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1

On the prognosis of the growth of a heterostructure from a gas phase to analyze the possibility of decreasing mismatch-induced stresses

Pankratov Evgeny L.

Computer Methods in Materials Science

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2021

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Vol. 21, No. 2

105--122

EN

An approach to decreasing mismatch-induced stress in a heterostructure by radiation processing during growth from the gas phase is introduced in this paper. Within the framework of the approach with decreasing mismatch-induced stresses, one can find the acceleration of the recombination and diffusion of radiation defects generated during radiation processing. An analytical approach for analyzing mass and heat transfer is also introduced. The approach provides the opportunity to simultaneously take into account spatial and temporal variations of mass transfer parameters. At the same time, the approach allows the nonlinearity of the considered processes to be taken into account.

2

A model for changing the technological process for the growth of epitaxial layers by means of the heating of the growth zone

Pankratov Evgeny L.

Computer Methods in Materials Science

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2021

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Vol. 21, No. 1

5--12

EN

The nonstationary transfer of heat during epitaxial layer growth in gas phase epitaxy reactors is analyzed within the work. Based on this analysis, several recommendations on the organization of the heating of the growth zone to increase the homogeneity of the epitaxial layers were formulated. An approach to analyze the transfer of heat during epitaxial layer growth from the gas phase is also introduced. The approach leads to the possibility of simultaneously accounting for heat transfer nonlinearity and changes of parameters of heat transfer in both space and time.

3

Designing of Steel CHS Columns Showing Maximum Compression Resistance

Marcinowski Jakub, Sadowski Mirosław

Civil and Environmental Engineering Reports

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2021

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Vol. 31, no. 1

79--92

EN

The paper deals with a shape optimisation procedure of steel, compressed bars. Circular hollow sections (CHS) of variable cross sections and variable wall thickness are taken into account. The proposed procedure for designing of steel rods exhibiting maximum compression resistance is effective and possible to use in engineering practice. The advantage of the proposed shape of the bar is that it allows to increase the value of its load carrying capacity, i.e. it ensures the transfer of a higher value of compressive force than similar, solid struts of the same mass and length. The extent of the increase in the load capacity relative to the load capacity of the reference solid, cylindrical bar depends on the slenderness of the reference bar and ranges from 60% to 170%. Due to this very beneficial fact, it can be used wherever it is required to maintain a certain stiffness and an increased value of compressive force is desired, as well as in constructions where it is necessary to reduce weight while maintaining the adopted mechanical parameters, e.g. values of load bearing capacity. Final results achieved in the research were presented in the form of the flow chart allowing to design the compressed columns of optimum shape.

4

Heave analysis of shallow foundations founded in swelling clayey soil at N’Gaous city in Algeria

Khennouf Abdelaziz, Baheddi Mohamed

Studia Geotechnica et Mechanica

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2020

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Vol. 42, nr 3

210--221

EN

The design of shallow foundations on swelling soils needs a thorough study to evaluate the effect of swelling potential soil on the final foundation heave. For this reason, a simple analytical approach based on the soil stress state under the foundation can be used to calculate the foundation heave. This paper reports a set of analytical and numerical analysis using the finite-difference code (FLAC 3D), performed on an isolated shallow foundation founded on a swelling soil mass at N’Gaous city in Batna Province, Algeria, subjected to distributed vertical loads. Further, the influence of some parameters on total heave was analyzed, such as the embedded foundation and soil stiffness. The analysis results from the proposed 3D modelling was compared and discussed with analytical results. The numerical results obtained show a good agreement with the analytical solutions based on oedometer tests proposed in the literature, and deliver a satisfactory prediction of the heave of the shallow foundations.

