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  1. 18 Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej
  2. 18 Scientific Research of the Institute of Mathematics and Computer Science
  3. 14 Journal of Applied Mathematics and Computational Mechanics
  4. 13 Archives of Foundry Engineering
  5. 3 Applied Computer Science
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  1. 69 Kukla S.
  2. 12 Siedlecka U.
  3. 9 Zamojska I.
  4. 7 Szewczyk M.
  5. 5 Zamorska I.
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  1. 1 2018
  2. 3 2017
  3. 6 2016
  4. 3 2015
  5. 8 2014
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1
Content available Fractional heat conduction in a sphere under mathematical and physical Robin conditions
Kukla S., Siedlecka U.
Journal of Theoretical and Applied Mechanics
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2018
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Vol. 56 nr 2
339--349
EN
In this paper, the effect of a fractional order of time-derivatives occurring in fractional heat conduction models on the temperature distribution in a composite sphere is investigated. The research concerns heat conduction in a sphere consisting of a solid sphere and a spherical layer which are in perfect thermal contact. The solution of the problem with a classical Robin boundary condition and continuity conditions at the interface in an analytical form has been derived. The fractional heat conduction is governed by the heat conduction equation with the Caputo time-derivative, a Robin boundary condition and a heat flux continuity condition with the Riemann-Liouville derivative. The solution of the problem of non-local heat conduction by using the Laplace transform technique has been determined, and the temperature distribution in the sphere by using a method of numerical inversion of the Laplace transforms has been obtained.
2
Content available An analytical solution to the problem of time-fractional heat conduction in a composite sphere
Kukla S., Siedlecka U.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2017
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Vol. 65, nr 2
179--186
EN
An analytical solution to the problem of time-fractional heat conduction in a sphere consisting of an inner solid sphere and concentric spherical layers is presented. In the heat conduction equation, the Caputo time-derivative of fractional order and the Robin boundary condition at the outer surface of the sphere are assumed. The spherical layers are characterized by different material properties and perfect thermal contact is assumed between the layers. The analytical solution to the problem of heat conduction in the sphere for time-dependent surrounding temperature and for time-space-dependent volumetric heat source is derived. Numerical examples are presented to show the effect of the harmonically varying intensity of the heat source and the harmonically varying surrounding temperature on the temperature in the sphere for different orders of the Caputo time-derivative.
3
Content available Improving Quality and Occupational Safety on Automated Casting Lines
Kukla S.
Archives of Foundry Engineering
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2017
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Vol. 17, iss. 3
69--72
EN
The paper presents a practical example of improving quality and occupational safety on automated casting lines. Working conditions on the line of box moulding with horizontal mould split were analysed due to low degree of automation at the stage of cores or filters installation as well as spheroidizing mortar dosing. A simulation analysis was carried out, which was related to the grounds of introducing an automatic mortar dispenser to the mould. To carry out the research, a simulation model of a line in universal Arena software for modelling and simulation of manufacturing systems by Rockwell Software Inc. was created. A simulation experiment was carried out on a model in order to determine basic parameters of the working system. Organization and working conditions in other sections of the line were also analysed, paying particular attention to quality, ergonomics and occupational safety. Ergonomics analysis was carried out on manual cores installation workplace and filters installation workplace, and changes to these workplaces were suggested in order to eliminate actions being unnecessary and onerous for employees.
4
Content available A Simulation Experiment and Multi-Criteria Assessment of Manufacturing Process Flow Variants Tested on a Computer Model
Kukla S., Smetana M.
Applied Computer Science
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2017
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Vol. 13, no 2
72--81
EN
The article presents issues relating to designing and improvement of manufacturing processes based on a modelling and simulation method. The 3D model of a production line has been designed and simulation experiment, conducted on the Arena model prepared in a versatile package for modelling and simulation of manufacturing systems and representing functioning of the system, has been carried out. The results obtained from the experiment and analyses of time and ergonomics of work at a work station were subject to multi-criteria assessment based on a point-by-point method of assessment according to Yager.
5
Content available An approach to free vibration analysis of axially graded beams
Kukla S., Rychlewska J.
Journal of Theoretical and Applied Mechanics
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2016
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Vol. 54 nr 3
859--870
EN
In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.
6
Content available Vibration analysis of composite circular and annular membranes
Siedlecka U., Zamorska I., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
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2016
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Vol. 15, nr 1
149--159
EN
In this paper a solution to the free vibration problem of composite circular and annular membranes is presented. The vibrations of membranes whose material densities and/or thicknesses varied step-wise with the radial co-ordinate are considered. This approach is applied to approximate the solution to the vibration problem of a membrane with continuously varying density and/or thickness with the radial co-ordinate. The obtained analytical solutions are used in numerical investigations into the effect of parameters characterizing the composite membranes on their eigenfrequencies.
