理论力学研究性教学新探索——质点系变分原理与弹性介质(结构)变分原理

A NEW RESEARCH-ORIENTED LECTURING METHODOLOGY OF CLASSICAL MECHANICS-VARIATIONAL PRINICPLES IN PARTICAL SYSTEMS AND ELASTIC CONTINUUM

本文从理论力学研究性教学角度探讨质点系经典变分原理与连续介质/结构变分原理之间的理论联系。弹性介质/结构属于空间连续分布的相互作用质点系,通过将质点之间的弹性相互作用力视作特殊的主动力(有势力),从而准确构造弹性相互作用所做的内力功,实现将质点系变分原理过渡到弹性介质/结构力学的变分原理。论文通过对比分析,将详细说明质点系变分原理与弹性介质/结构变分原理的理论对应关系,并强调在基础力学研究性教学中展示这一理论联系的必要性。

This paper investigates theoretical connections between classical variational principles of discrete particle systems and variational principles of continuum/structures,from the perspective of research-oriented lecturing of classical mechanics.As continuum/structures could be regarded as particle systems with continuous spatial distributions,the classical variational principles in discrete particle systems are demonstrated to smoothly turn into the form of variational principles of continuum/structures,if the elastic interaction forces among particles being regarded as particular(conservative)active forces rather than internal constraint forces,and if the work done by these internal forces being correctly constructed.Through a detailed comparative study,the theoretical connections between two versions of variational principles,i.e.,in discrete particle systems and in continuum/structures,respectively,will be explicitly demonstrated,and necessity of showing such connections in research-oriented lecturing of classical mechanics is also emphasized.