5

Using the Erfi function in the problem of the shape optimization of the compressed rod

Marcinowski J., Sadowski M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

75--87

EN

The shape of the optimal rod determined in the work meets the condition of mass conservation in relation to the reference rod. At the same time, this rod shows a significant increase in resistance to axial force. In the examples presented, this increase was 80% and 117%, respectively, for rods with slenderness of 125 and 175. A practical benefit from the use of compression rods of the proposed shapes is clearly visible. The example presented in this publication shows how great the utility in the structural mechanics can be, resulting from the applications of complex analysis (complex numbers). This approach to many problems can find its solutions, while they are lacking in the real numbers domains. What is more, although these are operations on complex numbers, these solutions have often their real representations, as the numerical example shows. There are too few applications of complex numbers in the technique and science, therefore it is obvious that the use of complex analysis should have an increasing range. One of the first people to use complex numbers was Girolamo Cardano. Cardano, using complex numbers, was solving cubic equations, unsolvable to his times – as the famous Franciscan and professor of mathematics Luca Pacioli put it in his paper Summa de arithmetica, geometria, proportioni et proportionalita (1494). It is worth mentioning that history has given Cardano priority in the use of complex numbers, but most probably they were discovered by another professor of mathematics – Scipione del Ferro (cf. [1]). We can see, that already then, they were definitely important (complex numbers).

6

Estimation of speed dependent fault parameters in a coupled rotor-bearing system

Lal M., Satapathy M.

Archive of Mechanical Engineering

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2018

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Vol. LXV, nr 3

327--347

EN

In rotating machineries, misalignment is considered as the second most major cause of failure after unbalance. In this article, model-based multiple fault identiﬁcation technique is presented to estimate speed-dependent coupling misalignment and bearing dynamic parameters in addition with speed independent residual unbalances. For brevity in analysis, a simple coupled rotor bearing system is considered and analytical approach is used to develop the identiﬁcation algorithm. Equations of motion ingeneralized co-ordinates are derived with the help of Lagrange’s equation and least squares ﬁtting approach is used to estimate the speed-dependent fault parameters. Present identiﬁcation algorithm requires independent sets of forced response data which are generated with the help of diﬀerent sets of trial unbalances. To avoid/suppress the ill-conditioning of regression equation, independent sets of forced response data are obtained by rotating the rotor in clock-wise and counter clock-wise directions, alternatively. Robustness of algorithm is checked for diﬀerent levels of measurement noise.

7

Application of reconstruction of variational iteration method on the laminar flow in a porous cylinder with regressing walls

Azimi M., Hedesh A. M., Karimian S.

Mechanics and Mechanical Engineering

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2017

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Vol. 21, nr 2

379--387

EN

A study of an incompressible two-dimensional flow in a channel with one porous wall is presented in this research. As usual, the cylindrical propellant grain of a solid rocket motor is modeled as a long tube with one end closed at the headwall, while the other remains open. The governing continuity and momentum equations together with the associated boundary conditions are first reduced to a set of self similar non-linear coupled ordinary differential equations using similarity transformations. Then we solved the ordinary differential equation by RVIM and the numerical method.

8

New analytical approaches for evaluating the performance of systematic pre-tensioned fully grouted rockbolts in tunnel stabilization

Ranjbarnia M., Fahimifar A., Oreste P.

Archives of Mining Sciences

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2016

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Vol. 61, no. 4

823--852

EN

In this paper, two new analytical approaches are presented on the basis of convergence-confinement method to compute both the ultimate convergence of circular tunnel and its plastic zone having been reinforced by systematically pre-tensioned fully grouted rockbolts. The models have two basic assumptions: (1) the grouted rockbolts increase the radial internal pressure within a broken rock mass by both the pre-tensioned force and the probable following induced force due to rock mass movement (2) tunnel convergence (specially short-term) occurs only due to reducing and diminishing of the radial constrained stress on tunnel surface provided by the working face. Hence, the values of both the pre-tensioned pressure and the mentioned radial constrained stress are specially taken into consideration in this paper. That is, according to their magnitudes, two different conditions occur: the magnitude of pre-tensioned pressure is greater than that of the constrained stress at bolt installation time and vice versa. The solutions are extended to each of conditions, and illustrative examples are solved. The proposed approaches predicting almost identical results show that pre-tensioning of grouted rockbolts will increase the efficiency and effectiveness of rockbolts.

