Service life of pressurized vessels

A study is made of the dependence of the time of propagation of a fracture front in thick-walled vessels subjected to internal pressure on the wall thickness and the employed version of kinetic theory of creep. The stress intensity is taken to be the equivalent stress. Recommendations on using the results in computational applications are formulated. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 173–182, September–October, 2007.     

Inverse doubly periodic problem of the theory of bending of a plate with elastic inclusions

Based on the balanced strength principle, a problem of determining the optimal interference for fitting elastic inclusions into holes of an isotropic elastic plate weakened by a doubly periodic system of circular holes is solved. A closed system of algebraic equations is derived, which allows solving this problem. The resultant interference increases the load-carrying capacity of the composite plate being bent. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 153–161, July–August, 2006.     

Optimization of the Parameters of the Magnetic Filtration Process Using Response Surface Methodology

In this study, we aimed at optimizing the parameters which govern the separation efficiency in the magnetic filtration of magnetizable dispersed particles from a water medium. Response surface methodology (RSM) was used to determine the influence of the process parameters. Also, the optimal processing conditions were determined in order to reduce the external magnetic field strength, diameter of the filter matrix elements, and filter length to a safe level. A three-level central composite design (CCRD) involving the variables, such as external magnetic field strength (148–282 kA/m), diameter of the filter elements (0.005–0.011 m), and the filter length (0.01–0.10 m) was developed for this purpose. Data obtained from the RSM was subjected to the analysis of variance (ANOVA) using a second-order polynomial equation, which provided the optimized process conditions as 298 kA/m for external magnetic field strength, 0.0015 m for diameter of the filter elements, and 0.095 m for the filter length. The separation efficiency was optimized for magnetic filtration of micron sized particles that can be magnetized in an external magnetic field and the value was found to be 97%.     

Blood flow in the capillary network of muscle tissue

The capillary network in skeletal muscle is a system of vessels oriented more or less parallel to the muscle fibers with cross links [1]. The blood enters the capillaries from precapillary arterioles oriented across the fibers and is drained into the postcapillary venules which also run in the transverse direction. Along the path of the muscle fibers the unit vascular complexes, comprising a precapillary arteriole, post-capillary venule (first-order vessels) and the connecting capillaries, are repeated. Successive complexes have common vessels of the second order: a blood-supplying arteriole and a blood-draining venule. Since the vessels are in an ordered arrangement and the density of the capillaries is fairly high (10²–10³ mm⁻²), to describe the motion of the blood in them it is natural to employ the theory of flow through porous media. This paper is concerned with the formulation and a general algorithm for the solution of the problem of blood flow in a system of capillaries and microvessels (arterial and venous) of the first two orders. The flow in the individual unit vascular complex is analyzed in detail. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–88, November–December, 1986.     

Optimal nonlinear observers for chaotic synchronization with message embedded

This paper presents an optimal nonlinear observer for synchronizing the transmitter-receiver pair with guaranteed optimal performance. In the proposed scheme, a generalized nonlinear state-space observer via uniform matrix transformations is constructed to estimate the transmitter state and the information signal, simultaneously. A nonlinear optimal design approach is used to synchronize chaotic systems. Solving the Hamilton–Jacobi–Bellman (H–J–B) equations we can obtain a linear optimal feedback scheme for piecewise-linear chaotic systems. Moreover, a robust scheme derived from the H _∞ optimization theory improves the synchronization performance of general nonlinear chaotic systems by suppressing the influence of their high order residual terms. Finally, two numerical simulation examples are illustrated by the chaotic Chua’s circuit system and the Lorenz chaotic system to demonstrate the effectiveness of our scheme.     

Strength of water under pulsed loading

Experiments were performed to study the strength of water under conditions of pulsed extension, which is typical of the interaction between a triangular compression pulse and a free surface. The tests were performed in a wide (40–1000 MPa) range of rariation in the amplitude of the compression pulse at deformation rates of 10⁴−10⁵ sec⁻¹. It is found that as the compression-pulse amplitude increases from 150 to 1050 MPa, the strength of water decreases from 46 to 22 MPa. The deformation rate was found to have little effect on the strength. The possibility of using the model of homogenous nucleation (formation of cavitation nuclei) to interpret the data obtained is discussed. Institute of Chemical Physical, Russian Academy of Sciences, Chernogolovka 142432. Translated from Prikladmaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 198–205, July–August, 2000.     

