Search results for "Circumscribed circle"
showing 5 items of 5 documents
A critical assessment of methods for the determination of the shear stress amplitude in multiaxial fatigue criteria belonging to critical plane class
2015
Abstract Multiaxial high cycle fatigue criteria based on the critical plane approach necessitate unambiguous definitions of the amplitude and mean value of the shear stress (τa and τm) acting on the material planes. Four of the existing definitions relate the values of τa and τm to a geometrical element of the curve described by the tip of the shear stress vector (curve Ψ), respectively, the radius of the Minimum Circumscribed Circle, the Longest Chord, the Longest Projection, the diagonal of the Maximum Rectangular Hull (MRH). In this paper a critical assessment of the above definitions is proposed, focusing on that based on the concept of MRH, which is the most recently developed. The mai…
Ultrametricity property of energy landscapes of multidisperse packing problems
2009
We consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment, such that the radius of the circumcircle is minimal. The subspace of the quasioptimum configurations of this problem exhibits the property of ultrametricity.
CONSIDERAZIONI TEORICHE E PRATICHE SUL METODO DEL MASSIMO RETTANGOLO CIRCOSCRITTO PER LA VALUTAZIONE DELL’AMPIEZZA DELLA TENSIONE TANGENZIALE NEI CRI…
2012
The multiaxial fatigue criteria based on the approach of the critical plane require the determination of the amplitude of the alternating shear stress τ aacting on different planes passing through the point of the material analyzed. In the case of non-proportional stresses the shear stress vector varies both in modulus and direction and its tip describes a curvedefined loading path. In these cases τ ais identified and evaluated by means of special procedures the most recent, and apparently more effective, of which is that of the Maximum Circumscribed Rectangle (MCR) to the loading path itself. In particular τ ais equal to the length of the diagonal of the MCR. In this paper, the MCR method …
Improvements in the algorithms for the determination of the shear stress components in critical plane class fatigue criteria
2010
This paper presents two improvements in the procedure for the evaluation of the amplitude and mean values of the shear stress in critical plane class fatigue criteria, when the method of the Minimum Circumscribed Circle (MCC) to the path of the tip of the vector is used. In particular, the paper shows how it is possible to reduce the number of material planes passing through the point of interest in which the MCC has to be determined and the number of points of each curve that has to be considered for the determination of the MCC, noticeably reducing the computational time.
Packing a multidisperse system of hard disks in a circular environment.
2008
We consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment, such that the radius of the circumcircle is minimal. With our approach, we are able to find denser packings for various problem instances than known from the literature. Both for the dynamics of the simulation and for the optimum values of the radii of the circumcircles, we find various scaling laws.