| 论弹性力学变分原理各类条件的完备性 |
| |
| 引用本文： | 梁立孚,冯晓九,宋海燕.论弹性力学变分原理各类条件的完备性[J].哈尔滨工程大学学报,2004,25(2):153-156. |
| |
| 作者姓名： | 梁立孚 冯晓九 宋海燕 |
| |
| 作者单位： | 哈尔滨工程大学,建筑工程学院,黑龙江,哈尔滨,150001;哈尔滨工程大学,建筑工程学院,黑龙江,哈尔滨,150001;哈尔滨工程大学,建筑工程学院,黑龙江,哈尔滨,150001 |
| |
| 基金项目： | 国家自然科学基金资助项目(1272034)，博士学科点专项科研基金资助项目(20010217003)，黑龙江省自然科学基金资助项目(A01-06). |
| |
| 摘 要： | 研究了弹性力学变分原理各类条件完备性.经过深入分析,并应用对合变换,表明弹性力学变分原理各类条件完备性具有2种含义:1)弹性力学变分原理的先决条件和驻值条件一起构成适定的微分方程组;2)弹性力学变分原理的先决条件、补充条件和反映的规律一起正是弹性力学全部基本方程.应用弹性力学变分原理各类条件完备性研究了最小余能原理、广义变分原理和组合变分原理中的有关问题.应用变分原理各类条件的完备性理论,可以检验变分原理的正确性、判定变分原理的种类,对建立新型变分原理具有指导意义.
|
| 关 键 词： | 变分原理 完备性 弹性力学 |
| 文章编号： | 1006-7043(2004)02-0153-04 |
| 修稿时间： | 2003年4月18日 |
Completeness of various conditions of variational principles |
| |
| LIANG Li-fu,FENG Xiao-jiu,SONG Hai-yan.Completeness of various conditions of variational principles[J].Journal of Harbin Engineering University,2004,25(2):153-156. |
| |
| Authors: | LIANG Li-fu FENG Xiao-jiu SONG Hai-yan |
| |
| Abstract: | The completeness of various conditions of variational principles is studied in this paper. By using analytical method and involutory transformations, it is discovered that the completeness of various conditions of variational principles has two meanings: 1) Preconditions and stationary conditions of variational principle constitute a closed differential equation group;2)The preconditions, additional conditions and reflection laws of variational principle are the complete elementary equations in elasticity. The completeness of various conditions of variational principles is applied to the research on the principle of complementary energy, generalized variational principles and combined variational principle. By means of the theory of the completeness of various conditions of variational principles, one can judge variational principles between right and wrong and can correctly establish new variational principles. |
| |
| Keywords: | variational principle completeness elasticity |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
|
