基于Bathe隐式算法的结构动力学显式算法  

Explicit algorithm for structural dynamics based on the Bathe implicit algorithm

作　　者：孟凡涛[1,2] 赵建锋 MENG Fantao;ZHAO Jianfeng(School of Civil Engineering,Qingdao University of Technology,Qingdao 266033,China;Shandong Huake Planning Architectural Design Co.,Ltd.,Liaocheng 252000,China)

机构地区：[1]青岛理工大学土木工程学院,山东青岛266033 [2]山东华科规划建筑设计有限公司,山东聊城252000

出　　处：《振动与冲击》2019年第6期226-232,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(51778314)

摘　　要：提出了一种新的计算时具有结构动力特性相关性的无条件稳定的结构动力学时间积分算法。该算法不仅位移与速度均具有显式表达的特点,而且具有了Bathe复合时间积分方案的优点。该新算法的数值特征与Bathe隐式复合积分算法的数值特性相同,但新算法不需要任何时间步长内的子步细分,相对于新提出的算法而言,时间步长内的子步细分成了Bathe隐式复合积分算法的缺点。为了进一步了解所提出的新方法的谱特性,对新算法的稳定性和精度进行了全面的分析,包括数值耗散和色散。此外,当采用提出的算法计算多自由度系统时,给出了两个积分参数的推导过程和表达式。通过计算线性和非线性问题并与采用现有算法的结果比较,验证了新算法的正确性和有效性。A new structure-dependent unconditionally stable time-integration method was presented for structural dynamic analysis. The proposed method not only benefits from an explicit formulation,but also inherits the advantage of the Bathe composite scheme. The numerical characteristics of the proposed algorithm are the same as those in the Bathe composite scheme,except that the suggested method does not require any time-subdividing,which is one of the drawbacks of the composite scheme. A comprehensive stability and accuracy analysis,including dissipation and dispersion,was carried out in order to gain an insight into the spectral properties of the proposed method. Also,when the proposed algorithm was used to analyse the multi degrees of freedom system,the derivation and expression of the two integral parameters were given. Finally,the correctness and effectiveness of the proposed algorithm was verified by comparing the results of linear and nonlinear problems calculated by the suggested method with those calculated by other existing algorithms.

关 键 词：显式算法 离散控制理论 复合积分方案 无条件稳定 结构动力学 

分 类 号：TU311.4[建筑科学—结构工程]