Long-term strength of metals and creep equations based on the Coulomb-Mohr criterion

It is proposed to construct long-term strength and creep relations for metals on the basis of the Coulomb-Mohr criterion. The creep equations and the long-term strength criterion for plane stress are analyzed in detail. Results of long-term strength calculations are compared with data of experiments with metallic materials. It is established that theoretical and experimental results are in satisfactory agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 115–123, November–December, 2007.     

Two-dimensional cellular metals as multifunctional structures: topology optimization

Highly porous two-dimensional (2D) cellular metals have multifunctional attributes, with tailorable structures to achieve multifunctional performance. The focus of this study is to explore the optimal cellular topology of 2D cellular metals for heat dissipation, and to investigate the eligibility of different heat enhancement techniques for more efficient heat dissipation. An analytical approach for the optimal design of metallic 2D cellular materials, cooled by single-phase laminar forced convection in various flow configurations, is proposed and validated by comparison with full numerical simulations. The optimal design is characterized by two subsidiary dimensionless parameters: one reflecting the trade-off between convection and fluid friction, and the other reflecting the optimal balance between conduction and convection. A heat transfer enhancement technique––boundary layer redevelopment––is subsequently introduced and its feasibility examined experimentally. Future research directions in specific areas are discussed.     

Investigation of the influence mechanisms of resin matrices on the strength of filamentary structures

The interrelationship between the burst strength of fiber-wound pressure vessels and resin properties has been investigated. Experimental results show that the effect of resin properties of the burst strength can be as large as 20–35 percent. Delamination occurring in the head region of a pressure vessel is identified as the main cause leading to the burst strength degradation, with help of the improved netting analysis. A special FORTRAN program is then developed to incorporate the spacial axisymmetric finite strain FEM approach, and the foregoing presupposition is further confirmed by numerical calculations. Interlaminar shear stresses are found to be the major cause in prompting the observed delaminations. It is argued then that the interlaminar shear strength (ILSS) of a composite should be considered as a fundamental parameter for vessel design and resin selection. Hydrostatic burst test results of glass fiber-wound pressure vessels correlate satisfactorily with this prediction. The best stress equilibrium coefficientK, being closely related to ILSS, is proposed as a proper criterion for resin matrix screening.     

Theoretical and experimental estimates of the brittle strength of solids produced by compaction of powders

The strength characteristics of pressed-powder compacts are obtained. The fractal structure of the compact samples is described. Complex thermal analysis shows that during compaction of dry powders, interatomic interaction is partially restored. Quantitatively estimates of the theoretical strength of the samples are obtained and a possible mechanism for the propagation of flat cracks is proposed. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 5, pp. 208–215, September–October, 1999.     

Application of a gradient approach to estimation of the local strength

Some problems associated with the use of the gradient approach for estimating the local strength are considered. It is shown that a physically unjustified choice of the gradient function in the strength criterion can lead to contradictory results. Institute of Physicotechnical Problems of the North, Siberian Division, Russian Academy of Sciences, Yakutsk 677891. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 222–228, July–August, 1999.     

Critical Stresses in Spalling and Dynamic Rupture of Metals

Results of dynamic rupture tests of a series of metals obtained using a composite Hopkinson bar and shock-wave loading of plane specimens are described. It is shown that the actual rupture strength at a strain rate of 5 · 10³ sec⁻¹ is very close to the spall strength at higher strain rates. Results of testing the same metals using a composite Hopkinson bar within a temperature range of 20–350°C are given. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 103–107, November–December, 2005.     

Experimental study of the strength of composite plates in bending

The strength of composite plates in bending and the effect of the angular parameters at the tips of the joint of the constituents on the strength are studied. An approximate experimental finite-stress curve (λ=1) that separates the low-stress zone from the stress-concentration zone near the angular point of the joint is obtained in the plane of the angles (α, β) by analyzing the photoelastic patterns (isochromatic curves), fracture lines, and rupture moments. A comparison with the theoretical curve obtained from the solution of the corresponding problem is performed. An experimental relation between the strength of the plate and the angular parameters of the constituents is obtained for the stress-concentration and low-stress states near the joint tips. Institute of Mechanics, Armenia National Academy of Sciences, Erevan 375019. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 211–215, July–August, 2000.     

