微分的阶与虚功原理的充分性

ORDERS OF DIFFERENTIAL AND SUFFICIENCY OF THE PRINCIPLE OF VIRTUAL WORK

本文讨论了一些文献中关于虚功原理充分性证明中至今尚未解决的问题,指出了其反证法所要求的动能一阶微分dT>0或(F_k+N_k)·dr_k>0实际上是得不到的。为了得到可信的证明,本文给出了二阶实位移的定义,Du_i=du_i+1/2d^2u_i,从而真正获得了反证法所要求的sum from iF_i·σr_i>0的结果。

This paper discusses the question which are quite obscure so far about sufficiency proof on the principle of virtual work in many literatures. It also points that dT>0 or (F1+N1)drk> 0 required to counter proof of sufficiency infact cannot obtain. In order to obtain reliable proof it is necessary to have a definition of the secoond order actual displacement,DU1 = du +1/2 d2Ui, so that we completely obtained a result of required tocounter proof.