强震作用下单层网壳结构动力破坏机理
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摘要
单层网壳结构兼具杆系结构与薄壳结构的优点和特性,在我国得到了较为广泛的应用。我国是地震多发国,许多新建和在建的地标性单层网壳建筑建设在强震区。目前对单层网壳结构进行抗震分析时,通常以有限元软件通用梁单元模拟杆件,以刚性连接模拟节点,将高估结构抗震承载力。为此,须建立准确反映单层网壳结构受力特性的结构计算模型,深入研究单层网壳结构在强震作用下的动力破坏机理。本文采取理论分析与数值模拟相结合的方法进行了以下四方面的研究工作。
(1)以杆件变形后的几何构型为基础建立平衡微分方程,推导了考虑二阶效应的空间梁单元位移插值函数,模拟结构中无轴力杆件;利用Maclaurin级数展开推导了考虑二阶效应、同时适用于受拉受压梁柱单元的统一位移插值函数,模拟结构中有轴力杆件;推导了考虑轴向变形、剪切变形、双向弯曲、扭转及其耦合效应影响的单元切线刚度矩阵,建立了单层网壳结构二阶弹性计算分析方法。
(2)提出了单层网壳结构杆件的两种失稳类型;引入国际标准化组织推荐的空间受力圆钢管失稳判定准则,采用考虑二阶效应的塑性铰模型模拟失稳前杆件,采用Marshall模型模拟失稳后杆件,建立了考虑失稳效应的杆件弹塑性计算模型,可模拟强震作用下单层网壳结构杆件可能反复经历的失稳—拉直过程与塑性铰形成—消失过程。
(3)研究了焊接空心球节点在循环荷载作用下荷载—位移曲线的变化规律与塑性变形发展过程,利用回归统计方法,建立了焊接空心球节点力学计算模型,可模拟强震作用下单层网壳结构焊接空心球节点反复经历的加载—卸载过程与破坏过程。
(4)基于本文提出的杆件弹塑性计算模型与焊接空心球节点力学计算模型建立不同形式单层网壳结构的数值计算模型;以结构承载力与地震作用不再平衡作为结构动态破坏的判定准则,以结构非线性动力平衡方程组不收敛的时刻作为结构破坏时刻,分析了不同形式单层网壳结构破坏时失稳杆件的数量与分布情况、塑性铰的数量与位置、节点的破坏形式,总结了不同形式单层网壳结构在强震作用下的动力破坏机理。
Single layer latticed shell, which has the characteristics and excellences of both member structure and shell structure, is widely used in our country. Our country has a high incidence of earthquake, and a great number of landmark constructions with the structural type of single layer latticed shell locate on the strong earthquake areas. Currently general beam element of finite element analysis program is used to simulate the structural member and rigid connection model is used to simulate the structural joint when study the anti earthquake behaviors of single layer latticed shells. By this method the bearing capacity of the structure is overestimated. Therefore, structural calculation model which can accurately simulate the mechanical hehaviors of single layer latticed shells should be established, and the dynamic damage mechanisms of single layer latticed shells under strong earthquakes should be deep investigated. In this paper some studies are carried out with theoretical analysis and numerical simulation.
(1) Differential equation is created based on the deformed figuration of the structural member, and displacement interpolation equations of spatial beam element are deduced to model the structural member without axial force. By Maclaurin series expansion, the uniform displacement interpolation equations considering the second order effect for both tension and compression beam-column element are deduced to model the structural member with axial force. The element tangent stiffness matrixes considering axial deformation, shear deformation, two-direction bending, torsional deformation and coupling effects of all the deformations metioned above are deduced and the second order elastic calculation method for single layer latticed shells are established.
(2) Two buckling types of the member of single layer latticed shells are presented. The plastic hinge member model considering the second order effect are used to simulate the pre-buckling member, and the Marshall model is used to simulate the post-buckling member. The ISO buckling criterion for spatial circular tube is introduced, and the elastic-plastic member model considering the buckling effect is established. By this model, the repeated buckling-straightening processes of the member of single layer latticed shells under strong earthquake and the forming-disappearing processes of plastic hinges can be simulated.
(3) The characteristics of the load-displacement curve and plastic deformation develop process of welded hollow spherical joint under loop loading are studied. Based on the regression statistic method, the mechanical calculation model for welded hollow spherical joint are established by which the repeated loading-unloading processes and the damage processes of the joint under strong earthquakes can be simulated.
