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Abstract

Author explains a necessity of supply optimization to construction sites with small storage areas. This paper takes account of conditions existing in Poland. From among all factors discussed by the author, first of all, we should point at construction works on plots located in densely built-up areas, obtained by demolition of existing buildings, as well as a necessity of plots utilization after demolished buildings that technical conditions do not allow for further exploitation.

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Authors and Affiliations

K.M. Kaczorek
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Abstract

The aim of the presented paper is to show the results of shape optimization of railway polynomial transition curves (TCs) of 5th, 7th, and 9th degrees through the use of the full vehicle model and new criteria of assessement concerning the jerk value. The search for the proper shape of TCs means that in this work, the evaluation of TC properties is based on select quantities and the generation of such a shape through the use of mathematically understood optimization methods. The studies presented have got a character of the numerical tests. For this work, advanced vehicle models describing dynamical track-vehicle and vehicle-passenger interactions as well as optimization methods were exploited. In the software vehicle model of a 2-axle freight car, the track discrete model, non-linear descriptions of wheel-rail contact are applied. This part of the software, the vehicle simulation software, is combined with a library optimization procedure into the final computer program.

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Authors and Affiliations

K. Zboiński
P. Woznica
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Abstract

This paper presents a model of scheduling of multi unit construction project based on an NP-hard permutation flow shop problem, in which the considered criterion is the sum of the costs of the works' execution of the project considering the time of the project as a constraint. It is also assumed that each job in the units constituting the project may be realized in up to three different ways with specific time and cost of execution. The optimization task relies on solving the problem with two different decision variables: the order of execution of units (permutation) and a set of ways to carry out the works in units. The task presented in the paper is performed with the use of a created algorithm which searches the space of solutions in which metaheuristic simulated annealing algorithm is used. The paper presents a calculation example showing the applicability of the model in the optimization of sub-contractors' work in the construction project.

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Authors and Affiliations

M. Podolski
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Abstract

The present study has been taken up to emphasize the role of the hybridization process for optimizing a given reinforced concrete (RC) frame. Although various primary techniques have been hybrid in the past with varying degree of success, the effect of hybridization of enhanced versions of standard optimization techniques has found little attention. The focus of the current study is to see if it is possible to maintain and carry the positive effects of enhanced versions of two different techniques while using their hybrid algorithms. For this purpose, enhanced versions of standard particle swarm optimization (PSO) and a standard gravitational search algorithm (GSA), were considered for optimizing an RC frame. The enhanced version of PSO involves its democratization by considering all good and bad experiences of the particles, whereas the enhanced version of the GSA is made self-adaptive by considering a specific range for certain parameters, like the gravitational constant and a set of agents with the best fitness values. The optimization process, being iterative in nature, has been coded in C++. The analysis and design procedure is based on the specifications of Indian codes. Two distinct advantages of enhanced versions of standard PSO and GSA, namely, better capability to escape from local optima and a faster convergence rate, have been tested for the hybrid algorithm. The entire formulation for optimal cost design of a frame includes the cost of beams and columns. The variables of each element of structural frame have been considered as continuous and rounded off appropriately to consider practical limitations. An example has also been considered to emphasize the validity of this optimum design procedure.

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Authors and Affiliations

Sonia Chutani
Jagbir Singh
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Abstract

The aim of this study is to find the cost design of RC tension with varying conditions using the Artificial Neural Network. Design constraints were used to cover all reliable design parameters, such as limiting cross sectional dimensions and; their reinforcement ratio and even the beahviour of optimally designed sections. The design of the RC tension members were made using Indian and European standard specifications which were discussed. The designed tension members according to both codes satisfy the strength and serviceability criteria. While no literature is available on the optimal design of RC tension members, the cross-sectional dimensions of the tension membersfor different grades of concrete and steel, and area of formwork are considered as the variables in the present optimum design model. A design example is explained and the results are presented. It is concluded that the proposed optimum design model yields rational, reliable, and practical designs.

