离散系统运动方程的Galerkin有限元EEP法自适应求解  

An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems

作　　者：邢沁妍[1] 杨杏[1] 袁驷[1] 

机构地区：[1]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：《应用数学和力学》2017年第2期133-143,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(51508305;51378293;51078199)~~

摘　　要：对于结构动力分析中的离散系统运动方程,现有算法的计算精度和效率均依赖于时间步长的选取,这是时间域问题求解的难点.基于EEP(element energy projection)超收敛计算的自适应有限元法,以EEP超收敛解代替未知真解,估计常规有限元解的误差,并自动细分网格,目前已对诸类以空间坐标为自变量的边值问题取得成功.对离散系统运动方程建立弱型Galerkin有限元解,引入基于EEP法的自适应求解策略,在时间域上自动划分网格,最终得到所求时域内任一时刻均满足给定误差限的动位移解,进而建立了一种时间域上的新型自适应求解算法.For the solution of structural dynamic equations-generally the accuracy of results and the efficiency of computation both depend on the selection of the time step lengths-which makes the key difficulty for efficient solution of time-dependent problems.With the element energy projection （EEP） super-convergent solution computed at the post-processing stage of the finite element method （FEM） to replace the unknown true solution and then to estimate the error of the conventional FEM solutionthe so-called EEP adaptive method can automatically refine the solution mesh and has achieved success in various boundary-value problems with spatial coordinates as the arguments.Based on the Galerkin FEM solution of the weak form-the EEP self-adaptive strategy was introduced and applied to the dynamic equations of discrete systems.As a result-an adaptive mesh was automatically produced in the time domain-and a dynamic displacement solution satisfying the pre-specified error tolerance at any moment was obtained-which leads to a new adaptive computation approach for time-dependent problems.

关 键 词：离散系统 运动方程 GALERKIN有限元 自适应求解 EEP法 

分 类 号：O242.21[理学—计算数学]