Measurement of dynamic characteristics of latex foams by the antiresonance method

Measuring and calculation methods for the dynamic characteristics of tubular specimens of low-modulus latex foams and composites based on them, under longitudinal vibrations in a low-frequency region (up to 200 Hz), are developed. The method is based on the effect of antiresonance. Data on the influence of the basic formulation-processing factors on the dynamic characteristics (gelatination time and content of the plasticizer and chopped fibers) are presented. The results obtained can be used to choose the composition of latex foams for lining acoustic channels, injectors, ejectors, and phase inverters, as well as to control products quality. This method can be applied directly to full-size articles. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 249–258, March–April 2000.     

Tensile behavior of plastic foams

The tensile stress-strain diagram of plastic foams is calculated on the basis of a previously proposed 14-faced cell model. An S-shaped inflection due to the flexural deformations of the ties is detected on the initial section of the diagram. It is shown that for closed-celled foams this inflection may degenerate. The results of testing PVC and polyurethane foams (volume content of polymer base about 3–6%) prove to be in satisfactory agreement with the calculations.Vladimir Scientific-Research Institute of Synthetic Resins. Translated from Mekhanika Polimerov, No. 4, pp. 670–675, July–August, 1971.     

Correlation between the strength of fiber-reinforced plastics and the adhesive strength of fiber—Matrix joints

The relationship between the strength (σc) of unidirectional fiber-reinforced plastics in different stressed states and the interfacial strength of their components is investigated. The shear adhesive strength (τ0) of fiber—matrix joints determined by the pull-out technique is used as a measure of the interfacial strength. To obtain the correlation curves betweenσc andτ0, the experimental results are used, where both the plastic and adhesive strength change under the influence of a single factor. In this case, such factors are the fiber surface treatment, nature and composition of polymer matrices, and test temperature. It is shown that the strength of the glass, carbon, and boron plastics increases practically linearly with increased interfacial strength. Such a behavior is observed in any loading conditions (tension, shear, bending, and compression). Sometimes, a small (10–20%) increase in the adhesive strength induces a significant (50–70%) growth in the material strength. Therefore, the interface is the “weak link” in these composites. The shape of theσc—τ0 curves for composites based on the high-strength and high-modulus aramid fibers and different thermoreactive matrices depends on the nature of the fiber and the type of stress state. In many cases, the composite strength does not depend on the interfacial strength. Then, the fiber itself is the “weak link” in these composites. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 291–304, May–June, 2000.     

Elastoplastic stress analysis of thick laminated metal-matrix composite plates by the finite-element method

The elastoplastic stress state of a laminated stainless-steel-fiber-reinforced aluminum-matrix plates, with or without a hole, subjected to a pressure on their top is examined by using the finite-element method. The analysis is carried out for three layouts: (0/90/0/90)_s, (45/-45/45/-45)_s, and (30/60/30/60)_s. The Newton-Raphson method is used to solve the nonlinear problem. The distributions of equivalent stresses and the plastic zones of the plates without a hole and with a hole of various diameters are determined. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 4, pp. 531–544, July–August, 2006.     

Automorphisms of Maps with a Given Underlying Graph and Their Application to Enumeration

A graph is called a semi-regular graph if its automorphism group action on its ordered pair of adjacent vertices is semi-regular. In this paper, a necessary and sufficient condition for an automorphism of the graph F to be an automorphism of a map with the underlying graph F is obtained. Using this result, all orientation-preserving automorphisms of maps on surfaces (orientable and non-orientable) or just orientable surfaces with a given underlying semi-regular graph F are determined. Formulas for the numbers of non-equivalent embeddings of this kind of graphs on surfaces (orientable, non-orientable or both) are established, and especially, the non-equivalent embeddings of circulant graphs of a prime order on orientable, non-orientable and general surfaces are enumerated.     

Some physical and mechanical properties of recycled polyurethane foam blends

Blends of secondary rigid polyurethane foams (RPUFs) with soft polyurethane foams (SPUFs) were investigated. The effect of SPUF content and its chemical nature on some physical and mechanical properties of the blends was evaluated. Owing to the stronger intermolecular interaction and higher values of cohesion energy, the blends of RPUFs with polyester SPUFs showed higher mechanical properties than those with polyether SPUFs. The density, hardness, ultimate strength, and the tensile, shear, and flexural moduli increased, while the impact toughness, ultimate elongation, and damping characteristics decreased with increasing RPUF content in the blends. Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 5, pp. 737–746, September–October, 2008.     

First-order convergence of multi-point flux approximation on triangular grids and comparison with mixed finite element methods

In this paper we show first-order convergence of a multi-point flux approximation control volume method (MPFA) on unstructured triangular grids. In this approach the flux approximation is derived directly in the physical space. In order to do this, we introduce a perturbed mixed finite element method that is equivalent to the MPFA scheme and prove the first-order convergence of this approach. Moreover, we carefully compare the computational performance properties of the MPFA method with those of a lowest order Raviart–Thomas and Brezzi–Douglas–Marini mixed finite element approximation.     

