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 MAJ 2019.**

**UTORAK, 07.05.2019. u 17:00, Sala 301f, MI SANU, Kneza Mihaila 36**

*Jochen Mau, Faculty of Medicine, Heinrich Heine University, Düsseldorf, Germany*

**A HOLISTIC AXIOMATIC APPROACH TO HUMAN-BODY SYSTEMS-DYNAMICS**

A hierarchically nested structure of functional compartments with effectuation dynamics emerging by successive translation from embedded functional units, themselves functional compartments composed from functional units is postulated. It spans from 10^{14} human-body cells to person's whole body in a bottom-up perspective, or from whole body to lower level functional components in drill-down. The latter per - spective leads to axiomatic "wirk-gefuege", a structure of effectuation and its dynamics, decomposable into three "wirk-components" for concerted effectuation of vital functions, production functions, and operational functions, that are canonical in production systems. The human-machine system of an excavator with human operator, the "greifbagger" model concept of whole human-body system, the Whole, is the motivating illustration. It is the advantage of an axiomatic approach to strip off all "companion information" and otherwise knowledge about the Whole when focusing on the interaction between those three level-one canonical functional components that expresses in and completely determines behavioral action of Whole. Generic in-component dynamics are postulated as simple first-order kinetics of "charge" transfers in a direct- current twin-circuit type of construct to comply with living nature's design principle of wake-sleep cycles.

The phenomenon of time-delay is very common in engineering systems, such as chemical systems, biological systems, mechanical systems, and networked control systems. In practice, the most real problems can be modelled by systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties. The time-delay, nonlinearities and parameter uncertainties can cause instability and poor performance of systems. In many practical applications, the concept of Lyapunov asymptotic stability is often insufficient to study the transient performances of a system. A system can be Lyapunov stable but completely useless because it possesses undesirable transient performances. In order to study these problems, the concept of finite-time stability (FTS) was introduced. In this lecture, the FTS concept is extended to the class of continuous and discrete-time systems with interval time-varying delay, nonlinear perturbations and parameter uncertainties, and some delay-dependent sufficient conditions for FTS are proposed in terms of linear matrix inequalities. The new continuous and discrete Lyapunov–Krasovskii functionals with exponential and power functions are used, respectively. In order to obtain less conservative results an integral inequality with exponential function and a summation inequality with power function are proposed. Numerical examples are given to illustrate the effectiveness of the proposed results.

The geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson’s method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author’s previous papers.

Due to geometrical complexity of hydraulic turbomachines and low pressure fans and complex nature of turbulent flow, the designing process requires the introduction of certain simplifications, the numerous empirical data in calculations and, finally, the model and prototype testing. Nowadays, fluid flow in turbomachinery can be numerically simulated using CFD methods and obtain flow parameters in the entire flow domain. This enables calculating the averaged flow parameters according to the circular coordinates, in numerous discrete points of the flow domain, using the methodology presented in the paper. The averaged axisymmetric flow surfaces and meridian streamlines can be obtained as well. For the turbomachinery designer it is of the greatest importance to be able to compare such obtained surfaces to axisymmetric flow surfaces which are used in blades profiling and determine how much they overlap. In this way a designer can make possible corrections of the impeller during the designing process, potentially saving the time and cost of prototype making and testing.

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.

Prof. dr Katica (Stevanović) Hedrih

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dr Ivana Atanasovska

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Milan Cajić

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