天然橡胶支座大变形压剪性能的双非线性超弹性理论和实验研究  

DOUBLE NONLINEAR HYPERELASTIC THEORY AND EXPERIMENTAL RESEARCH ON THE LARGE DEFORMATION OF NATURAL RUBBER BEARING IN COMPRESSION AND SHEAR

作　　者：杨静[1,2] 潘文 苏何先[1,2] 何颖成 管庆松[3] 张岩岩 YANG Jing;PAN Wen;SU He-xian;HE Ying-cheng;GUAN Qing-song;ZHANG Yan-yan(School of Civil Engineering,Kunming University of Science and Technology,Kunming,Yunnan 650500,China;Earthquake Engineering Researching Center of Yunnan,Kunming,Yunnan 650500,China;Zhenan Technology Co.,Ltd.,Kunming,Yunnan 650000,China;The Fifth Architectural Design Co.,Ltd.of Yunnan Design Institute,Kunming,Yunnan 650500,China)

机构地区：[1]昆明理工大学建筑工程学院,云南昆明650500 [2]云南省抗震工程技术研究中心,云南昆明650500 [3]震安科技股份有限公司,云南昆明650000 [4]云南省设计院第五建筑设计有限公司,云南昆明650000

出　　处：《工程力学》2022年第8期200-209,222,共11页Engineering Mechanics

摘　　要：基于非线性固体力学已经形成与材料微观结构紧密结合的发展局面,该文从微观上橡胶的超弹性本构方程出发,推导出单层橡胶内任一点的竖向应力满足调和函数,进一步对竖向应力积分得到单层橡胶的单轴等效弹性模量E_(c)与纯弯等效弯曲刚度E_(c)I_(s)。将隔震橡胶支座等效为符合E_(c)与E_(c)I_(s)的均质体,建立橡胶支座在两种外部荷载同时作用下,能宏观反映剪切变形与弯曲程度的偏微分平衡方程,并得到通用解答,解决了橡胶支座竖向与水平两种荷载耦合作用时大剪切变形的几何非线性问题。在此基础上,开展了足尺隔震橡胶支座压剪实验,依据实验剪切模量G和水平剪应变γ曲线,得到的支座水平推力F_(H)和γ的实验曲线与理论曲线几乎完全重叠,即通过将材料非线性引入以上微分平衡方程,实现了超弹性橡胶支座大剪切变形的双非线性问题。通过以上解答,得到了隔震橡胶支座内力分布规律,对判断支座薄弱部位有明确的指导意义。随后,对隔震橡胶支座比较重要的两个特性(剪应变相关性,轴压力相关性)进行了对比分析,结果表明:随着轴力增大,橡胶支座的P-Δ效应并不明显,而橡胶内应力的变化不可忽视,同时,剪应变越大,压力相关性越强。可以采用该文的理论方法,通过传感器监测到支座内部应力反演支座水平推力与位移,从而实现地震作用时隔震建筑的健康监测。Based on the fact that the development of nonlinear solid mechanics has been closely integrated with the material microstructure,it derived the vertical stress satisfying the harmonic function at any point from the super-elastic constitutive equation of the rubber;further,the uniaxial equivalent elastic modulus E_(c)and the pure bending equivalent bending stiffness E_(c)I_(s)of the single-layer rubber were obtained from the vertical stress integration.The seismic isolation rubber bearing was equivalent to a homogeneous body conforming to E_(c)and E_(c)I_(s),and the partial differential equilibrium equation macroscopically reflecting the degree of shear and bending deformation of the rubber bearing was established in the simultaneous action of two external load,and its general solution was obtained.The difficulties of the geometrical non-uniformity of large shear deformation of rubber support were solved in the vertical and horizontal loads.On this basis,a full-scale seismic isolation test of rubber bearing for compression and shear experiment was carried out.According to the experimental shear modulus and horizontal shear strainγcurves,the experimental curves of the horizontal thrust F_(H)andγof the bearing were obtained.It was almost completely overlapped with the theoretical curve.Therefore by introducing the material nonlinearity into the above differential equilibrium equation,the double nonlinear problem of large shear deformation of the superelastic rubber bearing was solved.Through the above answers,the internal force distribution law of the rubber bearing was obtained,which has a clear guiding significance for judging the weak part of the bearing.Subsequently,the comparative analysis of two more important characteristics(shear strain correlation and axial pressure correlation)of the rubber bearing was carried out,the results showed that as the axial force increased,the P-Δeffect of the rubber bearing was not obvious,but the change of internal stress in the rubber couldn’t be ignored,Concurrently,the

关 键 词：非线性连续介质力学 几何非线性 偏微分方程 材料非线性 超弹性本构方程 拉普拉斯算子 

分 类 号：TU352.1[建筑科学—结构工程]