7
Content available Fractional heat conduction in multilayer spherical bodies
Kukla S., Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
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2016
|
Vol. 15, nr 4
83--92
EN
In this paper an analytical solution of the time-fractional heat conduction problem in a spherical coordinate system is presented. The considerations deal the two-dimensional problem in multilayer spherical bodies including a hollow sphere, hemisphere and spherical wedge. The mathematical Robin conditions are assumed. The solution is a sum of time-dependent function satisfied homogenous boundary conditions and of a solution of the steady-state problem. Numerical example shows the temperature distributions in the hemisphere for various order of time-derivative.
8
Content available Static and Fatigue Strength of Linear Textile Products
Włochowicz A., Kukla S., Drobina R.
Fibres & Textiles in Eastern Europe
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2016
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Vol. 24, no. 3 (117)
8--16
EN
This publication is a review of the work directed or inspired by the late Professor Andrzej Włochowicz in comparison to the current state of knowledge, and developed by his colleagues as an expression of memory and recognition of the contribution that he made to research on the strength of linear textile products. The article describes issues related to the fatigue strength of yarns. An analysis of literature related to the development of research on fatigue strength was carried out, and quantities describing load cycles and selected cases of periodically variable states of loads are presented. The article attempts to systematise certain problems related to the fatigue of textile materials. The body of the article presents the state of knowledge as well as the manner and the methods of assessment of the fatigue strength of textile materials.
PL
Prezentowana publikacja jest przeglądem prac kierowanych lub inspirowanych przez nieżyjącego Profesora Andrzeja Włochowicza na tle obecnego stanu wiedzy a opracowana przez jego współpracowników, jako wyraz pamięci i uznania dla wkładu, który wniósł do badań wytrzymałości liniowych wyrobów włókienniczych. W artykule opisano zagadnienia związane z wytrzymałością zmęczeniową przędz. Dokonano analizy literatury przedmiotu związanej z rozwojem badań nad wytrzymałością zmęczeniową, przedstawiono wielkości charakteryzujące cykle obciążeń oraz wybrane przypadki okresowo zmiennych stanów obciążeń. W artykule podjęto próbę naukowego usystematyzowania pewnych problemów związanych ze zmęczeniem materiałów włókienniczych. W głównej części artykułu zaprezentowano stan wiedzy oraz sposób postępowania i metody oceny wytrzymałości zmęczeniowej wyrobów włókienniczych.
9
Content available Quality and Safety Assurance of Iron Casts and Manufacturing Processes
Kukla S.
Archives of Foundry Engineering
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2016
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Vol. 16, iss. 2
17--20
EN
The scope of this work focuses on the aspects of quality and safety assurance of the iron cast manufacturing processes. Special attention was given to the processes of quality control and after-machining of iron casts manufactured on automatic foundry lines. Due to low level of automation and huge work intensity at this stage of the process, a model area was established which underwent reorganization in accordance with the assumptions of the World Class Manufacturing (WCM). An analysis of work intensity was carried out and the costs were divided in order to identify operations with no value added, particularly at individual manufacturing departments. Also an analysis of ergonomics at work stations was carried out to eliminate activities that are uncomfortable and dangerous to the workers' health. Several solutions were proposed in terms of rationalization of work organization at iron cast after-machining work stations. The proposed solutions were assessed with the use of multi-criteria assessment tools and then the best variant was selected based on the assumed optimization criteria. The summary of the obtained results reflects benefits from implementation of the proposed solutions.
10
Content available Modelling and Optimization of Organization of Workplaces in a Foundry
Kukla S.
Archives of Foundry Engineering
|
2016
|
Vol. 16, iss. 3
55--58
EN
The paper presents a practical example of improvement of foundry production systems in terms of post-finishing of nodular iron castings produced in the conditions of bulk production for automotive industry. The attention was paid to high labour-intensive efforts, which are difficult to be subjected to mechanization and automation. The times of actions related to grinding processing of castings in three grinding positions connected with a belt conveyor were estimated with the use of a time study method. A bottleneck as well as limiting factors were specified in a system. A number of improvements were proposed, aimed at improving work organization on the castings post-finishing line. An analysis of work ergonomics at the workplace was made in order to eliminate unnecessary and onerous for the employee actions. A model of production system using the Arena software, on which a simulation experiment was conducted, was drawn up in order to visualize the analysed phenomena. The effects of the project were shown on graphs comparing times, costs, work ergonomics and overall efficiency of production equipment indicator.
11
Content available Laplace transform solution of the problem of time-fractional heat conduction in a two-layered slab
Kukla S., Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
Vol. 14, nr 4
105--113
EN
In this paper the Laplace transformation for solving the problem of fractional heat conduction in a two-layered slab has been applied. The different orders of Caputo derivative in the time-fractional equation governed the heat transfer in the layers are assumed. The inverse Laplace transform by using a numerical method is determined. The numerical results obtained by using of the eigenfunctions method and by numerically inverting the Laplace transform are compared.
