DEVELOPMENT OF STATISTICALLY AVERAGED MODELS OF DEFORMATION OF MATERIALS WITH RANDOM NETWORK STRUCTURE OF DIFFERENTLY ORIENTED FIBERS

The paper describes the developed statistically averaged models of deformation of materials with a random network structure of differently oriented fibers. New methods of stress-strain analysis and micromacromechanical models of material deformation in the volume of bodies made of material with a network structure taking into account structural and physical nonlinearities have been created. These models are based on the micromechanics of network structures at the level of statistical sets of their chains. The novelty of approaches, models, methods and results is the creation of theoretical foundations for the analysis of the deformation of non-traditional network materials. Nonlinear mathematical models of material deformation in the form of a chaotic network structure of one-dimensional fragments are proposed, which are constructed involving fundamentally new approaches to the description of physical and mechanical properties at the micro level of statistical sets of fiber chains and spatial homogenization of their macroproperties. Compared to traditional models, they more adequately model the features of material deformation in the form of spatial chaotic and ordered network structures, as they do not involve a number of additional non-physical hypotheses. This creates fundamentally new opportunities not only for analyzing the properties of such materials, but also when creating new ones with specified properties. Using the created methods, models and research tools, the basis for solving a number of model and applied problems has been created. The nature of deformation of non-traditional materials with a network structure of one-dimensional elements is determined. The macro-properties of these materials are established on the basis of the developed micromechanical models, variational formulations and averaging methods. Keywords: stress-strain state, network structures, contact interaction, finite element method, contact pressure, machine parts, variational formulation

Comparison of the Natural Vibration Frequencies of Timoshenko and Bernoulli Periodic Beams

This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions.

MODEL OF SWITCH-CONTROLLED PWM STRUCTURE FOR ANALYSIS OF PULSE VOLTAGE CONVERTERS WITH ARBITRARY TOPOLOGY

The article considers the problems of analyzing DC-DC voltage converters and analyzes the advantages, disadvantages, as well as the scope of full switched and averaged continuous models of the converters. The feasibility of using the complex of two models (full switch model and averaged continuous model) for analyzing their operation is proved. The general approach to the construction of continuous models of DC-DC voltage converters based on state-space averaging method is considered. Disadvantages of the averaged models using a classic approach are shown. The relevance of the development of universal continuous models of DC-DC converters is substantiated. The possibility of creating such models using averaged models of PWM switching structure included in the DC-DC voltage converter is shown. Analyzed the typical structure of the switch-mode power supply with feedback. An averaged model of the switching structure is proposed, basing on which continuous models of DC-DC converters with any topology can be built. The processes occurring in this switching structure in the mode of continuous and discontinuous choke current are analyzed. A method for constructing continuous models of the main types of DC-DC voltage converters based on switching structure averaged model is proposed. The adequacy of continuous models obtained by this method has been proven. The results of modeling transients on the continuous and full switch models for inverting voltage regulator are demonstrated. The possibility of accounting in the model of active resistances of switches and cumulative choke is shown. The possibility of using the proposed model to obtain the open loop transfer functions is demonstrated, in particular, the characteristics of the duty factor - output voltage. These transfer functions can be used to synthesize control system compensating circuits of the switch-mode power supply. The possibility of using a single generalized averaged model of the switching structure to build continuous models of converters with complex topology using both the Voltage Mode and Current Mode is shown. This creates prerequisites for developing a universal averaged continuous model for DC-DC converter based on this principle

From Millimeters to Micrometers; Re-introducing Myocytes in Models of Cardiac Electrophysiology

Computational modeling has contributed significantly to present understanding of cardiac electrophysiology including cardiac conduction, excitation-contraction coupling, and the effects and side-effects of drugs. However, the accuracy of in silico analysis of electrochemical wave dynamics in cardiac tissue is limited by the homogenization procedure (spatial averaging) intrinsic to standard continuum models of conduction. Averaged models cannot resolve the intricate dynamics in the vicinity of individual cardiomyocytes simply because the myocytes are not present in these models. Here we demonstrate how recently developed mathematical models based on representing every myocyte can significantly increase the accuracy, and thus the utility of modeling electrophysiological function and dysfunction in collections of coupled cardiomyocytes. The present gold standard of numerical simulation for cardiac electrophysiology is based on the bidomain model. In the bidomain model, the extracellular (E) space, the cell membrane (M) and the intracellular (I) space are all assumed to be present everywhere in the tissue. Consequently, it is impossible to study biophysical processes taking place close to individual myocytes. The bidomain model represents the tissue by averaging over several hundred myocytes and this inherently limits the accuracy of the model. In our alternative approach both E, M, and I are represented in the model which is therefore referred to as the EMI model. The EMI model approach allows for detailed analysis of the biophysical processes going on in functionally important spaces very close to individual myocytes, although at the cost of significantly increased CPU-requirements.

