一种新型高精度半显式基于模型的积分算法  

A New Semi-explicit Model-based Integration Algorithm with High Accuracy

作　　者：傅博 张付泰 陈瑾 FU Bo;ZHANG Futai;CHEN Jin(School of Civil Engineering,Chang’an University,Xi’an 710061,China)

机构地区：[1]长安大学建筑工程学院,陕西西安710061

出　　处：《同济大学学报（自然科学版）》2023年第5期738-746,共9页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金(51908048,52108432);陕西省高校科协青年人才托举计划(20200412);长安大学中央高校基本科研业务费专项资金(300102283201)。

摘　　要：提出了一种新型高精度基于模型的积分算法,该算法采用了半显式Chang算法的速度、位移表达式,但是具有不同的积分参数。采用离散控制理论中“零极点匹配”和二阶Pade近似推导出新算法的积分参数。对算法的精度、稳定性、周期延长和振幅衰减等数值特性进行分析。与Newmark族积分算法和两种典型的基于模型的积分算法相比,新算法具备四阶精度,并且有非常小的周期误差。最后,通过三个数值算例验证了新算法的高精度特性。A new model-based integration algorithm with high accuracy is proposed.The proposed algorithm adopts the formulations of velocity and displacement of the semiexplicit Chang algorithm but uses different integration parameters.The integration parameters of the new algorithm are derived by using the zero-pole matching in discrete control theory and second-order Pade approximation.The numerical properties including accuracy,stability,period elongation and amplitude decay are analyzed.Compared with the Newmark family algorithms and two typical model-based integration algorithms,the proposed algorithm is fourth-order accurate and possess extremely small period error.Finally,the high accuracy of the algorithm is demonstrated by three numerical examples.

关 键 词：积分算法 显式 基于模型 精度 周期延长 

分 类 号：TU311.3[建筑科学—结构工程]