线性元时程积分按最大模自适应步长公式的证明  

PROOF OF ADAPTIVE TIME-STEP SIZE FORMULA BASED ON MAXIMUM NORM IN TIME INTEGRATION OF LINEAR ELEMENTS

作　　者：袁全 袁驷[2] 李易[1] 闫维明[1] 邢沁妍[2] YUAN Quan;YUAN Si;LI Yi;YAN Wei-ming;XING Qin-yan(Beijing Key Laboratory of Earthquake Engineering and Structural Retrofit,Beijing University of Technology,Beijing 100124,China;Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Department of Civil Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]北京工业大学建筑工程学院,工程抗震与结构诊治北京市重点实验室,北京100124 [2]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2018年第8期9-13,共5页Engineering Mechanics

基　　金：国家自然科学基金项目(51378293,51078199,51508305)。

摘　　要：该文对运动方程时程积分解法曾提出一种线性有限元自适应步长求解的算法,给出了按最大模自适应步长的计算公式,其中含有步长h的5/2阶的分数阶次。该文对该公式给出数学证明,并通过单自由度和多自由度的数值算例验证了其5/2分数阶次是最优的。An algorithm for time integration of motion equations using linear finite elements with adaptive time-step size had been proposed by the authors,in which a formula for the calculation of adaptive time-step size h based on maximum norm,characterized by containing a term of 5/2 order of h,was also presented.This paper gives a mathematical proof for the proposed formula.In addition,the numerical examples of both single and multiple degreed systems are obtained to verify that 5/2 order is optimal.

关 键 词：有限元法 时程积分 线性单元 自适应步长 最大模 

分 类 号：TU311[建筑科学—结构工程] O241.81[理学—计算数学]