Estimation of laminate stiffness reduction due to cracking of a transverse ply by employing crack initiation-and propagation-based master curves

The applicability range of toughness-and strength-based criteria for progressive cracking of a transverse layer in a cross-ply composite laminate subjected to tensile loading is considered. Using a deterministic cracking model, approximate relations for the crack density as a function of stress are derived for initiation-and propagation-controlled types of cracking. The master-curve approach is applied to progressive cracking in glass/epoxy laminates. The accuracy of estimation of laminate stiffness reduction by using crack density master curves is evaluated. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 633–646, September–October, 2008.     

Design rules of flexible assembly and inspection cells

Every leading institution and manufacturing company in the world is dealing with some aspects of flexible automation. This is because they have found that designing and making goods and products on order rather than for stock is the key issue in cutting manufacturing costs and lead time, and eventually staying in business in the future. This paper discusses the way in which this above outlined goal can be implemented in the assembly business, as well as giving design rules on how to design flexible assembly and inspection cells and systems. The rules are justified by solid model simulation and the author's industrial and laboratory experience.     

Quadrature rules for qualocation

Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988‐2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions G_α form a Chebyshev–system on [0, 1/2] for arbitrary indices á and thus prove the existence of such quadrature rules for any J.     

Seventh degree integration rules for the cube

A family of integration rules for the cube is discussed and two such rules are compared with other seventh degree rules in the literature.     

Seventh degree integration rules for the sphere

A one-parameter family of rules is derived with all weights positive and all integration points within the sphere.     

Quadrature rules for rational functions

Summary. It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turán, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable. Received June 21, 1999 / Revised version received September 14, 1999 / Published online June 21, 2000     

Local rules for pentagonal quasi-crystals

The existence of different kinds of local rules is established for many sets of pentagonal quasi-crystal tilings. For eacht∈ℝ there is a set of pentagonal tilings of the same local isomorphism class; the caset=0 corresponds to the Penrose tilings. It is proved that the set admits a local rule which does not involve any colorings (or markings, decorations) if and only ift=m+nτ. In other words, this set of tilings is totally characterized by patches of some finite radius, orr-maps. When the set admits a local rule which involvescolorings. For the set of Penrose tilings the construction here leads exactly to the Penrose matching rules. Local rules for the caset=1/2 are presented.     

Change rules for hierarchical beliefs

The paper builds a belief hierarchy as a framework common to all uncertainty measures expressing that an actor is ambiguous about his uncertain beliefs. The belief hierarchy is further interpreted by distinguishing physical and psychical worlds, associated to objective and subjective probabilities. Various rules of transformation of a belief hierarchy are introduced, especially changing subjective beliefs into objective ones. These principles are applied in order to relate different contexts of belief change, revising, updating and even focusing. The numerous belief change rules already proposed in the literature receive epistemic justifications by associating them to specific belief hierarchies and change contexts. As a result, it is shown that the resiliency of probability judgments may have some limits and be reconciled with the possibility of learning from factual messages.     

Nearest-neighbour rules for emergency services

A policy for allocating each demand for an emergency service, arising within a region, to a currently available one of a set of service units, so as to minimise overall average response time, results in a straightforward generalisation of the elementary nearest-neighbour rule.

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Zusammenfassung Es wird gezeigt, daß die Zuordnung eines momentan verfügbaren Gerätes bei einer aus einer bestimmten Gegend kommenden Anforderung eines Notdienstes auf eine Verallgemeinerung der Regel des nächsten Nachbaumes führt, wenn die mittlere Gesamtantwortzeit minimiert werden soll.

     

Fully symmetric integration rules for the 4-cube

In this paper we discuss fully symmetric integration rules of degree 7 and 9 for the 4-cube. In particular we are interested in good rules. (i.e. rules with all the evaluation points inside the cube and all the weights positive).This work was supported by the Norwegian Research Council for Sciences and Humanities.     

Some questions relating to the strength of glass laminate

The ultimate strength of glass laminate is investigated in the plane-stress case, in which the directions of the principal stresses do not coincide with the axes of anisotropy of the material and one of the principal stresses is equal to zero. The experimental data are compared with the results of calculations based on expressions describing the onset of the limiting state proposed in [1]. The agreement is satisfactory.Mekhanika Polimerov, Vol. 4, No. 1, pp. 64–66, 1968     

TSD based framework for mining the induction rules

Sex determination mainly encompasses two aspects: genotypic sex determination (GSD) and temperature-dependent sex determination (TSD). Genotypic sex determination performs its task by observing the presence of sex chromosomes. In many reptiles sex determination is greatly influenced by the environmental conditions such as temperature of the nest, weight and size of eggs. A nature inspired algorithm which mimics the mechanism of temperature dependent sex determination (TSD) has been introduced for mining the classification rules from datasets. A comparison of proposed TSD algorithm with other well known rule induction algorithms like PRISM, C4.5, 1-R, CN2, and NN has been evaluated on some bench mark datasets.     

Searching for extensible Korobov rules

Extensible lattice sequences have been proposed and studied in [F.J. Hickernell, H.S. Hong, Computing multivariate normal probabilities using rank-1 lattice sequences, in: G.H. Golub, S.H. Lui, F.T. Luk, R.J. Plemmons (Eds.), Proceedings of the Workshop on Scientific Computing (Hong Kong), Singapore, Springer, Berlin, 1997, pp. 209–215; F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138; F.J. Hickernell, H.Niederreiter, The existence of good extensible rank-1 lattices, J. Complexity 19 (2003) 286–300]. For the special case of extensible Korobov sequences, parameters can be found in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C.Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138]. The searches made to obtain these parameters were based on quality measures that look at several projections of the lattice. Because it is often the case in practice that low-dimensional projections are very important, it is of interest to find parameters for these sequences based on measures that look more closely at these projections. In this paper, we prove the existence of “good” extensible Korobov rules with respect to a quality measure that considers two-dimensional projections. We also report results of experiments made on different problems where the newly obtained parameters compare favorably with those given in [F.J. Hickernell, H.S. Hong, P. L’Ecuyer, C. Lemieux, Extensible lattice sequences for quasi-Monte Carlo quadrature, SIAM J. Sci. Comput. 22 (2001) 1117–1138].     

On the prediction of structural layout for maximum stiffness

A variational formulation is presented for the problem of predicting the optimal structural system from among a discrete set of possible designs. The development is written for maximum stiffness design of single-purpose structures. The distribution among admissible structural configurations of the prescribed loads is determined as part of the solution. An extremum problem interpretation also provides the basis for evaluating relative efficiencies among locally optimal structural systems.     

On the multiplier rules

We establish new results of first-order necessary conditions of optimality for finite-dimensional problems with inequality constraints and for problems with equality and inequality constraints, in the form of John’s theorem and in the form of Karush–Kuhn–Tucker’s theorem. In comparison with existing results, we weaken assumptions of continuity and of differentiability.     

Variation of the properties of glass laminate in cyclic tension-compression

The deformation and dissipative properties of glass laminate have been investigated under extended cyclic loading. It is shown that the glass laminate fails at certain critical values of the absorption coefficient and compliance J, which have constant values at any load level for given cycle asymmetry, scale factor, and heat transfer conditions. The effects on and J of temperature and the accumulation of damage with increase in the number of loading cycles are determined separately. Possible variants of the solution of the temperature equation are considered with allowance for the variation of the dissipative properties of the material with temperature and fatigue damage.Mekhanika Polimerov, Vol. 3, No. 5, pp. 864–872, 1967Fourth All-Union Conference on Strength and Plasticity, Moscow, 2 February, 1967.