, the post-buckling and large deformation of beam-column based on two different models, which one is considering trans-verse shear deformation and another without considering, is comparative analyzed. First, by accurately considering the axial extension and without considering trans-verse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equation for beam-column subjected to loads is formulated, by using differential quadrature method the post-buckling and large deformation of beam-column is analyzed. Then by accurately considering the axial extension and considering trans-verse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equation for f beam-column subjected to loads is formulated. Finally, by using differential quadrature method, the post-buckling and large deformation of beam-column is comparative analyzed.
(5) The post-buckling and large deformation of laminated rubber bearings and series seismic isolation system is investigated. Taking laminated rubber bearings as an equivalent homogeneous elastomer and accurately considering the axial extension and considering trans-verse shear deformation, geometrically nonlinear governing equation for bearings subjected to loads is formulated, by using differential quadrature method, the post-buckling and large deformation of laminated rubber bearings is analyzed. For series seismic isolation system, geometrically nonlinear governing equation accurately considering the axial extension and considering trans-verse shear deformation is formulated. Because series seismic isolation system in connection position material and geometrical discontinuous, differential quadrature method can not be used. So by using differential quadrature element method, the post-buckling and large deformation of series seismic isolation system is analyzed. Through analysis on comparing with the result of pseudo-static test, it is shown that the calculated and experimental results consistent with law.
(1)针对串联隔震系统的稳定性问题,建立临界荷载的控制方程,探讨参数变化对临界荷载的影响。首先建立单个叠层橡胶支座稳定性分析的场矩阵;其次根据传递矩阵法建立了串联隔震系统稳定性分析的场矩阵,并根据所得的场矩阵建立了其临界荷载的控制方程,避免了繁琐的力学推导过程;最后计算了两种不同型号的串联隔震系统的稳定性,着重探讨了叠层橡胶支座和地下室柱参数变化对串联隔震系统临界荷载的影响。
(2)针对串联隔震系统的水平刚度问题,建立水平刚度计算公式,探讨了压应力对水平刚度及结构地震响应的影响。首先建立了单个叠层橡胶支座的场矩阵;其次根据传递矩阵法建立了串联隔震系统的场矩阵,推导出串联隔震系统的水平刚度计算公式;最后探讨了压应力对水平刚度及结构地震响应的影响。
(3)为了解决带连梁串联隔震系统的稳定性问题,建立了基于传递矩阵法的临界荷载求解公式。首先建立稳定性分析单个支座的场矩阵和连梁等效成抗弯弹簧的点矩阵;其次根据传递矩阵法建立串联隔震系统稳定性分析的特征矩阵,并根据所得特征矩阵建立其临界荷载的控制方程;最后通过计算两种不同型号的串联隔震系统的临界荷载和探讨连梁参数变化对串联隔震系统临界荷载的影响。
(4)利用微分求积法计算分析了基于考虑剪切变形和不考虑剪切变形两种模型梁柱的大变形和后屈曲力学行为。首先以不考虑剪切变形及考虑轴线伸长的模型,建立了大挠度非线性几何方程,利用微分求积法求解了梁柱的后屈曲和大变形力学行为;其次以考虑剪切变形和轴线伸长的模型,建立了精确大挠度非线性几何方程,并利用微分求积法对比分析了基于两种不同模型梁柱的后屈曲和大变形行为。
(5)探讨了叠层橡胶隔震支座和串联隔震体系的后屈曲和大变形力学行为。把叠层橡胶隔震等效成均质弹性体,考虑轴线伸长和剪切变形,建立了大挠度非线性几何控制方程,利用微分求积法求解叠层橡胶隔震支座的后屈曲和大变形力学行为;对串联隔震体系,建立考虑轴向伸长和剪切变形的大挠度非线性几何控制方程,因为串联隔震体系在连接位置材料和几何不连续,不能利用微分求积法求解,采用微分求积单元法把串联隔震体系分解为橡胶隔震支座和地下室悬臂柱两个单元,在连接位置考虑力的平衡和变形协调,把控制方程组装成整体微分求积格式,求解串联隔震体系后屈曲和大变形行为。所得结果与串联隔震体系拟静力试验进行比较,结果表明计算结果和试验结果规律吻合。
The base isolation technology among existing building structure control technology shows excellent performance in effectively reducing the damage resulted from the recent ground motion. In engineering practice, most isolated structures are taken up by serial seismic isolation system which is composed of multilayer electrometric bearings and cantilever column of basement. To ensure the stability of serial seismic isolation system becomes very important. The deformation of the basement cantilever column and second-order effect has negative effect on bearing capacity and reduction capacity of isolation components. The security problem of serial seismic isolation system has become focus of attention by engineers and researchers. To solve such the problem, in this paper the buckling, post buckling and large deformation of serial seismic isolation system have been studied systematically. The main work and conclusions gained are listed as follows:
(1) According to the stability of laminated rubber bearing serially connected with column, which concerned engineering field, the critical load governing equation is established and investigated the influences on the stability. First, field matrix of stability of single laminated rubber bearing is established; Secondly, field matrix of the stability of laminated rubber bearing serially connected with column and the stability governing equation based on transfer matrix method are established , respectively, which avoids tedious mechanical derivation; Finally, calculated the stability of two kinds of series seismic isolation system using numerical calculation method, and investigate parameter variation of multilayer electrometric bearings influence on the stability of series seismic isolation system., some of the conclusions drawn useful for practical engineering applications.
