加速度极小原理及其应用  

Acceleration Minimum Principle and Its Application

作　　者：郑巍[1] 高卫民[1] 洪善桃[1] 

机构地区：[1]同济大学汽车学院,上海200092

出　　处：《力学季刊》2003年第4期445-453,共9页Chinese Quarterly of Mechanics

摘　　要：本文首先简要介绍了经典力学中的吉布斯-阿沛耳方程以及加速度极小原理。接着使用加速度极小原理推演了平面柔性多体系统的运动方程并与采用拉氏方程建立的该系统运动方程进行比较,证明了运用加速度极小原理建立运动方程要优于利用拉氏方程建立运动方程。此外,还运用加速度极小原理建立了大应变梁的运动方程。最后,基于加速度极小原理对大应变梁弹塑性运动进行直接求解,并将所得计算结果与采用ANSYS程序计算所得的结果进行了比较。按本文所得的结果与按ANSYS程序所得的结果很好地吻合,这证明了本文方法的正确性。应该指出,运用加速度极小原理是解决力学问题的很好的途径,它不仅可以简便地建立力学的控制方程,而且还可以得到较好的近似解答。The Gibbs-Appell equation and the acceleration minimum principle were simply introduced. The motion equation for flexible multibody system in plane was derived by using the acceleration minimum principle. The use of acceleration minimum principle to establish the motion equation was compared with the use of Lagrange equation to establish the motion equation. It is shown that the use of acceleration minimum principle is better than that of Lagrange equation. In addition, the motion equation for elastic-plastic beam with large strain was set up by using acceleration minimum principle as well. Finally, based on the acceleration minimum principle, the direct solution method for elastic-plastic beam with large strain was given, and the computational results were compared with those obtained by using ANSYS code. The results obtained by present method agree with those given by ANSYS code. It is shown that the present method is correct by comparing with ANSYS code. It should be pointed out that it is the best way to solve mechanical problems by using acceleration minimum principle, because not only the governing equation can be easily set up, but also the better approximation solution can be obtained.

关 键 词：加速度极小原理 拉格朗日方程 变分 直接解 

分 类 号：O322[理学—一般力学与力学基础]