ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Seminar
MECHANICS OF MACHINES AND MECHANISMS - MODELS AND MATHEMATICAL METHODS

 

PROGRAM


Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za SEPTEMBAR 2020.




UTORAK, 08.09.2020. u 17:00, Live stream Beograd
Ana Petrović, Faculty of Mechanical Engineering, University of Belgrade, Serbia
MEHODS FOR NUMERICAL AND EXPERIMENTAL DIAGNOSTICS OF COMPLEXE STRUCTURES' STRENGTH-WITH SPECIAL REFERENCE TO MODEL ANALYSIS
There are numerous examples of failure of steel structures. There are various causes, such as error in design, error in production, error in exploitation or unexpected loads. When failure occurs, standard series of operations should be performed. Solving the problem most often requires numerical and experimental analysis that is applied iteratively. Inevitable is performing numerical calculation of the structure, using well-known FEM analysis. In principle, if stress concentrations coincide with locations of cracks, this indicates a bad design solution and proposal for redesign of the structure should be given. However, stress is not the only indicator of defect in design. It is necessary to know free frequencies of the structure, and distribution of potential and kinetic energy in the main modes of oscillation. Reanalysis method and dynamic modification are procedures based on different relations between potential and kinetic energy, and gives recommendations for redesign. The main objective of a dynamic modification of the structure is to increase the first frequency of oscillation, and that the gap between adjacent frequencies is as big as possible, but this method can be used to reduce the stress concentration as well. Several examples of everyday engineering practice will show the importance of reanalysis method, and that it can be applied to all types of structures, from very simple to complex. Considering experimental approach, possibilities of performing experiments on real constructions are often limited, especially in case of large constructions. One of the solutions is to create a sub-scaled model in order to anticipate the behavior of the real construction, regarding the behavior of the model, with sufficient accuracy. So, the idea is making a sub-scaled model of the construction itself, which will provide the possibility of numerical-experimental "learning" about the strength and rigidity of this construction. Advantages of model testing will be shown by example of the bucket wheel excavator substructures. Model testing includes: (1) creating sub-scaled model (physical and numerical), (2) assessment of load applied to model using recommendations given by similarity method, (3) performing (static and dynamic) numerical calculations of a real construction and its sub-scaled model, and formulating of coefficients connecting these two models, (4) performing experiments of a model in order to verify all the numerical models. Also, model testing allows testing in a laboratory "clean" environment, which also allows the application of sensitive test equipment, such as system for non-contact stress and strain measurement based on Digital Image Correlation (Aramis system).



UTORAK, 22.09.2020. u 17:00, Live stream Beograd
Vladan D. Djordjević, Serbian Academy of Sciences and Arts, Belgrade, Serbia
A CRITICAL ASSESSMENT OF THE GOVERNING EQUATIONS AND THE BOUNDARY CONDITIONS FOR THE RAREFIED GAS FLOW IN MICRO-CHANNELS
Dynamics of rarefied gas flows is a fast developing part of general gas dynamics, finding increased applications in a variety of industrial and medical fields of Micro-Electro-Mechanical-Systems (MEMS) technologies. These include: several types of sensors for measuring pressure, temperature, mass flow rate and velocity, actuators for linear and angular motion, micro-heat-exchangers for cooling of electronic circuits, reactors for separating biological cells, blood analyzers, etc. They are all very tiny devices with the characteristic length scale measured in micrometers, so that even at normal conditions the values of the Knudsen number are not small enough to treat the flow with Navier-Stokes (N-S) equations and classical no-slip conditions.
In the reviewing part of the paper both pressure driven and shear driven micro- flows are encountered. In an asymptotic analysis based on geometrical, kinematical and dynamical properties of the flow in micro-channels, N-S equations are simplified and two characteristic cases are considered separately: low Mach number flow and arbitrary Mach number flow. At that, special emphasis is given to the slip boundary conditions, i.e. to the velocity slip, temperature jump and creep boundary conditions, and their use in different cases of flow.
In the very complex flow with arbitrary values of the Mach number it is shown that the solution for an isothermal flow can be obtained by reduction to the flow of an incompressible fluid, i.e. by „mapping“ the „compressible“ plane onto an „incompressible“ one. Some new directions in the research of the rarefied flow in micro-channels are also pointed out.



Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.

dr Ivana Atanasovska
Rukovodilac seminara
Djordje Jovanović
Sekretar seminara