T-Spanner Problem

The t-spanner problem is a popular combinatorial optimization problem and has different applications in communication networks and distributed systems. This chapter considers the problem of constructing a t-spanner subgraph H in a given undirected edge-weighted graph G in the sense that the distance between every pair of vertices in H is at most t times the shortest distance between the two vertices in G. The value of t, called the stretch factor, quantifies the quality of the distance approximation of the corresponding t-spanner subgraph. This chapter studies two variations of the problem, the Minimum t-Spanner Subgraph (MtSS) and the Minimum Maximum Stretch Spanning Tree(MMST). Given a value for the stretch factor t, the MtSS problem asks to find the t-spanner subgraph of the minimum total weight in G. The MMST problem looks for a tree T in G that minimizes the maximum distance between all pairs of vertices in V (i.e., minimizing the stretch factor of the constructed tree). It is easy to conclude from the literatures that the above problems are NP-hard. This chapter presents genetic algorithms that returns a high quality solution for those two problems.

Experimental Study of Mullins Effect in Natural Rubber for Different Stretch Conditions

We subjected rubber coupons to cyclical uniaxial tension to investigate the softening effect, where the primary loading at its initial position was followed by additional unloading and reloading. Less stress was required upon reloading than that required in the previous loading for the same degree of stretch, reached on the first loading. This stress softening is significant when reloading follows virgin loading. The magnitude of stress softening is related to the maximum stretch elastomers can achieve in each cycle. To investigate this phenomenon, rubber coupons were subjected to four cycles of simple tension until the desired stretch was reached. We expected that several tests under the same conditions would provide almost identical results. However, we observed different stress requirements for different degrees of stretch when multiple cycles of the same stretch were performed. For three different experimental tests of the same amount of stretch, we saw huge differences in each cycle of loading-relaxation-reloading, a phenomenon that was more obvious during stress relaxation.

ВПЛИВ НАНОНАПОВНЮВАЧА НА РЕОЛОГІЧНІ ВЛАСТИВОСТІ РОЗПЛАВІВ ПОЛІМЕРІВ ТА ЇХ СУМІШЕЙ

Studying the influence of additives of nano-sized aluminium oxide on the patterns of Polypropylene (PP) and mixture PP/CPA (copolyamide) melt flow. The mixtures were obtained by the prior injection of the nano-filler to the PP melt with the further mixing of granula with CPA on the worm-disk extruder. Viscosity (η) of melts was examined by the method of capillary viscometry and the elasticity was studied by value of extrudate equilibrium swelling. The melts ability to longitudinal deformation was evaluated by the maximum stretch rating.

DC dynamic pull-in instability of a dielectric elastomer balloon: an energy-based approach

This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.

T-Spanner Problem

The t-spanner problem is a popular combinatorial optimization problem and has different applications in communication networks and distributed systems. This chapter considers the problem of constructing a t-spanner subgraph H in a given undirected edge-weighted graph G in the sense that the distance between every pair of vertices in H is at most t times the shortest distance between the two vertices in G. The value of t, called the stretch factor, quantifies the quality of the distance approximation of the corresponding t-spanner subgraph. This chapter studies two variations of the problem, the Minimum t-Spanner Subgraph (MtSS) and the Minimum Maximum Stretch Spanning Tree(MMST). Given a value for the stretch factor t, the MtSS problem asks to find the t-spanner subgraph of the minimum total weight in G. The MMST problem looks for a tree T in G that minimizes the maximum distance between all pairs of vertices in V (i.e., minimizing the stretch factor of the constructed tree). It is easy to conclude from the literatures that the above problems are NP-hard. This chapter presents genetic algorithms that returns a high quality solution for those two problems.

Comparison of Maximum Stretch Forces between Femtosecond Laser-Assisted Capsulotomy and Continuous Curvilinear Capsulorhexis

The current study reports comparing the postoperative mechanical properties of the anterior capsule between femtosecond laser capsulotomy (FLC) and continuous curvilinear capsulorhexis (CCC) of variable size and shape in porcine eyes. All CCCs were created using capsule forceps. Irregular or eccentric CCCs were also created to simulate real cataract surgery. For FLC, capsulotomies 5.3 mm in diameter were created using the LenSx® (Alcon) platform. Fresh porcine eyes were used in all experiments. The edges of the capsule openings were pulled at a constant speed using two L-shaped jigs. Stretch force and distance were recorded over time, and the maximum values in this regard were defined as those that were recorded when the capsule broke. There was no difference in maximum stretch force between CCC and FLC. There were no differences in circularity between FLC and same-sized CCC. However, same-sized CCC did show significantly higher maximum stretch forces than FLC. Teardrop-shaped CCC showed lower maximum stretch forces than same-sized CCC and FLC. Heart-shaped CCC showed lower maximum stretch forces than same-sized CCC. Conclusively, while capsule edge strength after CCC varied depending on size or irregularities, FLC had the advantage of stable maximum stretch forces.

Application of the Particle Finite Element Method in Machining Simulation Discussion of the Alpha-Shape Method in the Context of Strength of Materials

In particle finite element simulations, a continuous body is represented by a set of particles that carry all physical information of the body, such as the deformation. In order to form this body, the boundary of the particle set needs to be determined. This is accomplished by the α-shape method, where the crucial parameter α controls the level of detail of the detected shape. However, in solid mechanics, it can be observed that α has an influence on the structural integrity as well. In this paper, we study a single boundary segment of a body during a deformation and it is shown that α can be interpreted as the maximum stretch of this segment. On the continuum level, a relation between α and the eigenvalues of the right Cauchy–Green tensor is presented.