连续介质分析动力学及其应用

梁立孚; 郭庆勇; 宋海燕

doi:10.6052/1000-0992-17-019

连续介质分析动力学及其应用

doi: 10.6052/1000-0992-17-019

哈尔滨工程大学航天与建筑工程学院, 哈尔滨 150001

基金项目: 国家自然科学基金项目资助课题 (一般力学的广义变分原理研究10272034);黑龙江省自然科学基金项目资助课题(电磁热弹性体耦合理论模型和计算方法研究A2015013).

详细信息

作者简介:
null

作者简介：梁立孚, 1939年生, 哈尔滨工程大学教授, 博士生导师.主要研究方向:变分原理及其应用、连续介质分析动力学和耦合分析动力学.通过长期的研究, 提出变分的逆运算------变积的概念, 建立了变积方法,使得微积分学中的积分、微分和导数在变分学中都有了对应的概念------变积、变分和变导,从而初步地将变分学扩充为变积分学.变积的建立解决了建立变分原理(含广义变分原理)难的问题; 变导的应用,结合Lagrange-Hamilton体系,解决了将Lagrange方程应用于连续介质力学和其他学科的问题.研究耦合分析动力学(或者称为分析耦合动力学);解决了将Hamilton型变分原理和Lagrange方程应用于刚--弹、刚--液、刚--弹--液等耦合系统的问题;在航空、航天、航海等领域获得重要应用.应用可变函数选值域的理论和可变函数曲线接近度的理论研究非完整系统分析动力学,较好地解释了非完整力学中的一些长期存在的但难以说明的问题,进而研究了非完整系统分析动力学的理论框架.

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出版历程
- 收稿日期: 2017-09-27
- 刊出日期: 2019-02-08

Analytical dynamics of continuous medium and its application

College of Aerospace and Civil Engineering, Harbin Engineering University,Harbin 150001, China

摘要

摘要: 综述了国内和国外学者研究连续介质分析动力学问题的进展,阐明了本文主要论述将Lagrange方程应用于连续介质动力学的问题.论文采用Lagrange-Hamilton体系,分别论述了非保守非线性弹性动力学、不可压缩黏性流体动力学、黏弹性动力学、热弹性动力学、刚--弹耦合动力学和刚--液耦合动力学的Lagrange方程及其应用.论述了应用Lagrange方程建立有限元计算模型的问题. 最后,展望了将Lagrange方程应用于连续介质动力学问题的研究前景.
- 连续介质分析动力学 /
- Lagrange方程 /
- Hamilton原理 /
- Lagrange- Hamilton体系
Abstract: First, the studying progress of domestic and foreign scholars on analytical dynamics of continuum is reviewed. This paper mainly studies the problem of applying the Lagrange equation to the continuum dynamics. By using Lagrange-Hamilton system, Lagrange equations and their applications are investigated for non-conservative nonlinear elastic dynamics, incompressible viscous fluid dynamics, viscoelastic dynamics, thermal elastic dynamics, rigid-elastic coupling dynamics and rigid-liquid coupling dynamics. The establishment of finite element calculation model by using Lagrange equation was analyzed. Finally, the prospects of applying the Lagrange equation to problems of the continuum dynamics are discussed.
- continuum analytical dynamics /
- Lagrange equation /
- Hamilton principle /
- Lagrange-Hamilton system

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