广义连续统场论的简略综述评论

一、理论的发展古典连续介质力学常常局限于在力学范围内考虑和处理问题。随着科学技术的发展和生产实际的要求,提出了许多按古典连续介质力学所不能解释或不能解决的现象和问题。此外,就是在按传统的看法认为用不着多少力学或者认为看来不一定能够用上力学的部门和学科中,实际也存在着许多力学现象和问题,这是通过各学科间的相互渗透和相互促进过程中认识到的。所以除了继续加强古典连续统理论外,还要建立新的连续统模型和相应的新理     

Renewal of basic laws and principles for polar continuum theories （XI）——consistency problems

Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.     

RENEWAL OF BASIC LAWS AND PRINCIPLES FOR POLAR CONTINUUM THEORIES(Ⅸ)—THERMOMECHANICS

The existing fundamental laws of thermodynamics for micropolar continuum field theories are restudied and their incompleteness is pointed out. New first and second fundamental laws for thermostatics and thermodynamics for micropolar continua are postulated. From them all equilibrium equations and the entropy inequality of thermostatics as well as all balance equations and the entropy rate inequalities are naturally and simultaneously deduced. The comparisons between the new results presented here and the corresponding results demonstrated in existing monographs and textbooks concerning micropolar continuum mechanics are made at any time. It should be emphasized to note that, the problem of why the local balance equation of energy and the local entropy inequality could not be obtained from the existing fundamental laws of thermodynamics for micropolar continua, is believed to be clarified.     

略论Cosserat连续统理论的发展

本文对Cosserat 连续统理论的发展历史作了简述,并对广义连续统力学的意义和今后发展作了短评.     

New Conservation Laws of Energy and C-D Inequalities in Continua with Microstructure

ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｕｒｐｒｅｃｅｅｄｉｎｇｐａｐｅｒ[1 ]ｔｈｅｆｕｎｄａｍｅｎｔａｌｌａｗｓ,ｂａｌａｎｃｅｅｑｕａｔｉｏｎｓａｎｄＣ＿Ｄｉｎｅｑｕａｌｉｔｉｅｓｉｎｃｏｎｔｉｎｕａｗｉｔｈｏｕｔｍｉｃｒｏｓｔｒｕｃｔｕｒｅａｒｅｓｙｓｔｅｍａｔｉｃａｌｌｙｒｅｓｔｕｄｉｅｄ ,ａｎｄｔｈｅｎｅｗｃｏｎｓｅｒｖａｔｉｏｎｌａｗｓａｎｄｔｈｅｒｅｌａｔｅｄＣ＿Ｄｉｎｅｑｕａｌｉｔｉｅｓａｒｅｅｓｔａｂｌｉｓｈｅｄ .Ｉｎｔｈｉｓｐａｐｅｒｓｏｍｅｒｅｍａｒｋｓｏｎｔｈｅｒｅｓｕｌｔｓｉｎｃ…     

带有微结构的连续统中新的能量守恒定律和C—D不等式

对带有微结构的连续统中现有的基本定律、均衡方程和Clausius-Duhem不等式进行了系统的再研究,发现所有的能量均衡方程和相关的C-D不等式都是不完整的。本文对现有的结果进行了评注,并提出新的能量均衡方程和相关的C-D不等式。     

重建极性连续统理论的基本定律和原理(Ⅸ) --热力学

对现有的微极连续统场论的基本定律进行了再研究,并指出了它们的不完整性·　建立起新的微极连续统热静力学和热动力学的第一和第二基本定律·　从这些定律可以很自然地和同时推导出热静力学的所有平衡方程和熵不等式以及热动力学的所有均衡方程和熵率不等式·　随时对这里得到的新结果与现有微极连续力学专著和教科书中的相应结果进行了比较·　着重指出的是,为什么从现有的微极连续统热动力学基本定律不能推导出局部能量均衡方程和局部熵不等式问题已经得到阐明·     

重建极性连续统理论的基本定律和原理(Ⅷ) --全功能原理

进一步阐明了现有极性连续统力学的能量守恒定律在理论上的不完整性·　为能使之完整起见,提出了全功能原理及增率型全功能原理·　通过对它们的全变分,即可分别得到虚位移＿微转动和虚应力＿偶应力原理及虚速度＿角速度和虚应力率＿偶应力率原理·　从这些原理可以同时而且很自然推导出微极连续统力学的所有均衡方程和边界条件·　所得到非传统结果与现有能量守恒定律问题存在的本质性差异作了说明·     

论非线性弹性理论的各种变分原理

本文从“全能量原理”出发推导出非线性弹性理论中各种可能的主要的变分原理的泛函,其中有几个是在我们所能见到的文献中还没有的.通过本文的推导过程,我们提出了胡海昌的专著[1]中表6.1的第11类和第6类变分原理不存在的猜想.     

CONCERNING“VARIOUS RECIPROCAL THEOREMS AND VARIATIONAL PRINCIPLES IN THE THEORIES OF NONLOCAL MICROPOLAR LINEAR ELASTIC MEDIUMS”

"Various Reciprocal Theorems and Variational Principles in the Theories ofNonlocal Micropolar Linear Elastic Mediums",Appl.Math.Mech,Vol.1.No.1,pp.91—111,1980.