(2) According to horizontal stiffness of laminated rubber bearing serially connected with column, which concerned engineering field, the horizontal stiffness formula was established and compressive stress influence on horizontal stiffness and dynamic response of isolated structure were investigated. First, field matrix of single laminated rubber bearing was established. Secondly, field matrix of the laminated rubber bearing serially connected with column, the relation between internal force and displacement at arbitrary cross sections and state variable at end of laminated rubber bearing serially connected with column, the horizontal stiffness formula based on transfer matrix method were derived, avoiding tedious mechanical derivation. Finally, compressive stress influence on horizontal stiffness and seismic response of isolated structure were investigated. The results shows that the horizontal stiffness decrease with the rise of the compressive stress, laminated rubber bearings fixed in foundation should be adopted in near fault area.
(3) To solve the stability of series seismic isolation system connected with column and coupling beam, which concerned engineering field, the critical load governing equation based on transfer matrix method was established. First, field matrix of stability on single laminated rubber bearing and point matrix of stability on coupling beam were established; Secondly, characteristic matrix of the stability on series seismic isolation system and the stability governing equation based on the characteristic matrix were established , which avoided tedious mechanical derivation; Finally, calculated the stability of two kinds of series seismic isolation system using semi-analytic method, and investigated parameters variation influence on the stability of series seismic isolation system, some of the conclusions drawn useful for practical engineering applications.
(4) By using differential quadrature method, the post-buckling and large deformation of beam-column based on two different models, which one is considering trans-verse shear deformation and another without considering, is comparative analyzed. First, by accurately considering the axial extension and without considering trans-verse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equation for beam-column subjected to loads is formulated, by using differential quadrature method the post-buckling and large deformation of beam-column is analyzed. Then by accurately considering the axial extension and considering trans-verse shear deformation in the sense of theory of Timoshenko beam, geometrically nonlinear governing equation for f beam-column subjected to loads is formulated. Finally, by using differential quadrature method, the post-buckling and large deformation of beam-column is comparative analyzed.
(5) The post-buckling and large deformation of laminated rubber bearings and series seismic isolation system is investigated. Taking laminated rubber bearings as an equivalent homogeneous elastomer and accurately considering the axial extension and considering trans-verse shear deformation, geometrically nonlinear governing equation for bearings subjected to loads is formulated, by using differential quadrature method, the post-buckling and large deformation of laminated rubber bearings is analyzed. For series seismic isolation system, geometrically nonlinear governing equation accurately considering the axial extension and considering trans-verse shear deformation is formulated. Because series seismic isolation system in connection position material and geometrical discontinuous, differential quadrature method can not be used. So by using differential quadrature element method, the post-buckling and large deformation of series seismic isolation system is analyzed. Through analysis on comparing with the result of pseudo-static test, it is shown that the calculated and experimental results consistent with law.
引文
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