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Authors and Affiliations

N. Karthiga Shenbagam
N. Arunachalam
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Abstract

Games are among problems that can be reduced to optimization, for which one of the most universal and productive solving method is a heuristic approach. In this article we present results of benchmark tests on using 5 heuristic methods to solve a physical model of the darts game. Discussion of the scores and conclusions from the research have shown that application of heuristic methods can simulate artificial intelligence as a regular player with very good results.
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Authors and Affiliations

Kamil Książek
Dawid Połap
Marcin Woźniak
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Abstract

This paper proposes a power system stabilizer (PSS) with optimal controller parameters for damping low-frequency power oscillations in the power system. A novel meta-heuristic, weighted grey wolf optimizer (WGWO) has been proposed, it is a variant of the grey wolf optimizer (GWO). The proposed WGWO algorithm has been executed in the selection of controller parameters of a PSS in a multi-area power system. A two-area fourmachine test system has been considered for the performance evaluation of an optimally tuned PSS. A multi-objective function based on system eigenvalues has been minimized for obtained optimal controller parameters. The damping characteristics and eigenvalue location in the proposed approach have been compared with the other state-of-the-art methods, which illustrates the effectiveness of the proposed approach.
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Authors and Affiliations

Murali Krishna Gude
1
ORCID: ORCID
Umme Salma Salma
1
ORCID: ORCID

  1. Gandhi Institute of Technology and Management (GITAM), Visakhapatnam, India
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Abstract

In the paper the new paradigm for structural optimization without volume constraint is presented. Since the problem of stiffest design (compliance minimization) has no solution without additional assumptions, usually the volume of the material in the design domain is limited. The biomimetic approach, based on trabecular bone remodeling phenomenon is used to eliminate the volume constraint from the topology optimization procedure. Instead of the volume constraint, the Lagrange multiplier is assumed to have a constant value during the whole optimization procedure. Well known MATLAB topology based optimization code, developed by Ole Sigmund, was used as a tool for the new approach testing. The code was modified and the comparison of the original and the modified optimization algorithm is also presented. With the use of the new optimization paradigm, it is possible to minimize the compliance by obtaining different topologies for different materials. It is also possible to obtain different topologies for different load magnitudes. Both features of the presented approach are crucial for the design of lightweight structures, allowing the actual weight of the structure to be minimized. The final volume is not assumed at the beginning of the optimization process (no material volume constraint), but depends on the material’s properties and the forces acting upon the structure. The cantilever beam example, the classical problem in topology optimization is used to illustrate the presented approach.
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Bibliography

  1.  W. Wang et al., “Space-time topology optimization for additive manufacturing”, Struct. Multidiscip. Optim., vol. 61, no. 1, pp. 1‒18, 2020, doi: 10.1007/s00158-019-02420-6.
  2.  Y. Saadlaoui, et al., “Topology optimization and additive manufacturing: Comparison of conception methods using industrial codes”, J. Manuf. Syst., vol. 43, pp. 178‒286, 2017, doi: 10.1016/j.jmsy.2017.03.006.
  3.  J. Zhu, et al., “A review of topology optimization for additive manufacturing: Status and challenges”, Chin. J. Aeronaut., vol. 34, no. 1, pp. 9‒110, 2021, doi: 10.1016/j.cja.2020.09.020.
  4.  O. Sigmund, “A 99 line topology optimization code written in Matlab”, Struct. Multidiscip. Optim., vol. 21, no. 2, pp. 120‒127, 2001, doi: 10.1007/s001580050176.
  5.  M. Bendsoe and O. Sigmund, Topology optimization. Theory, methods and applications, Berlin Heidelberg New York, Springer, 2003, doi: 10.1007/978-3-662-05086-6.
  6.  M. Bendsoe and N. Kikuchi, “Generating optimal topologies in structural design using a homogenization method”, Comput. Methods Appl. Mech. Eng., vol. 71, pp. 197‒224, 1988.
  7.  O. Sigmund and K. Maute, “Topology optimization approaches”, Struct. Multidiscip. Optim., vol. 48, pp. 1031‒1055, 2013, doi: 10.1007/ s00158‒013‒0978‒6.
  8.  Z. Ming and R. Fleury, “Fail-safe topology optimization”, Struct. Multidiscip. Optim., vol. 54, no. 5, pp. 1225‒1243, 2016, doi: 10.1007/ s00158-016-1507-1.
  9.  L. Krog et al., “Topology optimization of aircraft wing box ribs”, AIAA Paper, 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Albany, New York, 2004, doi: 10.2514/6.2004-4481.
  10.  Z. Luo et al., “A new procedure for aerodynamic missile designs using topological optimization approach of continuum structures”, Aerosp. Sci. Technol., vol. 10, pp. 364‒373, 2006, doi: 10.1016/j.ast.2005.12.006.
  11.  M. Zhou et al., “Industrial application of topology optimization for combined conductive and convective heat transfer problems”, Struct. Multidiscip. Optim., vol. 54, no 4, pp. 1045‒1060, 2016, doi: 10.1007/s00158-016-1433-2.
  12.  G. Allaire et al., “The homogenization method for topology optimization of structures: old and new”, Interdiscip. Inf. Sci., vol.25/2, pp. 75‒146, 2019, doi: 10.4036/iis.2019.B.01.
  13.  G. Allaire and R.V. Kohn, “Topology Optimization and Optimal Shape Design Using Homogenization”, Topology Design of Structures. NATO ASI Series – Series E: Applied Sciences, M. Bendsoe, C. Soares – eds., vol. 227, pp. 207‒218, 1993, doi: 10.1007/978-94-011- 1804-0_14.
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  23.  M. Nowak, J. Sokołowski, and A. Żochowski, “Biomimetic approach to compliance optimization and multiple load cases”, J. Optim. Theory Appl., vol. 184, no. 1, pp. 210‒225, 2020, doi: 10.1007/s10957-019-01502-1.
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Authors and Affiliations