12
Content available A solution to the problem of time-fractional heat conduction in a multi-layer slab
Siedlecka U., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
|
2015
|
Vol. 14, nr 3
95--102
EN
In this paper a solution of the time-fractional heat conduction problem in a multilayer slab is presented. The boundary conditions of the third kind and the perfect contact at the interfaces are assumed. A space-time dependent volumetric heat source in the slab and time dependent surroundings temperatures are taken into account in the formulation of the problem. The solution is obtained in the form of a series expansion with respect to eigenfunctions of an auxiliary problem. A numerical example shows temperature distribution in the slab for various values of the order of the Caputo fractional derivative in the heat conduction equation.
13
Content available Improving the Organization of Iron Casts Finishing Processes
Kukla S.
Archives of Foundry Engineering
|
2015
|
Vol. 15, iss. 2 spec.
55--58
EN
The paper presents issues of production processes improvement in foundries in terms of finishing treatment of iron casts on grinding workstations. Basing on the conducted analysis of work ergonomics on the grinding line and the observation of work at workstations, a range of improvements related to organizing grinding treatment processes was proposed. In order to visualize the production system functioning and estimate its efficiency, a simulation model of a grinding line has been created, on which a simulation experiment was carried out. Due to many factors influencing the effectiveness of processes, it was suggested to use multi-criteria evaluation tools to choose the most rational solution. Three criteria have been assumed, according to which particular improvement variants were evaluated. Also, criteria weights have been set according to the Saaty’s method, and particular solution variants have been assessed separately with respect to each criterion. On the basis of the presented course of action, the best solution has been selected from among the analyzed options.
14
Content available Power series solution of first order matrix differential equations
Kukla S., Zamorska I.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 3
123--128
EN
In the paper, the solution of second order differential equations with various coefficients is presented. The concerning equations are written as first order matrix differential equations and solved with the use of the power series method. Examples of application of the proposed method to the equations occurring in the technical problems are presented.
15
Content available Green's function for heat conduction problems in a multi-layered hollow cylinder
Kukla S., Siedlecka U.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 3
115--122
EN
In this paper, derivation of the Green’s function for the heat conduction problems in a finite multi-layered hollow cylinder is presented. Formulation and solution of the problem includes an arbitrary number of the cylinder layers characterized by various thermal properties. At the interfaces perfect thermal contact was assumed. The Green’s function for the three-dimensional heat conduction problems in the cylindrical coordinate has been presented in the form of a product of two other Green’s functions.
16
Content available Frequency analysis of a double-walled nanotubes system
Ciekot A., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 4
27--34
EN
In the present paper, a problem of free vibration of a double-walled nanotubes system is considered. The nanotubes of the system are coupled by an arbitrary number of elastic rings. The Green’s functions method was used to obtain a solution to the problem. Numerical results are presented graphically.
17
Content available Frequency analysis of a double-nanobeam system
Ciekot A., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 1
23--31
EN
In this paper, a problem of transverse free vibration of a double-nanobeam-system is considered. The nanobeams of the system are coupled by an arbitrary number of translational springs. The solution of the problem by using the Green’s functions properties is obtained. A numerical example is presented.
18
Content available Free vibration to a system of cantilever nanobeams
Ciekot A., Kukla S.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 3
29--36
EN
This paper presents a solution to the free vibration problem of a system of two cantilever nanobeams. The nanobeams of the system are axially loaded and coupled by discrete translational springs. The solution of the problem by using the Green’s function method has been obtained. A numerical example shows the effect of the small scale on free vibration frequencies of the nanobeam system considered.
19
Content available Free vibration of axially functionally graded Euler-Bernoulli beams
Kukla S., Rychlewska J.
Journal of Applied Mathematics and Computational Mechanics
|
2014
|
Vol. 13, nr 1
39--44
EN
In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.
20
Content available Quality Management in the Manufacturing Process of Iron Casts on Foundry Lines
Kukla S.
Archives of Foundry Engineering
|
2014
|
Vol. 14, iss. 1 spec.
13--16
EN
The paper presents issues of quality management related to iron casts manufactured on automated foundry lines for automobile industry. The influence of the choice of electric furnace and automated foundry line with vertical or horizontal mould division on the quality of casts made of nodular or grey cast iron was presented. Analysis of different scenarios of the course of action manufacturing processes was performed basing on a simulation experiment, record data related to the quality of the manufactured casts and manufacturing prime costs analysis. The research used universal tools applied in simulation analysis of production systems (Rockwell Automation: Arena Simulation Software) and a spreadsheet used for cast manufacture cost estimation. The proposed variants have been assessed using the Pareto analysis on the basis of results of reports generated for a simulation experiment. The paper also presents suggestions of activities aimed at further improvement of the quality of foundry processes.
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