New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary...New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.展开更多
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...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 anti virtual couple stress with c ross terms of incremental rate type a new principle of power anti 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.展开更多
The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existin...The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola's theorem. These basic equations and the boundary conditions together with the initial conditions may be. used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.展开更多
文摘New principles of work and energy as well as power and energy rate with cross terms for polar and nonlocal polar continuum field theories were presented and from them all corresponding equations of motion and boundary conditions as well as complete equations of energy and energy rate with the help of generalized Piola's theorems were naturally derived in all and without any additional requirement. Finally, some new balance laws of energy and energy rate for generalized continuum mechanics were established. The new principles of work and energy as well as power and energy rate with cross terms presented in this paper are believed to be new and they have corrected the incompleteness of all existing corresponding principles and laws without cross terms in literatures of generalized continuum field theories.
文摘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 anti virtual couple stress with c ross terms of incremental rate type a new principle of power anti 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.
文摘The dynamical theories of elastic solids with microstructure are restudied and the reason why so many notations have been introduced for derivation of basic equations for such theories is given. In view of the existing problems in those theories the rather general principle of power and energy rate is postulated and the equations of motion, the balance equations of energy rate and energy and the boundary conditions for local and nonlocal theories are naturally derived with help of that principle and the generalized Piola's theorem. These basic equations and the boundary conditions together with the initial conditions may be. used to solve the mixed problems of the dynamical theory of elastic solids with microstructure.