Michał Nowak
1
ORCID: ORCID
Aron Boguszewski
1

  1. Poznan University of Technology, Division of Virtual Engineering, ul. Jana Pawła II 24, 60-965 Poznań, Poland
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Abstract

In the paper an approach to decision making in situations with non-point-like characterisation and subjective evaluation of the actions is considered. The decision situation is represented mathematically as fuzzy multiobjective linear programming (fMOLP) model, where we apply the reduced fuzzy matrices instead of fuzzy classical numbers. The fMOLP model with reduced parameters is decomposable into the set of point-like models and the point-like models enable effective construction of an optimisation procedure – fBIP, see Wojewnik (2006ab), extending the bireference procedure by Michalowski and Szapiro (1992). The approach is applied to a fuzzy optimization problem in the area of telecommunication services.

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Authors and Affiliations

Piotr Wojewnik
Tomasz Szapiro
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Abstract

This paper presents a new modified method for the synthesis of non-uniform linear antenna arrays. Based on the recently developed invasive weeds optimization technique (IWO), the modified invasive weeds optimization method (MIWO) uses the mutation process for the calculation of standard deviation (SD). Since the good choice of SD is particularly important in such algorithm, MIWO uses new values of this parameter to optimize the spacing between the array elements, which can improve the overall efficiency of the classical IWO method in terms of side lobe level (SLL) suppression and nulls control. Numerical examples are presented and compared to the existing array designs found in the literature, such as ant colony optimization (ACO), particle swarm optimization (PSO), and comprehensive learning PSO (CLPSO). Results show that MIWO method can be a good alternative in the design of non-uniform linear antenna array.
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Authors and Affiliations

El Hadi Kenane
Farid Djahli
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Abstract

In order to overcome the shortcomings of the dolphin algorithm, which is prone to falling into local optimum and premature convergence, an improved dolphin swarm algorithm, based on the standard dolphin algorithm, was proposed. As a measure of uncertainty, information entropy was used to measure the search stage in the dolphin swarm algorithm. Adaptive step size parameters and dynamic balance factors were introduced to correlate the search step size with the number of iterations and fitness, and to perform adaptive adjustment of the algorithm. Simulation experiments show that, comparing with the basic algorithm and other algorithms, the improved dolphin swarm algorithm is feasible and effective.

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Authors and Affiliations

Y. Li
X. Wang
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Abstract

In this paper, the energy losses in big band saw machines are investigated. These losses are caused by the geometric and angular inaccuracies with which the leading wheels are made. Expressions for calculating the kinetic energy of the mechanical system in the ideal and the real cases are obtained. For this purpose, expressions for calculating the velocities of the centers of the masses in two mutually perpendicular planes are obtained. A dependence for calculation of the kinetic energy losses of the mechanical system in final form is received. Optimization procedure is used to determine the values of the parameters at which these losses have minimum values. The proposed study can be used to minimize energy losses in other classes of woodworking machines.

