最小耗能率原理及其在固体力学中的某些应用

PRINCIPLE OF LEAST RATE OF ENERGY CONSUMPTION AND SOME APPLICATIONS OF ITS IN SOLID MECHANICS

本文提出并证明存在着一个最小耗能率原理,即“在线性非平衡系统中发生的任何耗能过程.都将在相应约束条件下以最小耗能的方式进行”.根据这个原理,完成了对这样三个问题的讨论,即塑性力学中建立塑性位势理论的理论依据、断裂力学中Griffith断裂准则的推导和现代连续介质力学中的内变量演变方程的建立.这些结果可以认为是对这个原理正确性的一种验证.同时还指出,最小耗能率原理将人们已感觉到的大自然的节约法则,提到了一个理性认识的高度.可以预料,由它出发还可能导出更多的有用结果.

There exists one principle of least rate of energy consump- tion which has been put forward and verified in the paper,i.e.any counse of energy consumption happening in the system of linear nonquili- brium region will be carried out by means of least consumption of energy corresponding to the condition of restraint.According to the principle, the discussion about these three problems has been carried out,i.e.the theortical basis for establishing the theory of plastic potential in plastic theory,deivation of Griffith fracture criterion in fracture mechanics and the foundation of the evolution equtions for internal variables in modern continuum mechanics,and all these can also be regarded as an inspection to the correctness of the principle.The principle of least rate of energy consumption make economizing law of nature,which has perceived by people,raise to a height of rational knowledge.It may be expected that deriving more results of use from the principle is possible.