Long-term strength of metals under an equiaxial plane stress state

This paper reports test results suggesting a significant dependence of the long-term strength of metals on the form of the stress state and the method of short-term loading. The experimental data obtained are described using a modification of the kinetic theory of long-term strength containing a vector damage parameter and taking into account strength anisotropy and the damage due to short-term loading. It is shown that the experimental and theoretical values of the time to rupture are in good agreement. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 150–157, July–August, 2009.     

Sharp Gagliardo–Nirenberg Inequalities and Mass Transport Theory

It is known that best constants and extremals of many geometric inequalities can be obtained via the Monge–Kantorovich theory of mass transport. But so far this approach has been successful for a special subclass of the Gagliardo–Nirenberg inequalities, namely, those for which the optimal functions involve only power laws. In this paper, we explore the link between Mass transport theory and all classes of the Gagliardo–Nirenberg inequalities. Sharp constants and optimal functions of all the Gagliardo–Nirenberg inequalities are obtained explicitly in dimension n = 1, and the link between these inequalities and Mass transport theory is discussed.     

A New Device for Mechanical Testing of Blood Vessels at Cryogenic Temperatures

As part of an ongoing program to study the thermo-mechanical effects associated with cryopreservation via vitrification (vitreous in Latin means glassy), the current study focuses on the development of a new device for mechanical testing of blood vessels at cryogenic temperatures. This device is demonstrated on a bovine carotid artery model, permeated with the cryoprotectant cocktail VS55 and a reference solution of 7.05M DMSO, below glass transition. Results are also presented for crystallized specimens, in the absence of cryoprotectants. Results indicate that the elastic modulus of a specimen with no cryoprotectant, at about −140°C (8.6 and 15.5°C below the glass transition temperature of 7.05M DMSO and VS55, respectively), is 1038.8 ± 25.2 MPa, which is 8 and 3% higher than that of a vitrified specimen permeated with 7.05M DMSO and VS55, respectively. The elastic modulus of a crystallized material at −50°C is lower by ∼20% lower from that at −140°C.     

Optimal-contour design for a plane hypersonic engine output unit with account for the boundary layer, length, outer flow, and base end effects

The direct method of solving the variational problem for determining the optimal contour of a jet engine output unit with account for gas viscosity is developed. The optimal contours of two-dimensional output units with account for the boundary layer, length, outer flow, and base end effects are calculated numerically. In particular, the influence of turbulent boundary layers on the shape and thrust of the optimal output unit is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 174–184, July–August, 2000.     

Estimate of the strength of a plate with an elliptic hole in tension and compression

The strength of a plate with an elliptic hole under uniaxial tension or compression is estimated for arbitrary angles between the ellipse axes and the direction of loading with the use of the gradient strength criterion. The calculated critical stress agrees with the existing experimental data. Institute of Physicotechnical Problems of the North, Siberian, Division, Russian Academy of Sciences, Yakutsk 677891. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 163–168, May–June, 2000.     

Optimization of the shape of a wing in a hypersonic nonequilibrium gas flow

A variational technique of obtaining the optimal shape of a low-aspect-ratio wing with allowance for the nonequilibrium character of the flow is developed. The technique is applied to the problem of determining optimal wing shapes under terrestrial atmosphere conditions. The real-gas effect on the optimal shapes and maximum lift-drag ratio is studied. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 160–170, March–April, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 96-01-00629).     

Strength reduction of metals upon hydrogen chemisorption at the tip of a crack

When hydrogen interacts with the freshly formed surface, the interatomic bonds at the tip of a crack in the single crystal of a metal are known to break. The decrease in the brittle strength of the single crystals of metals in the presence of hydrogen in the crack compared with the strength of the same metal in the absence of hydrogen is estimated quantitatively using comparative criteria of brittle strength. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 173–178, May–June, 1998.