• ## Some aspects of remote exams

pg(s) 29-32

The paper is devoted to distance exams, as in that the focus is on mathematical disciplines. Some advantages are standing out, as well as significant disadvantages have been discussed. Current modern tools are considered, which are applied both in the preparation of students and in distance exams.

• ## Special cases in determining the critical buckling load of Euler elastic columns

pg(s) 33-35

The Energy method is widely applied to determine the critical loads in elastic systems. A widely used variant of the method applies the Rayleigh-Ritz approach where the approximation of the buckling mode of the column is a function that satisfies the boundary conditions. A numerical example of a two-storey column is considered. An important aspect in the problem is the solution the complex integrals that emerge during the solution process. That problem could be overcome by the use of math software. The investigated column is hinged at its both ends and has an additional lateral support in the middle. It is loaded with a compressive distributed load alongside its length.

• ## A General 2-D CFD Code Development and Verification in Python

pg(s) 36-42

The technological progress in computer technologies gave rise to new possibilities and progresses for numerical and iterative methods. As being one of the computational studies, computational fluid dynamics is highly related to today’s advances. There are various types of methods and algorithms developed to model complex phenomena of fluid flow. In this study, we will introduce a new, still in development stage, CFD code with a pre-processor and a solver. Our research is focused on developing and studying a CFD code for mainly internal flows. Laminar and turbulent 2-dimensional flows can be analyzed using the software. The code is equipped with a graphical user interface (GUI) to make it simple to use. The GUI has the all-necessary components to define and analyze a fluid flow problem. We used an open-source post processor in order to visualize flow data and linked it to GUI, so the resulting software is a complete CFD package. The entire software is written using Python which has an easy code structure and rich code libraries. In order to decrease the time for convergence, code is modified with Numba and Cython libraries. To confirm accuracy of the solver, various basic test cases from the literature such as backward facing step flow, impinging jet flow, flow across a square cylinder, lid driven cavity flow are tested for both laminar and turbulent flows and the results was described in detail.

• ## Four-point bending of thin or thick beams

pg(s) 43-46

A paper recently published explains the differential equations for deflection of beams under bending, including the deflection due to transversal force [1]. The present article contains derivation of the main equations, according to the mentioned approach, for deformations of a simply supported beam that is symmetrically loaded with two forces, also known as four-point bending. These deformations are rotation and deflection of the neutral line due to bending moment and transversal force. For thick beams, deflection due to the transverse force is more than 1% from deflection caused by the bending moment. Special attention was paid to the third-point loading test. The presented model is applicable for calculating deflection due to bending moment and transverse force for both thin and thick beams.

• ## Numerical investigation of wind-assisted ship propulsion systems

pg(s) 47-50

The paper studies three of the most applicable wind-assisted ship propulsion systems: soft sails, Dynarig sails and Flettner rotors, in particular the wind forces on the sails. Traditionally, and still most reliably, these forces are determined by model testing in wind tunnels. Unfortunately, experimental results of different WAPS are quite scarce. On the other hand, the intensive development of Computational Fluid Dynamics (CFD) nowadays allows faster and more economical evaluation of aerodynamic forces and optimization of shapes. CFD modelling is applied here for evaluation of the aerodynamic forces on sails.

• ## Optimization of the rubber forming process for the sheet metal part using numerical simulation

pg(s) 51-54

This article focuses on the optimization of manufacturability for the aluminium cover produced by rubber forming. Aluminium Al6016 was considered as a material for the cover and its constitutive equations Hill 48 and Hollomon described its properties. The Mooney-Rivlin hyperelastic material model defined material properties for a punch made of rubber. Pam stamp software was used to create the simulation model and evaluation. Results were optimized from the view of thickness reduction and punch stroke when two different rubber hardness were selected.

• ## Experimental and statistical models for determining the critical values of external action parameters on optical elements in extreme conditions of their operation

pg(s) 55-58

The study has been carried out and experimental and statistical models have been developed to determine the critical values of external extreme action parameters (intense heat flows, times of their action, increased external pressures) on optical elements made of glass and ceramics, the excess of which leads to their surface destruction (the appearance of cracks, chips and other defects) and, ultimately, to the failure of optoelectronic devices.

• ## Concept of an energy system emulator

pg(s) 59-62

Research, optimization and practical implementation of the optimization processes of energy subsystems of power, heating and industrial plants is a relatively complex task that is unimaginable today without specialized computer support tools. The energy system emulator itself represents a tool for development and application work with energy systems, which is based on today’s standard decentralized control systems. The basic principles of the modular construction of the emulator and an example of its implementation based on the Siemens SIMATIC-S7 DCS system are shown. In addition to the design of the energy systems emulator concept, the article also presents a design of a hydraulic turbine model as the most important subsystem of a hydropower plant, the efficiency calculation of which is analytically demanding and dependent on parameters that are often obtained only by a theoretical estimation. In this article, a fuzzy system was used to create the model based on measured operating data of the turbine flow rate and the height of its water column without any need to know the exact turbine parameters.

• ## An approach for design and management of a supply chain for biodiesel production taking into account the uncertainties at two scenarios with different locations of the fuel blending centers

pg(s) 63-66

This study proposes a mixed integer linear programming (MILP) approach to the design and management of the biodiesel / diesel (SC) supply chain. The approach was applied to two scenarios with different locations of the fuel blending centers. For both scenarios, optimization problems were formulated and solved while satisfying environmental and economic criteria. The latter are defined in terms of minimum total costs and minimum greenhouse gas emissions generated during the performance of all activities included in the supply chain. The approach was applied to a real case from Bulgaria, where its 27 administrative regions were considered. An analysis was carried out in terms of uncertainties regarding the obtained optimal routes for transportation of raw materials and products, the optimal quantities of feedstocks for cultivation and optimal quantities of biodiesel produced, which is transported to the search areas under both scenarios.

• ## Intellectualized information-analytical system monitoring air pollution

pg(s) 67-70

The article develops a simulation model, structural and functional schemes of an intellectualized information-analytical system for monitoring air pollution (for high concentrations of carbon dioxide and sulfur, as well as dust particles with a dispersion of 2-5 microns) within the industrial area of the city. A feature of such a system is the ability to determine, dynamically monitor in real t ime the spatial map of the distribution of the concentration of the above harmful impurities and its forecasting, which would quickly determine areas of the city where the concentration of such impurities exceeds the allowable norm. The main advantage of the developed information -analytical system is the ability to conduct intelligent monitoring of air quality, which will allow for highly accurate and objective forecasting of changes in distribution and redistribution in space over time of harmful impurities. Tests of the developed information -analytical system allowed to investigate its work under different conditions and modes of measuring experiment, as well as to virtually determine the rational parameters of such a monitoring system. A satisfactory discrepancy of the results obtained with the help of experimental measurements wa s found in 7-13% in comparison with the data obtained by simulation, which confirms the correctness and adequacy of the compiled model.