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The paper deals with stress and reliability calculation of a gas pipeline straight section buried in a ground (elastic foundation) loaded by heating and internal overpressure. Mathematical derivation of relations necessary for reliability calculation of the pipeline section by stochastic approach is also included in the paper. Resulting values are obtained by software Anthill using the Monte Carlo method. Input random parameters of the examined pipeline section are shown by bounded histograms.

One of the possible ways to transfer the tractive power of a drive unit to the traction element is to use fibre friction. When a steel rope is used as the traction element, there is a transfer of tractive power in the groove created on the perimeter of the rim of the driving rope sheave. The transmission capability of the drive is directly proportional to the size of the angle of wrap and the shear friction coefficient of the rope surface when the rope is in contact with the surface of the groove wall. The relationship for calculating the size of friction coefficient in the grooves is given by relevant technical standards. The coefficient of friction determined in this way does not take into account the state of possible operational contamination of the groove or the diameter of the rope used. Using a unique laboratory instrument, tensile forces were measured for both rope sides in the state of a non-rotating sheave or when the sheave started to rotate rope. Experimental measurements were carried out for two different diameters of steel ropes, which were guided by two types of grooves for the rope sheave under two limit operating states of the groove wall surface: clean and dirty with oil. By evaluating the measured tensile forces in the approaching and outrunning rope side girded with the groove of the rope sheave, it was found (using a measuring apparatus) that a rope of a larger diameter acquires a higher value of the friction coefficient for the groove than a rope of a smaller diameter. The coefficient of friction in the groove decreases with the increasing size of the sum of the acting tensile forces on both sides of the rope. Lower values of the coefficient of friction achieve semi-circular grooves, and V-shaped grooves show higher values. Lower values for the coefficient of friction, close to theoretical values which were calculated using the relevant relationships specified in the standards, were found for grooves contaminated with oil as opposed to dry and clean grooves. Web of Science 10 7 art. no. 590

The aim of this paper is the biomechanical evaluation of the interaction between load forces to which a sitting man and the seat are exposed. All loads, which consider actual anthropometry histograms of human population (i.e. segmentation of human weight, height, centroids, gravity and shape of seat) are determined using the direct Monte Carlo Method. All inputs are based on the theory of probability (i.e. random/probabilistic inputs and outputs with respect their variabilities). A simple plane model (i.e. probabilistic normal forces and bending moments) shows a sufficient stochastic/probabilistic evaluation connected with biomechanics, ergonomics, medical engineering (implants, rehabilitation, traumatology, orthopaedics, surgery etc.) or industrial design.

This article deals with strength and stiffness analysis of headless screw. This issue was solved in cooperation with engineering industry and doctors. The problem was solved using a stochastic approach, which utilizes the field of random events (simulations), which are applied for determination of input values. The prototype of headless (Herbert) screw Ti4.0/1.4x30/75 was used for solving this problem. Mathematical equations for analytical calculation of the maximal equivalent stress in screw were established. This issue is statically indeterminate problem in compressive and tensile stresses and needs one more equation (i.e. the condition of deformation), which describes relationship between extension of screw and contraction of bone. Resulting values are not defined for one specific model, but the simulation is taking into account a large amount of random samples (specifically 5x10(6) random simulations), which are distributed by bounded histograms. Furthermore, the probabilistic functions of simulated screw were determined. Due to stochastic strength analysis of headless screw, it meets reliability conditions for practical application in osteosynthetic treatment, see [Frydrysek 2016] Web of Science 2020 3840 3837

Presented article deals with realization and evaluation of the tensile tests. The tensile tests are used for determining of material properties of thin polymers (plastic) films that are used for manufacturing windows. These plastic films are placed between plates glasses and reflects thermal energy back (insulation). From measurements, Youngs moduli, fracture limits, force-displacement relationships and engineering and logarithmic stress-strain relationships were evaluated. The results were approximated by two straight lines and by suitable chosen functions. The obtained data can be used for analytical, numerical and stochastic modelling of problems connected with manufacturing.