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Bibliography

[1] M. Sarwar, M. Persson, H. Hellbergh, and J. Haider. Measurement of specific cutting energy for evaluating the efficiency of band sawing different workpiece materials. International Journal of Machine Tools and Manufacture, 49(11-12):958–965, 2009. doi: 10.1016/j.ijmachtools.2009.06.008.
[2] M. Mandic, S. Svrzic, and G. Danon. The comparative analysis of two methods for the power consumption measurement in circular saw cutting of laminated particle board. Wood Research, 60(1):125–136, 2015.
[3] Z. Kopecký, L. Hlaskova, and K. Orlowski. An innovative approach to prediction energetic effects of wood cutting process with circular-saw blades. Wood Research, 59(5):827–834, 2014.
[4] K. Orlowski, T. Ochrymiuk, A. Atkins, and D. Chuchala. Application of fracture mechanics for energetic effects predictions while wood sawing. Wood Science and Technology, 47(5):949–963, 2013. doi: 10.1007/s00226-013-0551-x.
[5] P. Iskra, C. Tanaka, and T. Ohtani. Energy balance of the orthogonal cutting process. Holz Als Roh- und Werkstoff, 63:358–364, 2005. doi: 10.1007/s00107-005-0021-8.
[6] P. Obreshkov. Woodworking Machines. Publishing House ``BM'', 1995. (in Bulgarian).
[7] A. Pisarev, Ts. Paraskov, and C. Bachvarov. Course in Theoretical Mechanics. Second part – Dynamics. State Publishing House Technics, 1988. (in Bulgarian).
[8] R.M. Dreizler, and C.S. Lüdde. Theoretical Mechanics: Theoretical Physics 1. Springer, Berlin, Heidelberg, 2010. doi: 10.1007/978-3-642-11138-9.
[9] F. Scheck. Mechanics. From Newton's Laws to Deterministic Chaos. 5th edition, Springer, Berlin, Heidelberg, 2010.
[10] B. Marinov. Dynamic and Shock Processes in Some Classes of Woodworking Machines. Analysis and Optimization. Omniscriptum Publishing Group-Germany/LAP LAMBERT Academic Publishing, 2018.
[11] B. Cheshankov. Theory of the Vibrations. Publishing House in TU, 1992. (in Bulgarian).
[12] B. Marinov. Spatial deformations in the transmissions of certain classes of woodworking machines. Mechanism and Machine Theory, 82:1–16, 2014. doi: 10.1016/j.mechmachtheory.2014.07.010.
[13] Zh. Gochev. Handbook for Exercise of Wood Cutting and Woodworking Tools. Publishing House in LTU, 2005. (in Bulgarian).
[14] Yo. Tonchev. Matlab, Part 3. Publishing House Technique, 2009. (in Bulgarian).
[15] R. Peters. Band Saw Fundamentals: The Complete Guide. Hearst Communications Inc, 2006.
[16] L. Bird. The Bandsaw Book. Taunton Press Inc, 2000.
[17] W. Turner. A Comprehensive Handbook on Uses and Applications of the Band Saw and Jig Saw. Literary Licensing LLC, 2013.
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Authors and Affiliations

Boycho Marinov
1

  1. The Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria.
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Abstract

The problem that this paper investigates, namely, optimization of overlay computing systems, follows naturally from growing need for effective processing and consequently, fast development of various distributed systems. We consider an overlay-based computing system, i.e., a virtual computing system is deployed on the top of an existing physical network (e.g., Internet) providing connectivity between computing nodes. The main motivation behind the overlay concept is simple provision of network functionalities (e.g., diversity, flexibility, manageability) in a relatively cost-effective way as well as regardless of physical and logical structure of underlying networks. The workflow of tasks processed in the computing system assumes that there are many sources of input data and many destinations of output data, i.e., many-to-many transmissions are used in the system. The addressed optimization problem is formulatedin the form of an ILP (Integer Linear Programing) model. Since the model is computationally demanding and NP-complete, besides the branch-and-bound algorithm included in the CPLEX solver, we propose additional cut inequalities. Moreover, we present and test two effective heuristic algorithms: tabu search and greedy. Both methods yield satisfactory results close to optimal.
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Authors and Affiliations

Krzysztof Walkowiak
Andrzej Kasprzak
Karol Andrusieczko
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Abstract