Solving the Asymmetric Travelling Salesman Problem with time windows by branch-and-cut

Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSP-TW) from such a point of view. The real–world application we aim at is the control of a stacker crane in a warehouse.?We have implemented codes based on three alternative integer programming formulations of the ATSP-TW and more than ten heuristics. Computational results for real-world instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered – at least for our special application – and that the heuristics provide acceptable solutions. Received: August 1999 / Accepted: September 2000?Published online April 12, 2001     

Modelling a new composite from a recycled GFRP

The mechanical reprocessing of different types of plastic scrap in high-energy disintegrator mills in direct and selective milling systems is considered. The grindabilty and separation of components of composites-an acrylic plastic and glass fibers-are analyzed. The relation between the density of the filler material and the fractions of a polymethylmethacrylate powder is modelled on the basis of experimental data. Artificial neural networks and a hybrid genetic algorithm are used to design a new composite from a recycled glass-fiber-reinforced plastic. Russian translation in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 6, pp. 881–894, November–December, 2008.     

Finite element approximation of spatially extended predator–prey interactions with the Holling type II functional response

We study the numerical approximation of the solutions of a class of nonlinear reaction–diffusion systems modelling predator–prey interactions, where the local growth of prey is logistic and the predator displays the Holling type II functional response. The fully discrete scheme results from a finite element discretisation in space (with lumped mass) and a semi-implicit discretisation in time. We establish a priori estimates and error bounds for the semi discrete and fully discrete finite element approximations. Numerical results illustrating the theoretical results and spatiotemporal phenomena are presented in one and two space dimensions. The class of problems studied in this paper are real experimental systems where the parameters are associated with real kinetics, expressed in nondimensional form. The theoretical techniques were adapted from a previous study of an idealised reaction–diffusion system (Garvie and Blowey in Eur J Appl Math 16(5):621–646, 2005).     

Semilinear Mixed Problems on Hilbert Complexes and Their Numerical Approximation

Arnold, Falk, and Winther recently showed (Bull. Am. Math. Soc. 47:281–354, 2010) that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article (arXiv:), we extended the Arnold–Falk–Winther framework by analyzing variational crimes (à la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace–Beltrami operator on 2- and 3-surfaces, due to Dziuk (Lecture Notes in Math., vol. 1357:142–155, 1988) and later Demlow (SIAM J. Numer. Anal. 47:805–827, 2009), as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold–Falk–Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.     

Normal Bases and Their Dual-Bases over Finite Fields

In this paper, we prove the following results： 1） A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2） The normal basis N is self-dual if and only if its multiplication table is symmetric and Tr（α^2） = 1, where α generates N; 3） An optimal normal basis N is self-dual if and only if N is a type-Ⅰ optimal normal basis with q = n = 2 or N is a type-Ⅱ optimal normal basis.     

Structural Modeling in the Mechanics of Porous Materials

A new method for analyzing the deformation behavior of rigid and elastic foams with a small volume content of solid phase ( < 0.2) is developed. Various structural models for describing the elastic behavior of rigid and elastic plastic foams are used and compared. The results of structural simulation of anisotropic auxetic (i.e., having a negative Poisson ratio) foams with concave cells are presented. For cyclic uniaxial compression of rigid foams and volumetric deformation of elastic foams, the stress-strain curves are obtained. The general shape of the curves agrees well with the nonlinearly elastic behavior of plastic foams observed in experiments.     

Nonlinear 0–1 programming: I. Linearization techniques

Any real-valued nonlinear function in 0–1 variables can be rewritten as a multilinear function. We discuss classes of lower and upper bounding linear expressions for multilinear functions in 0–1 variables. For any multilinear inequality in 0–1 variables, we define an equivalent family of linear inequalities. This family contains the well-known system of generalized covering inequalities, as well as other linear equivalents of the multilinear inequality that are more compact, i.e., of smaller cardinality. In a companion paper [7]. we discuss dominance relations between various linear equivalents of a multilinear inequality, and describe a class of algorithms for multilinear 0–1 programming based on these results. Research supported by the National Science Foundation under grant ECS7902506 and by the Office of Naval Research under contract N00014-75-C-0621 NR 047-048.     

Structure of coordinate groups for algebraic sets in partially commutative nilpotent groups

The results obtained deal in algebraic geometry over partially commutative class two nilpotent ℚ-groups, where ℚ is a field of rationals. It is proved that two arbitrary non-Abelian partially commutative class two nilpotent ℚ-groups are geometrically equivalent. A necessary and sufficient condition of being universally geometrically equivalent is specified for two partially commutative class two nilpotent ℚ-groups. Algebraic sets for systems of equations in one variable, as well as for some special systems in several variables, are described. Dedicated to V. N. Remeslennikov on the occasion of his 70th birthday Translated from Algebra i Logika, Vol. 48, No. 2, pp. 378–399, May–June, 2009.     