(4) Numerical calculation model of single layer latticed shells based on the elastic-plastic member model and mechanical welded hollow spherical joint model are established. Whether the structural bearing capacity can keep balance with the seismic action is defined to be the dynamic damage criterion of single layer latticed shells, and the time that the structural nonlinear dynamic equilibrium equations do not converge is defined to be the structural damage time. The number and distribution of buckling members, the number and the position of plastic hinges and the damaged joints when the structures damage are studied, and the dynamic damage mechanisms of single layer latticed shells of different types under earthquake are summarized consequently.
(1)以杆件变形后的几何构型为基础建立平衡微分方程,推导了考虑二阶效应的空间梁单元位移插值函数,模拟结构中无轴力杆件;利用Maclaurin级数展开推导了考虑二阶效应、同时适用于受拉受压梁柱单元的统一位移插值函数,模拟结构中有轴力杆件;推导了考虑轴向变形、剪切变形、双向弯曲、扭转及其耦合效应影响的单元切线刚度矩阵,建立了单层网壳结构二阶弹性计算分析方法。
(2)提出了单层网壳结构杆件的两种失稳类型;引入国际标准化组织推荐的空间受力圆钢管失稳判定准则,采用考虑二阶效应的塑性铰模型模拟失稳前杆件,采用Marshall模型模拟失稳后杆件,建立了考虑失稳效应的杆件弹塑性计算模型,可模拟强震作用下单层网壳结构杆件可能反复经历的失稳—拉直过程与塑性铰形成—消失过程。
(3)研究了焊接空心球节点在循环荷载作用下荷载—位移曲线的变化规律与塑性变形发展过程,利用回归统计方法,建立了焊接空心球节点力学计算模型,可模拟强震作用下单层网壳结构焊接空心球节点反复经历的加载—卸载过程与破坏过程。
(4)基于本文提出的杆件弹塑性计算模型与焊接空心球节点力学计算模型建立不同形式单层网壳结构的数值计算模型;以结构承载力与地震作用不再平衡作为结构动态破坏的判定准则,以结构非线性动力平衡方程组不收敛的时刻作为结构破坏时刻,分析了不同形式单层网壳结构破坏时失稳杆件的数量与分布情况、塑性铰的数量与位置、节点的破坏形式,总结了不同形式单层网壳结构在强震作用下的动力破坏机理。
Single layer latticed shell, which has the characteristics and excellences of both member structure and shell structure, is widely used in our country. Our country has a high incidence of earthquake, and a great number of landmark constructions with the structural type of single layer latticed shell locate on the strong earthquake areas. Currently general beam element of finite element analysis program is used to simulate the structural member and rigid connection model is used to simulate the structural joint when study the anti earthquake behaviors of single layer latticed shells. By this method the bearing capacity of the structure is overestimated. Therefore, structural calculation model which can accurately simulate the mechanical hehaviors of single layer latticed shells should be established, and the dynamic damage mechanisms of single layer latticed shells under strong earthquakes should be deep investigated. In this paper some studies are carried out with theoretical analysis and numerical simulation.
(1) Differential equation is created based on the deformed figuration of the structural member, and displacement interpolation equations of spatial beam element are deduced to model the structural member without axial force. By Maclaurin series expansion, the uniform displacement interpolation equations considering the second order effect for both tension and compression beam-column element are deduced to model the structural member with axial force. The element tangent stiffness matrixes considering axial deformation, shear deformation, two-direction bending, torsional deformation and coupling effects of all the deformations metioned above are deduced and the second order elastic calculation method for single layer latticed shells are established.
(2) Two buckling types of the member of single layer latticed shells are presented. The plastic hinge member model considering the second order effect are used to simulate the pre-buckling member, and the Marshall model is used to simulate the post-buckling member. The ISO buckling criterion for spatial circular tube is introduced, and the elastic-plastic member model considering the buckling effect is established. By this model, the repeated buckling-straightening processes of the member of single layer latticed shells under strong earthquake and the forming-disappearing processes of plastic hinges can be simulated.
(3) The characteristics of the load-displacement curve and plastic deformation develop process of welded hollow spherical joint under loop loading are studied. Based on the regression statistic method, the mechanical calculation model for welded hollow spherical joint are established by which the repeated loading-unloading processes and the damage processes of the joint under strong earthquakes can be simulated.
(4) Numerical calculation model of single layer latticed shells based on the elastic-plastic member model and mechanical welded hollow spherical joint model are established. Whether the structural bearing capacity can keep balance with the seismic action is defined to be the dynamic damage criterion of single layer latticed shells, and the time that the structural nonlinear dynamic equilibrium equations do not converge is defined to be the structural damage time. The number and distribution of buckling members, the number and the position of plastic hinges and the damaged joints when the structures damage are studied, and the dynamic damage mechanisms of single layer latticed shells of different types under earthquake are summarized consequently.
引文
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