自适应步长时程分析的新进展:从凝聚单元到降阶单元  

NEW PROGRESS IN ADAPTIVE TIME-STEPPING FOR TIME INTEGRATION ANALYSIS:FROM CONDENSED ELEMENT TO REDUCED ELEMENT

作　　者：袁驷[1] 袁全 YUAN Si;YUAN Quan(Department of Civil Engineering,Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Tsinghua University,Beijing 100084,China)

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：《工程力学》2023年第1期32-39,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51878383,51378293)。

摘　　要：研究发现,按最大模度量的自适应步长时程单元的成功求解,需要有限元解的结点精度与单元精度之比,以不低于2为佳;亦即■次单元的单元精度为■,则其结点精度宜达至■。作者提出的凝聚单元,符合此精度比条件,自适应求解表现出色。该文研究发现,■次常规单元的解答,包含了■次凝聚单元的解,进而提出了无须凝聚、无须超收敛计算、无须结点修正的简便高效的单元算法——降阶单元。该文对这一研究进展做一简介,并给出初步算例验证了该法的可行性和有效性。It has been found in research that the successful implementation of adaptive time-stepping,measured by maximum norm,for time integration analysis by the finite element method requires the accuracy ratio between the nodal solution and element solution to be no less than 2.In other words,if the element accuracy is■with■degreed element,the nodal accuracy should be best up to■.The condensed element proposed by the authors meets this requirement and has great performance in time-stepping adaptivity.Further,it has been found that the solution of the conventional element of degree■contains the complete solution of the condensed element of degree■.Thus,a simple and efficient element algorithm,called the reduced element,is proposed in this paper,which needs neither additional condensing procedure and nodal accuracy improvement,nor super-convergence calculation needed in other element models.The paper gives a brief description of the new progress in this related study with some preliminary numerical examples given to show the feasibility and effectiveness of the proposed approach.

关 键 词：GALERKIN有限元法 运动方程 降阶单元 自适应步长 最大模 

分 类 号：TB115[理学—数学]