The multicriteria decision process consists of five main steps: definition of the optimisation problem, determination of the weight structure of the decision criteria, design of the evaluation matrix, selection of the optimal evaluation method and ranking of solutions. It is often difficult to obtain the optimal solution to a multicriterion problem. The main reason is the subjective element of the model – the weight functions of the decision criteria. Expert opinions are usually taken into account in their determination. The aim of this article is to present a novel method of minimizing the uncertainty of the weights of the decision criteria using Monte Carlo simulation and method of data reconciliation. The proposed method is illustrated by the example of multicriterion social effectiveness evaluation for electric power supply to a building using renewable energy sources.
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Authors and Affiliations

Barbara Mendecka
Joachim Kozioł
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Abstract

Organic Rankine cycle (ORC) is used, amongst the others, in geothermal facilities, in waste heat recovery or in domestic combined heat and power (CHP) generation. The paper presents optimization of an idealized ORC equivalent of the Carnot cycle with non-zero temperature difference in heat exchangers and with energy dissipation caused by the viscous fluid flow. In this analysis the amount of heat outgoing from the ORC is given. Such a case corresponds to the application of an ORC in domestic CHP. This assumption is different from the most of ORC models where the incoming amount of heat is given.

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Authors and Affiliations

Jarosław Mikielewicz
Witold Rybiński
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Abstract

Within the boundaries of many municipal urbanized areas, large grounds are found, from which the noise is emitted into the environment, surrounded by the regions liable to acoustic protection. Such a condition generates many problems including also those ones related to the lack of the fulfillment of requirements concerning environmental protection against excessive noise. Therefore the aim of vital importance is the proper management of municipal grounds, both in view of the investment in policy steering, especially of new investments, and in the case of activities aimed at maintaining or restoring (revitalizing) the acoustic properties on the grounds that have already been used or simply degraded before.

Keeping the scale of the problem in mind, such activities must be carried on not temporarily, but must have a systemic character. The structure of every system is characterized by the appropriate relationships among their elements and the properties of those relationships. In case of the noise management system, the elements of such a system are the activities connected with the management itself that are the actions which rely on specifying the aims and causing their realization within the scope and on the grounds subject to the managing entity. The superior aim of such activities should be to supply the tools for improvement of management and in the process of taking decisions that relate to investments including the of optimization conditions and maintenance of socio-economic importance of such areas.

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Authors and Affiliations

Janusz Kompała
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Abstract

This paper presents a new strategy for optimal placement of multi-type FACTS devices with a view to minimize losses besides enhancing the voltage profile using biogeography based optimization. The strategy places three types of FACTS devices that include static VAR compensator, thyristor controlled series compensator and unified power flow controller; and offers optimal locations for placement, type and parameters of the FACTS devices. Test results on IEEE 14, 30 and 57 bus systems reveal the superiority of the algorithm.

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Authors and Affiliations

A. Subramanian
G. Ravi
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Abstract

The 802.11ax standard final specification is expected in 2019, however first parameters are just released. The target of the new standard is four times improvement of the average throughput within the given area. This standard is dedicated for usage in dense environment such as stadiums, means of municipal communication, conference halls and others. The main target is to support many users at the same time with the single access point. The question arises if the new standard will have higher throughput then previous ones in the single user mode. The author calculated the maximal theoretical throughput of the 802.11ax standard and compared the results with the throughput of older 802.11 standards such as 802.11n and 802.11ac. The new he-wifi-network example included in the ns-3.27 release of the NS-3 simulator was used to simulate the throughput between the access point and the user terminal. The results indicate that in some conditions the 802.11ac standard has higher throughput than the new 802.11ax standard.

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Authors and Affiliations

Antoni Masiukiewicz
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Abstract

This paper presents the idea of increasing the effectiveness of slag decopperisation in an electric furnace in the "Głogów II" Copper Smelter by replacing the currently added CaCO3with a less energy-intensive technological additive. As a result of this conversion, one may expect improved parameters of the process, including process time or power consumption per cycle. The incentives to optimize the process are the benefits of increasing copper production in the company and the growing global demand for this metal. The paper also describes other factors that may have a significant impact on the optimization of the copper production process. Based on the literature analysis, a solution has been developed that improves the copper production process. The benefits of using a new technology additive primarily include increased share of copper in the alloy, reduced production costs, reduced amount of power consumed per cycle and reduced time it takes to melt. At the conclusion of the paper, the issues raised are highlighted, stressing that mastering the slag slurry process in electric furnaces requires continuous improvement.

