In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect...In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.展开更多
Under the condition that all the perfectly plastic stress components at a crack tip are the functions of only, making use of the Mises yield condition , steady-state moving equations and elastic perfectly-plastic cons...Under the condition that all the perfectly plastic stress components at a crack tip are the functions of only, making use of the Mises yield condition , steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly plastic fields at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic fields at the rapidly propagating tips of modes I and II plane-stress cracks.展开更多
文摘In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.
文摘Under the condition that all the perfectly plastic stress components at a crack tip are the functions of only, making use of the Mises yield condition , steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly plastic fields at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic fields at the rapidly propagating tips of modes I and II plane-stress cracks.