This paper focuses on the probabilistic numerical solution of the problems in biomechanics and mining. Applications of Simulation-Based Reliability Assessment (SBRA) Method are presented in the solution of designing of the external fixators applied in traumatology and orthopaedics (these fixators can be applied for the treatment of open and unstable fractures etc.) and in the solution of a hard rock (ore) disintegration process (i.e. the bit moves into the ore and subsequently disintegrates it, the results are compared with experiments, new design of excavation tool is proposed., {"references":["K. Frydr├¢┼íek, Pravd─øpodobnostn├¡ v├¢po─ìty v mechanice 1 (Probabilistic\nCalculations in Mechanics 1), written in Czech language, ISBN: 978-80-\n248-2314-0, V┼áB - Technical University of Ostrava, 2010, pp. 1-149.","K. FrydrÛšek, \"Stochastic Solution and Evaluation of the Ore\nDisintegration Process\", in Proceedings of the 2009 International\nConference on Scientific Computing CSC2009, ISBN: 1-60132-098-1,\nCSREA Press, Las Vegas, USA, 2009, pp. 40-46.","K. FrydrÛšek, P. Koštial, K. Barabaszova, J. Kukutschová, \"New ways\nfor Designing External Fixators Applied in Treatment of Open and\nUnstable Fractures\", in journal World Academy of Science, Engineering\nand Technology, ISSN 2010-376X (print version) ISSN 2010-3778\n(electronic version), vol. 7, issue 76, 2011, pp. 639-644.","K. FrydrÛšek, P. Marek, \"Probabilistic Solution and Reliability\nAssessment of the Hard Rock Disintegration Process\" (Chapter:\nStructural Reliability and Design Codes - pp. 1443-1450), in book: R.\nBri┼í, C. G. Soares, S. Martorell (editors): Reliability, Risk and Safety:\nTheory and Applications (ESREL 2009), vol. 2, ISBN 978-0-415-55509-\n8, Taylor Francis Group, London, 2010, UK.","K. FrydrÛšek, M. NikodÛm, Beams and Frames on Elastic Foundation\n3, ISBN 978-80-248-2257-0, V┼áB - Technical University of Ostrava,\nOstrava, Czech Republic, 2010, pp. 1-611.","K. FrydrÛšek, L. Pleva, P. Koštiál, \"New Ways for Designing External\nFixators Intended for the Treatment of Open and Unstable Fractures\", in\nApplied Mechanics 2010, 12th. International Scientific Conference\n(Proceedings), Department of Applied Mechanics, Faculty of\nMechanical Engineering, Technical University of Liberec, Liberec,\nCzech Republic, ISBN 978-80-7372-586-0, 2010, pp. 43-47.","A. Haldar, S. Mahadevan, Probability, Reliability and Statistical\nMethods in Engineering Design, John Willey & Sons, Inc, ISBN 0-471-\n33119-8, New York, 2001, USA.","Z. Kala, \"Sensitivity Analysis of Steel Plane Frames with Initial\nImperfections\", in Engineering Structures, vol.33, no.8, 2011, pp. 2342-\n2349.","R. Madeja, L. Pleva, P. V├ívrov├í, \"Navigation in Traumatology\", j.\n├Üraz. chir., 17, no. 3, Czech Republic, 2009, pp. 1-6.\n[10] P. Marek, J. Brozzetti, M. Gu┼ítar, P. Tikalsky, Probabilistic Assessment\nof Structures Using Monte Carlo Simulation Background, Exercises and\nSoftware, (2nd extended edition), ISBN 80-86246-19-1, ITAM CAS,\nPrague, Czech Republic, 2003.\n[11] P. Marek, M. Gu┼ítar, T. Anagnos, Simulation-Based Reliability\nAssessment For Structural Engineers, CRC Press, Boca Raton, USA,\nISBN 0-8493-8286-6, 1995.\n[12] L. Pleva, External Fixator for Treatment of Acetabulum Fractures, final\nreport of the project IGA MZ ─îR, reg. ─ì. 3522-4, written in Czech\nlanguage, FNsP - Ostrava-Poruba, Czech Republic, pp. 1-77, 1999.\n[13] K. Rozum, External Fixators for the Treatment of Open Unstable\nFractures, inaugural work written in Czech language, FME, V┼áB -\nTechnical University of Ostrava, Czech Republic, ISBN 978-80-248-\n1670-8, pp. 1-43, 2008.\n[14] J. TokarskÛ, P. Čapková, D. Rafaja, V. Klemm, M. Valášková, J.\nKukutschov├í, V. Tom├í┼íek, \"Adhesion of Silver Nanoparticles on the\nClay Substrates; Modeling and Experiment\", in Applied Surface Science,\nISSN: 0169-4332, (2009), doi:10.1016/j.apsusc.2009.11.037.\n[15] M. Val├í┼íkov├í, G. Simha Martynkov├í, V. Mat─øjka, K. Barabaszov├í, E.\nPlevov├í, D. M─øř├¡nsk├í, \"Organovermiculite Nanofillers in\nPolypropylene\", in Applied Clay Science, ISSN 0169-1317, 43, 2009,\npp. 108-112."]}

This paper is focused on a numerical analysis of the hard rock (ore) disintegration process. There is discussed the possibility of using computational modelling for the mechanical contact problem between the hard rock and a cutting bit. The bit (i.e. an excavation tool with a flat frontal side and a conical edge) moves and sinks into the hard rock and subsequently disintegrates it. The whole problem of the hard rock disintegration process (i.e. stress-strain relationship, contact forces, reaction forces and fracture of the ore) is solved via Finite Element Method (MSC.MARC/MENTAT software). The rock disintegration process was solved via deactivation of finite elements which satisfy conditions of fracture. Some results (i.e. reaction forces in the cutting bit) are also compared with experimental measurements. Tento článek je zaměřen na numerickou analýzu rozpojování tvrdých hornin (rud). Je rozebírán problém možností počítačového modelování problematiky mechanického kontaktu mezi tvrdou horninou a řezným nástrojem. Nůž (tj. rozpojovací nástroj s plochým čelem a kuželovým břitem) se pohybuje a vniká do tvrdé horniny a následně ji rozpojuje. Celá problematika rozpojování tvrdých hornin (tj. napěťově-deformační stav, kontaktní síly, reakční síly a lom rudy) je řešená pomocí Metody konečných prvků (MSC.MARC/MENTAT software). Proces rozpojování hornin je řešen pomocí deaktivace elementů, které splňují podmínky lomu. Některé výsledky (tj. reakční síly v řezném nástroji) jsou také porovnány s experimentálními měřeními.

This paper is focused on the solution of simple beam continually supported by elastic (Winkler's) foundation. The foundation contains longitudinal nonlinearity. For the calculation of displacements and bending stresses are used analytical procedures (approximate solution in the form of polynomial function) and probabilistic approaches (SBRA method, Monte Carlo Simulation Method, AntHill software). Probabilistic approach includes influences of variability of load, shape and material of the beam, and variability of modulus of the foundation. Probabilistic approach is used for the reliability expertise of the beam and calculation of safety.