Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevan...Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevant conclusions in singularity theory, the plastic yield criterion is discussed in detail. We found that the most general form of the plastic yield criterionshould be f(J1,J2,J23 ) = 0.Obviously, this form is more precise than the form f(J1,J2,J3) = 0which is given in the usual literature. Finally, we shall also give some practical examples forexplanation.展开更多
The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method...The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.展开更多
文摘Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevant conclusions in singularity theory, the plastic yield criterion is discussed in detail. We found that the most general form of the plastic yield criterionshould be f(J1,J2,J23 ) = 0.Obviously, this form is more precise than the form f(J1,J2,J3) = 0which is given in the usual literature. Finally, we shall also give some practical examples forexplanation.
文摘The dynamical equations of a thin rectangle plate subjected to the friction support boundary and its plane force are established in this paper. The local bifurcation of this system is investigated by using L S method and the singularity theory. The Z 2 bifurcation in non degenerate case is discussed. The local bifurcation diagrams of the unfolding parameters and the bifurcation response characters referred to the physical parameters of the system are obtained by numerical simulation. The results of the computer simulation are coincident with the theoretical analysis and experimental results.