PL

W pracy tej przedstawiono dwie analityczne metody oparte na metodzie badania konwergencji i naprężeń wymuszonych wykorzystane do obliczania zarówno granicznej konwergencji tunelu o przekroju koła oraz zachowania strefy plastycznej, po wzmocnieniu tunelu za pomocą wstępnie naprężanych i zacementowanych kotew. Model opiera się dwóch założeniach: (1) zacementowane kotwy prowadzą do wzrostu ciśnienia wewnętrznego w kierunku promieniowym w kruszonym materiale skalnym, spowodowanego siłą wstępnego naprężenia oraz siłą spowodowaną przez ruchy górotworu; (2) – konwergencja tunelu (zwłaszcza w ujęciu krótkoterminowym) pojawia się jedynie wskutek zmniejszenia wymuszonego naprężenia promieniowego na powierzchni tunelu generowanego w rejonie przodka wydobywczego. W metodzie zwrócono szczególną uwagę na wartości ciśnienia wstępnego naprężenia jak i naprężenia wymuszonego. W zależności od wielkości tych naprężeń mamy do czynienia z dwiema zupełnie odmiennym sytuacjami: wielkość ciśnienia wstępnego naprężenia jest większa niż naprężenia wymuszonego w trakcie mocowania kotew, lub odwrotnie. Podano rozwiązania dla obydwu rozważanych przypadków i zaprezentowano przykłady. Prawie identyczne wyniki otrzymane przy użyciu obydwu metod wskazują, że wstępne naprężenia cementowanych kotew poprawia ich skuteczność działania.

9

An analytical approach for bending and stress analysis of cross/angle-ply laminated composite plates under arbitrary non-uniform loads and elastic foundations

Alipour M. M.

Archives of Civil and Mechanical Engineering

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2016

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Vol. 16, no. 2

193--210

EN

In the present study, a new analytical approach is developed for bending and stress analysis of angle-ply laminated composite and sandwich plates subjected to arbitrary non-uniform loads. Governing equations are derived based on the Mindlin–Reissner plate theory. For the first time, a system of three second order coupled partial differential equations is analytically solved by using power-series solution. The transverse shear stress is determined based on the three-dimensional theory of elasticity. Most of the available analytical solutions of the rectangular plates were presented for specific load and edge conditions. The proposed method can be applied for plates with arbitrary boundary conditions and various distributed loads. To demonstrate the generality and accuracy of the present method, comprehensive numerical examples are presented and compared with other available published results. The results show that the proposed solution can be applied for analysis of cross/angle-ply laminated composite and sandwich plates with various combinations of the edge conditions, orientation angle of the laminated composite plate, arbitrary non-uniform transversely distributed loads and non-uniform elastic foundation. The proposed method predicts excellent results for laminated composite plates. Also even for moderately thick sandwich plates, accuracy of the present results are in a good agreement with the exact solutions.

10

Reliability assessment of an exemplary system operating at variable conditions

Kołowrocki K., Kuligowska E., Soszyńska-Budny J.

Journal of Polish Safety and Reliability Association

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2015

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Vol. 6, No. 1

129--137

EN

The reliability analysis of a multistate complex system subjected to varying in time its operation process is performed. A semi-Markov process is applied to construct the multistate model of the system operation process and its main characteristics are determined. Analytical linking of the system operation process model with the system multistate reliability model is proposed to get a general reliability model of the complex system operating at varying in time operation conditions and to find its reliability characteristics. The constructed integrated general model of a complex multistate system reliability, linking its reliability model and its operation process model and considering variable at different operation states its reliability structure and its components reliability parameters is applied to the reliability evaluation of an exemplary system.

11

Flow Modeling in a Porous Cylinder with Regressing Walls Using Semi Analytical Approach

Azimi M., Hedesh A. M., Karimian S.

