直接求解法在结构多点输入地震响应计算中的应用与改进.pdf

第28 卷第1 期 Vol.28 No.1 工 程 力 学 2011 年 1 月 Jan. 2011 ENGINEERING MECHANICS 75 文章编号：1000-4750(2011)01-0075-07 直接求解法在结构多点输入地震响应计算中的 应用与改进 *石永久，江 洋，王元清 (土木工程安全与耐久教育部重点实验室，清华大学土木工程系，北京 100084) 摘 要：将以绝对位移形式求解动力方程的直接求解法引入结构多点输入地震响应计算。与常用的将位移分解为 拟静力绝对位移和相对动力位移的分解法相比，直接法的概念更为简洁，计算量小，且更适用于非线性计算。对 于采用振型叠加法的直接法，仅使用少量低阶振型可能导致较大误差。引入静力修正方法，提出了高效的改进直 接法。算例结果表明，修正直接法只需少量低阶振型即可获得足够的精度，精度与分解法相当。 关键词：多点输入；地震响应；直接求解法；静力修正方法；虚拟激励法 中图分类号：TU311.3 文献标识码：A APPLICATION AND IMPROVEMENT OF DIRECT SOLVING METHOD IN SEISMIC RESPONSE ANALYSIS OF STRUCTURES UNDER MULTI-SUPPORT EXCITATIONS * SHI Yong-jiu , JIANG Yang , WANG Yuan-qing (Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Department of Civil Engineering, Tsinghua University, Beijing 100084, China) Abstract: The direct solving method, in which absolute displacement is utilized to solve dynamic equations, is proposed to analyze the seismic response of structures under multi-support excitations. Compared with the commonly used decomposition method, which decomposes the displacement into absolute pseudo-static displacement and relative dynamic displacement, the direct solving method is of a more concise concept as well as lower calculation complexity. And it is more suitable for nonlinear problems. As for the direct solving method combined with mode superposition method, calculation with only low order modes may cause large error. Thus static correction method is adopted to improve the precision of direct solving method. Results of numerica