实时子结构试验中显式算法对比分析  

COMPARISONS OF MODEL-BASED EXPLICIT INTEGRATION ALGORITHMS IN REAL-TIME SUBSTRUCTURE TESTING

作　　者：唐玉 覃晖 TANG Yu;QIN Hui(School of Hydraulic Engineering,Dalian University of Technology,Dalian,Liaoning 116024,China;School of Civil Engineering,Dalian University of Technology,Dalian,Liaoning 116024,China)

机构地区：[1]大连理工大学水利工程学院,辽宁大连116024 [2]大连理工大学土木工程学院,辽宁大连116024

出　　处：《工程力学》2020年第S01期1-5,12,共6页Engineering Mechanics

基　　金：国家自然科学基金项目(41904095,51979027);中央高校基本科研业务费项目(DUT19JC23,DUT19RC(4)024)。

摘　　要：实时子结构试验技术中的一个关键问题是求解数值子结构的动力响应,而这一过程可选取合适的数值积分算法来实现。针对目前已建立的三种基于模型的显式积分算法(Chang法、CR法和实时子结构RST法),对比分析了各算法在线性系统和非线性系统中的数值特性。结果表明:三种算法在线性系统和具有刚度软化特性的非线性系统中均是无条件稳定的,在具有刚度硬化特性的非线性系统中变为有条件稳定。当结构阻尼比为零时,三种算法均无数值阻尼,且周期延长率结果完全一致,并随Ω的增加而增大;当结构阻尼比不为零时,三种算法均存在数值阻尼,且CR法的数值阻尼绝对值最小,而RST法的周期延长率最小。两个算例表明,RST法和Chang法的精度要优于CR法,但因Chang法是半显式的,因此RST法更适于实时子结构试验中数值子结构的仿真计算。In real-time substructure testing,a key issue is the numerical simulation of the numerical substructure,which can be done by applying appropriate integration algorithms to solve the step-by-step structural equations of motion.Three well-developed model-based explicit integration algorithms,that is,Chang,CR and RST methods,are discussed and compared in terms of the numerical properties in linear and non-linear systems.Stability analysis indicates that the three methods are unconditionally stable for linear and instantaneous stiffness softening systems while they are only conditionally stable for instantaneous stiffness hardening systems.The three methods show exactly the same characteristics for zero-damping systems as no numerical damping is produced and the period error(PE)increases with the increase ofΩ.However,the three methods introduce numerical damping into the simulation for damped systems,and the numerical damping caused by the CR method is the smallest at a certain value ofΩ.Meanwhile,the RST method has a smaller PE than the other two methods for damped systems.Two examples indicate that the RST method and Chang method have a better accuracy than the CR method in solving dynamic problems of both linear and non-liner systems.Since the velocity of the Chang method is in an implicit form,the RST is more advantageous in real-time substructure testing.

关 键 词：实时子结构试验 显式积分算法 基于模型 稳定性分析 数值损耗 瞬时非线性度 

分 类 号：TU317[建筑科学—结构工程]