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Authors and Affiliations

M. Wędrychowicz
W. Wołczyński
A.W. Bydałek
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Abstract

This article considers Steven Pinker’s recent outlook presented in his book Enlightenment Now. The Case for Reason, Science, Humanism and Progress. The paper discusses not only current political and philosophical Pinker’s views on a considerable number of evidences in favor of mankind’s progress in the last period. The authors claims that Pinker’s views may serve as an antidote to the contemporary pessimism that is being spread inter alia by mass media. The reader is pulled into a debate regarding issues surrounding the contemporary state of being of the human race. This is something more than just pop-scientific excursion of a well-established specialist beyond his area of expertise, but a valuable aggregate of data enticing also to professionals from the realm of sociology, philosophy and politics. Above all Pinker’s voice should be regarded as a counterbalance to all-pervasive pejorism and however momentary relief.

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Authors and Affiliations

Paweł Dziedziul
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Abstract

The demand for energy on a global scale increases day by day. Unlike renewable energy sources, fossil fuels have limited reserves and meet most of the world’s energy needs despite their adverse environmental effects. This study presents a new forecast strategy, including an optimization-based S-curve approach for coal consumption in Turkey. For this approach, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), and Whale Optimization Algorithm (WOA) are among the meta-heuristic optimization techniques used to determine the optimum parameters of the S-curve. In addition, these algorithms and Artificial Neural Network (ANN) have also been used to estimate coal consumption. In evaluating coal consumption with ANN, energy and economic parameters such as installed capacity, gross generation, net electric consumption, import, export, and population energy are used for input parameters. In ANN modeling, the Feed Forward Multilayer Perceptron Network structure was used, and Levenberg-Marquardt Back Propagation has used to perform network training. S-curves have been calculated using optimization, and their performance in predicting coal consumption has been evaluated statistically. The findings reveal that the optimization-based S-curve approach gives higher accuracy than ANN in solving the presented problem. The statistical results calculated by the GWO have higher accuracy than the PSO, WOA, and GA with R 2 = 0.9881, RE = 0.011, RMSE = 1.079, MAE = 1.3584, and STD = 1.5187. The novelty of this study, the presented methodology does not need more input parameters for analysis. Therefore, it can be easily used with high accuracy to estimate coal consumption within other countries with an increasing trend in coal consumption, such as Turkey.
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Authors and Affiliations

Mustafa Seker
1
ORCID: ORCID
Neslihan Unal Kartal
2
Selin Karadirek
3
Cevdet Bertan Gulludag
3

  1. Sivas Cumhuriyet University, Turkey
  2. Burdur Mehmet Akif Ersoy University, Turkey
  3. Akdeniz University, Antalya, Turkey
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Abstract

This research deals with the development of an optimization system to minimize employee noise exposure in the work environment. It is known from the literature that continuous exposure to high noise levels can cause heart overload, stress, fatigue, and increase accident numbers at a production line. Thus, it is necessary to develop acoustic solutions at an industrial level that could minimize failures and accident occurrences. The rules that regulate occupational noise exposures allow an assessment of the degrees of exposure and subsequent corrections of working conditions. It is observed that the exposure is necessary for further evaluation and correction. Therefore, this research proposes to simulate occupational noise exposure conditions through mathematical models implemented in C++, using the GUROBI linear optimization package and to act previously to minimize ONIHL (Occupational Noise-Induced Hearing Loss). One of this work results is based on Doses Values, TWA (Time Weighted Average) and Distances Covered, using these three factors simultaneously through the optimization, it obtains a route that minimizes exposure and avoids ONIHL. Although there is a need for balanced doses between employees, to this end, the Designation Problem was implemented. Thus, with the routes obtained by optimization, an efficient allocation task was made for the maintenance crew, resulting in minimized and balanced doses. This model was applied to a real industrial plant that will not be identified, only methodology and results obtained will be presented.
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Authors and Affiliations

Déborah Reis
1
João Miranda
1
Jorge Reis
1
Marcus Duarte
1

  1. Department of Mechanics, Faculty of Mechanical Engineering, UFU Universidade Federal de Uberlândia, Uberlândia, Brazil

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