广义连续统场论中新的增率型功率和能率原理

目的是建立广义连续统场论的增率型功率和能率原理.通过组合具有交叉项的增率型虚速度和虚角度原理以及虚应力和虚偶应力原理提出了微极连续统场论中具有交叉项的增率型功率和能率原理,并借助广义Piola定理同时而且无需其它附加要求地推导出微极和非局部微极连续统场论的所有增率型运动方程和边界条件以及能率方程.类似地可以推导出微态连续统的相应结果.文中给出的结果是新的,并可作为建立广义连续统力学相关的增率型有限元方法的理论基础.

New Principles of Power and Energy Rate of Incremental Rate Type for Generalized Continuum Field Theories

The aim of this paper is to establish new principles of power and energy rate of incremental type in generalized continuum mechanics. By combining new principles of virtual velocity and virtual angular velocity as well as of virtual stress and virtual couple stress with cross terms of incremental rate type a new principle of power and energy rate of incremental rate type with cross terms for micropolar continuum field theories is presented and from it all corresponding equations of motion and boundary conditions as well as power and energy rate equations of incremental rate type for micropolar and nonlocal micropolar continua with the help of generalized Piola's theorems in all and without any additional requirement are derived.Complete results for micromorphic continua could be similarly derived.The derived results in the present paper are believed to be new.They could be used to establish corresponding finite element methods of incremental rate type for generalized continuum mechanics.