The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for ra...The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.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
Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha...Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.展开更多
Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incr...Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.展开更多
文摘The purpose is to establish the rather complete equations of motion, boundary conditions and equation of energy rate of incremental rate type for micropolar continua. To this end the rather complete definitions for rates of deformation gradient and its inverse are made. The new relations between various stress and couple stress rate tensors are derived. Finally, the coupled equations of motion, boundary conditions and equation of energy rate of incremental rate type for continuum mechanics are obtained as a special case.
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Let {X(t), t greater than or equal to 0} be a fractional Brownian motion of order 2 alpha with 0 < alpha < 1,beta > 0 be a real number, alpha(T) be a function of T and 0 < alpha(T), [GRAPHICS] (log T/alpha(T))/log T = r, (0 less than or equal to r less than or equal to infinity). In this paper, we proved that [GRAPHICS] where c(1), c(2) are two positive constants depending only on alpha,beta.
文摘Theoretical incompleteness of the existing conservation laws of energy for polar continuum mechanics is further clarified. For completeness, the principles of total work and energy and of total work and energy of incremental rate type are postulated. Via total variations of the former and the latter of them, the principles of virtual displacement and microrotation & stress and couple stress as well as virtual velocity and angular velocity & stress rate and couple stress rate are immediately obtained, respectively. From these principles all balance equations and boundary conditions for micropolar mechanics are naturally and simultaneously deduced. The essential differences between the nontraditional results obtained in this paper and the existing conservation laws of energy are expounded.
