LRB基础隔震结构非线性动力响应的非迭代时程计算方法
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摘要
提出了一种求解使用铅芯橡胶支座(LRB)的基础隔震结构非线性动力响应的非迭代时程计算方法。该方法首先将层间剪力向量作为非线性二阶运动微分方程的参量,引入状态变量将非线性二阶运动微分方程降阶为一阶状态空间方程,通过使用描述非线性滞回模型的Masing准则确定隔震层剪力并给出了计算隔震层剪力的流程图,利用经典的Runge-Kutta方法进行求解。这样本文所提出的非迭代算法可以避免繁琐的迭代运算,方便编制程序。在数值试验中,利用本文提出的非迭代算法与传统的Newton-Raphson迭代算法进行了比较,结果表明:利用本文提出的非迭代算法得到的时程结果与使用Newton-Raphson迭代算法得到的时程结果十分接近并且峰值的相对误差比较小,能够满足工程计算的精度要求。
Non-iterative computational method for the nonlinear time-history response of base-isolated structures e- quipped with lead-rubber hearings (LRB) was presented.In the method proposed,the base-isolated structure was mod- eled as inter-story shear model with bilinear hysteresis at the isolation level,and the inter-story shear force vector was used as variable in the nonlinear second-order differential equation of motion.By introducing state variables,the equation was reduced to first-order state-space differential equation.The shear force at the isolation level was determined by use of Mas- ing criteria,which is suitable for the nonlinear hysteretic model.The flow chart to calculate the shear force at the isolation level was provided.Classical Runge-Kutta method was used to solve the first-order state-space differential equation.The non-iterative computational method proposed can avoid the iterative operation and make programming easier.In the nu- merical experiment,comparison between the method proposed and the conventional Newton-Raphson iterative method was carried out,which shows that time-history results obtained by both methods are very close to each other.The relative er- rors are small and accuracy demand of engineering computation can be satisfied.
Non-iterative computational method for the nonlinear time-history response of base-isolated structures e- quipped with lead-rubber hearings (LRB) was presented.In the method proposed,the base-isolated structure was mod- eled as inter-story shear model with bilinear hysteresis at the isolation level,and the inter-story shear force vector was used as variable in the nonlinear second-order differential equation of motion.By introducing state variables,the equation was reduced to first-order state-space differential equation.The shear force at the isolation level was determined by use of Mas- ing criteria,which is suitable for the nonlinear hysteretic model.The flow chart to calculate the shear force at the isolation level was provided.Classical Runge-Kutta method was used to solve the first-order state-space differential equation.The non-iterative computational method proposed can avoid the iterative operation and make programming easier.In the nu- merical experiment,comparison between the method proposed and the conventional Newton-Raphson iterative method was carried out,which shows that time-history results obtained by both methods are very close to each other.The relative er- rors are small and accuracy demand of engineering computation can be satisfied.
引文
[1]龙晓鸿，李黎．基于ANSYS的LRB性能模拟验证分析[J]．工程抗震与加固，2007．29(4)：53-56．
[2]王建平，邹银生．结构非线性恢复力分析中的恢复力拐点的非迭代处理方法[C]．全国第三届地震工程会议论文集(Ⅲ)．大连：中国地震学会地震工程专业委员会，1990：1072—1078．
[3]肖明葵，刘刚，白绍良．滞回恢复力模型中求折点的一种方法[J]．重庆大学学报(自然科学版)，2001，25(1)：13—16．
[4]黄海生，王柏生，基础隔震建筑非线性动力响应的时程计算方法[J]．振动与冲击，2005．24(3)：50-52．
[5]韩爱红，张新中，邓子辰，等．基础隔震结构地震响应时程分析新方法[J]．振动与冲击，2007．26(7)：145-148．
[6]Tan R Y,Huang M C.System identification of a bridge with lead-rubber bearings[J].Computers & Structures,2000,74 (3):267-280.
[7]Jangid R S,Optimum lead-rubber isolation bearings for near- fault motions[J].Engineering Structures,2007,29(10): 2503-2513.
[2]王建平，邹银生．结构非线性恢复力分析中的恢复力拐点的非迭代处理方法[C]．全国第三届地震工程会议论文集(Ⅲ)．大连：中国地震学会地震工程专业委员会，1990：1072—1078．
[3]肖明葵，刘刚，白绍良．滞回恢复力模型中求折点的一种方法[J]．重庆大学学报(自然科学版)，2001，25(1)：13—16．
[4]黄海生，王柏生，基础隔震建筑非线性动力响应的时程计算方法[J]．振动与冲击，2005．24(3)：50-52．
[5]韩爱红，张新中，邓子辰，等．基础隔震结构地震响应时程分析新方法[J]．振动与冲击，2007．26(7)：145-148．
[6]Tan R Y,Huang M C.System identification of a bridge with lead-rubber bearings[J].Computers & Structures,2000,74 (3):267-280.
[7]Jangid R S,Optimum lead-rubber isolation bearings for near- fault motions[J].Engineering Structures,2007,29(10): 2503-2513.
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