时空降阶单元及其自适应分析初探  

INITIAL STUDY ON SPACE-TIME REDUCED ELEMENT AND ITS ADAPTIVE ANALYSIS

作　　者：袁驷[1] 袁全 YUAN Si;YUAN Quan(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]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》2025年第1期10-19,共10页Engineering Mechanics

基　　金：国家自然科学基金项目(51878383,51378293)。

摘　　要：基于初值问题和边值问题中降阶单元的成功实现,进一步提出时空降阶单元,以弹性弦振动方程(波动方程)为例,构造了自适应有限元分析算法。时空降阶单元继承了初值和边值问题中降阶单元的所有优点,可以给出按最大模度量满足误差限的降阶单元的解答。该文对这一研究进展做一简要介绍,并给出包括若干强迫振动以及移动荷载反应的典型算例以展示本法的可行性、有效性和可靠性。Based on the successful developments of reduced element for initial value problems(IVPs)and boundary value problems(BVPs),a space-time reduced element is further proposed by taking the elastic string vibration problem(wave equation)as a model problem,and subsequently constructs the corresponding adaptive analysis algorithm.The space-time reduced element inherits all advantages of the reduced elements in IVPs and BVPs and can provide solutions from the reduced element that satisfy the error tolerances in the maximum norm.This paper gives a brief and general introduction to the research progress and presents several typical examples,including forced vibrations and moving load problems,to demonstrate the feasibility,effectiveness and reliability of this method.

关 键 词：时空有限元 弦振动方程 降阶单元 最大模 自适应有限元法 

分 类 号：TB53[理学—物理]