精细积分法应用于地震碰撞力反应谱计算研究

相邻结构的碰撞时程分析是计算地震碰撞力反应谱的基础。结构碰撞时程分析要求采用稳定性好、精度高及计算效率高的数值分析方法。精细积分法将二阶动力微分方程通过增元降阶的方式转换成Hamilton对偶变量体系,得到了动力微分方程的精确解。基于此,本文将精细积分法引入结构碰撞时程分析及地震碰撞力反应谱计算中。在推导精细积分法公式的基础上,在MATLAB环境下编制了结构碰撞时程分析程序和碰撞力反应谱计算程序,并实现了碰撞力反应谱程序的并行化。经算例验证,精细积分法应用于结构碰撞时程分析及地震碰撞力反应谱计算是可行的,程序计算结果准确。

Study of earthquake pounding force response spectrum computing using precise integration method

The computation of earthquake pounding force response spectrum is base on the pounding time history analysis of two adjacent structures.The analysis requires an application of numerical analysis with good stability,high precision and efficiency.The precise integration method,which is a method to convert the two order dynamic equation into Hamiltonian dual variables system by means of element addition and order reduction,provides an accurate solution for the time history problem.Based on this point,the paper introduced the precise integration method to simulate the pounding process of adjacent structures and compute the earthquake pounding force response spectrum.The PIM formulas correspond to structure pounding problems were derived,the structure pounding analysis program and earthquake pounding force response spectra program were coded in environment of Matlab.And furthermore,the parallelization of the pounding force response spectra program was implemented.An example was applied to verify the program.The results indicate that the method adopted by this paper can be effectively applied to simulate structure pounding process as well as compute the earthquake pounding force response spectrum with a high accuracy solution.