Calculation of Dependent Elastic Constants of Plastic Foams with a Pronounced Strut-Like Structure

Seven dependent elastic constants of monotropic plastic foams with an expressed strut-like structure are calculated. For this purpose, the basic results of the previously elaborated mathematical model for light-weight plastic foams is used. The model includes a model cell of local structure for monotropic/isotropic plastic foams and an ensemble of structural elements, which allows one to calculate the seven dependent elastic constants, taking into account the pronounced polydispersity of the structure of plastic foams. The numerical values of the constants are compared with the available experimental data, and a satisfactory agreement is found to exist. As a final result, a full set of general expressions and numerical values are obtained for all 12 elastic constants of monotropic plastic foams.     

Duality and optimality conditions for generalized equilibrium problems involving DC functions

We consider a generalized equilibrium problem involving DC functions which is called (GEP). For this problem we establish two new dual formulations based on Toland-Fenchel-Lagrange duality for DC programming problems. The first one allows us to obtain a unified dual analysis for many interesting problems. So, this dual coincides with the dual problem proposed by Martinez-Legaz and Sosa (J Glob Optim 25:311–319, 2006) for equilibrium problems in the sense of Blum and Oettli. Furthermore it is equivalent to Mosco’s dual problem (Mosco in J Math Anal Appl 40:202–206, 1972) when applied to a variational inequality problem. The second dual problem generalizes to our problem another dual scheme that has been recently introduced by Jacinto and Scheimberg (Optimization 57:795–805, 2008) for convex equilibrium problems. Through these schemes, as by products, we obtain new optimality conditions for (GEP) and also, gap functions for (GEP), which cover the ones in Antangerel et al. (J Oper Res 24:353–371, 2007, Pac J Optim 2:667–678, 2006) for variational inequalities and standard convex equilibrium problems. These results, in turn, when applied to DC and convex optimization problems with convex constraints (considered as special cases of (GEP)) lead to Toland-Fenchel-Lagrange duality for DC problems in Dinh et al. (Optimization 1–20, 2008, J Convex Anal 15:235–262, 2008), Fenchel-Lagrange and Lagrange dualities for convex problems as in Antangerel et al. (Pac J Optim 2:667–678, 2006), Bot and Wanka (Nonlinear Anal to appear), Jeyakumar et al. (Applied Mathematics research report AMR04/8, 2004). Besides, as consequences of the main results, we obtain some new optimality conditions for DC and convex problems.     

A continuous model for investigation of physically nonlinear deformation of orthotropic sandwich plates

A phenomenological yield condition for quasi-brittle and plastic orthotropic materials with initial stresses is suggested. All components of the yield tensor are determined from experiments on uniaxial loading. The reliability estimates of the criterion suggested is discussed. For a plastic material without initial stresses, the given condition transforms into the Marin—Hu criterion. The defining equations of the deformation theory of plasticity with isotropic and “anisotropic” hardening, associated with the yield condition suggested, are obtained. These equations are used as the basis for a highly accurate nonclassical continuous model for nonlinear deformation of thick sandwich plates. The approximations with respect to the transverse coordinate take into account the flexural and nonflexural deformations in transverse shear and compression. The high-order approximations allow us to model the occurrence of layer delamination cracks by introducing thin nonrigid interlayers without violating the continuity concept of the theory. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. pp. 329–340, May–June, 2000.     

Markov model of connection between the distribution of static strength and fatigue life of a fibrous composite

Within the framework of a unified mathematical model based on the Markov chain theory, an attempt is made to describe the distribution of static strength, the fatigue curve, and the accumulation of fatigue damages. It is assumed that the fatigue failure of a test specimen occurs after the destruction of some its critical microvolume consisting of two — elastic (brittle fibers) and plastic (matrix) — parts. In the second part, plastic strains accumulate as soon as the cyclic load exceeds some level. Numerical examples are presented. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 42, No. 5, pp. 615–630, September–October, 2006.     

Biplastic pipes for high-pressure oil pipeline systems

A high-performance, corrosion-resistant biplastic pipe for high-pressure oil pipeline systems is presented. The pipe combines an outer load-carrying layer formed from unidirectionally glass-reinforced plastic (GRP) sublayers by wet multi-circuit winding and an inner sealing layer of high-density polyethylene. Both demountable and permanent joints, tees, and other parts are constructed for these pipes. The biplastic pipes ensure reliable operation of oil pipeline systems under a pressure of up to 200 bar. The experimental results and calculated estimates of the strength of biplastic pipes are presented. The results of using these pipes in oil pipeline systems in the Perm’ region are discussed. Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 407–418, 2000.