Mechanics and Mechanical Engineering

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2014

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Vol. 18, nr 2

77--84

EN

In this paper, the mathematical modeling of the flow in a porous cylinder with a focus on applications to solid rocket motors is presented. As usual, the cylindrical propellant grain of a solid rocket motor is modeled as a long tube with one end closed at the headwall, while the other remains open. The cylindrical wall is assumed to be permeable so as to simulate the propellant burning and normal gas injection. At first, the problem description and formulation are considered. The Navier–Stokes equations for the viscous flow in a porous cylinder with regressing walls are reduced to a nonlinear ODE by using a similarity transformation in time and space. Application of Differential Transformation Method (DTM) as an approximate analytical method has been successfully applied. Finally the results have been presented for various cases.

12

Analysis of system operation process influence on its reliability

Kuligowska E.

Journal of Polish Safety and Reliability Association

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2014

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Vol. 5, No. 1

125--135

EN

The paper presents analytical and Monte Carlo simulation methods applied to the reliability evaluation of a system operating in two different operation states. A semi-Markov process is applied to construct the system operation model and its main characteristics are determined. Analytical linking of this operation model with the system reliability model is proposed to get a general reliability model of the system operating at two varying in time operation conditions and to find its reliability characteristics. The application of Monte Carlo simulation based on this general model to the reliability evaluation of this system is proposed as well. The exemplary results obtained from those two considered methods are illustrated.

13

Flow modeling in a jet engine

Hlavńa V., Rajčan P.

Journal of KONES

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2010

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Vol. 17, No. 4

191-197

EN

It is possible to monitor effects related to flow in a jet aircraft engine by the three basic approaches - analytical, numerical and experimental Each approach has undergone changes and has been developed to the stage of its effective use. To efficiently manage the scientific and research work it is appropriate to use effective links among all three basic approaches. An experimental approach requires a test stand on which the characteristics of a usually geometrically reduced object or the actual object itself are verified. The principles of geometric and hydrodynamic similarities are applied. This approach is time and economically demanding and not all aerodynamic processes can be reliably simulated. Other disaavantages can be the occurrence of measurement errors, errors due to changes in the scale, influences of chemical reactions and influence of Reynolds number. Due to a very fast onset, development and challenges of IT, the numerical approach has become mostly used. It can provide sufficient information on an examined phenomenon in a particular object. It does not need any substantial simpliflcations, it is less financially demanding than the experimental approach, but it needs efficient processors with a huge memory capacity. Its disadvantage is a relatively large dependence of achieved results accuracy on the perfection of numerical models and models of turbulence in the areas with prevailing influence ofviscosity. The usage ofanalytical relations from mathematical andphysical analysis of the flow fleld is the fundamental of the analytical approach of observing the laws related to flowing. The paper deals with possibilities, procedures, advantages, and disadvantages of the mentioned approaches together with a presentation of some results from research and development activities carried out by the authors.

14

Thermal stresses in a single elastic fiber embedded in an infinite matrix

Esparragoza I. E., Levy C., Caudill N. E.

International Journal of Applied Mechanics and Engineering

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2006

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Vol. 11, no 3

577-591

EN

In this work, an analytical solution of the thermal stresses for a fiber embedded in a matrix is presented based on the idea of the boundary layer and under some simplifying assumptions. These assumptions include: the properties of both materials, fiber and matrix, remain constant; both materials remain in the elastic range so no plastic-deformation are considered; there exists a perfect bonding between the fiber and matrix so the condition of no-opening holds over the entire interface; and the composite is subjected to an uniform change of temperature. The analytical solution to the problem is found for the case when the length of the embedded bar (fiber) is much greater than its radius, and the Young's modulus of the matrix is much less than that of the fiber. The problem is also solved numerically by means of finite element analysis using a commercial package. Both results are compared and it is shown that both approaches coincide very close qualitatively and quantitatively although significant discrepancies may appear at specific points for specific cases.