The Stability Analysis of Periodic Beams Interacting with Periodic Elastic Foundation with the Use of the Tolerance Averaging Technique

In this paper a stability analysis of microperiodic beams resting on the periodic inhomogeneous foundation is carried out. The main issue of this considerations, which is the analytical solution to the governing equations characterised by periodic, highly oscillating and non-continuous coefficients, is overwhelmed by the application of the tolerance averaging technique. As a result of such application, the governing equation is transformed into a form with constant coefficients which can be solved using well-known mathematical methods. In several calculation examples, the convergence of the results of two derived averaged models is examined, as well as the convergence of the lowest value of the critical force parameter derived from the averaged models with the FEM model. The results prove the superiority of the presented analytical solution over the FEM analysis in the optimisation process.

Is There a Long-Term Criminogenic Effect of the Exposure to a Paternal Conviction During Upbringing? An Analysis of Full Siblings Using Swedish Register Data

Objectives The current study analyzed the association between a final paternal conviction that occurred sometime 10 years prior to birth through age 14 and subsequent child conviction risk to age 25. Methods We used Swedish register-based data on a two-generation dataset originating from a parental generation born in 1953. We employed a combination of population-averaged models that controlled for measured confounding together with an analysis of full siblings that ruled out unmeasured confounding shared between full siblings. Results The results showed that boys, but not girls, who were exposed to a paternal conviction during upbringing had an increased risk of being convicted themselves, net of measured and unmeasured familial confounds. There was, however, little indication for an age-effect at the time of a final paternal conviction, and there were no significant differences in violent crime between exposure-discordant siblings. Conclusions The results provide evidence for an effect of the exposure to a paternal conviction on child subsequent conviction risk that cannot merely be explained by familial factors shared between full siblings. These results are, however, conditional on gender and on the type of criminal outcome.

A single-phase DC-AC dual-active-bridge based resonant converter for grid-connected photovoltaic applications

In the wake of the global energy crisis, the integration of renewable energy resources, energy storage devices, and electric vehicles into the electric grid has been of great interest towards replacing conventional, fossil-fuel-dependent energy resources. This thesis presents the circuit topology and a control strategy for a 250-W single-phase gridconnected dc-ac converter for photovoltaic (PV) solar applications. The converter is based on the dual active bridge (DAB) kernel employing a series-resonant link and a high-frequency isolation stage. For interfacing the 60-Hz ac grid with the 78-kHz resonant circuit, the converter utilizes a four-quadrant switch array that functions as an ac-ac stage. Therefore, a bipolar low-frequency voltage source, that is the grid voltage, is used to synthesize a symmetrical high-frequency voltage pulse-train for the resonant circuit. Thus, soft switching and the use of a compact ferrite-core transformer have been possible. Then, a fast current-control loop ensures that the converter injects a sinusoidal current in phase with the grid voltage, while a relatively slower feedback loop regulates the converter dc-side voltage, that is, the PV array voltage, at a desired value. To simulate the converter and to design the controllers, the thesis also presents nonlinear large-signal and linearized small-signal state-space averaged models. The performance of the converter is assessed through simulation studies conducted using the aforementioned averaged models, a detailed topological model in the PLECS software environment, and a prototype. Keywords: Photovoltaic, PV, Microinverter, Dual Active Bridge, Phase-shift Modulation, High Frequency Transformer

A single-phase DC-AC dual-active-bridge based resonant converter for grid-connected photovoltaic applications

In the wake of the global energy crisis, the integration of renewable energy resources, energy storage devices, and electric vehicles into the electric grid has been of great interest towards replacing conventional, fossil-fuel-dependent energy resources. This thesis presents the circuit topology and a control strategy for a 250-W single-phase gridconnected dc-ac converter for photovoltaic (PV) solar applications. The converter is based on the dual active bridge (DAB) kernel employing a series-resonant link and a high-frequency isolation stage. For interfacing the 60-Hz ac grid with the 78-kHz resonant circuit, the converter utilizes a four-quadrant switch array that functions as an ac-ac stage. Therefore, a bipolar low-frequency voltage source, that is the grid voltage, is used to synthesize a symmetrical high-frequency voltage pulse-train for the resonant circuit. Thus, soft switching and the use of a compact ferrite-core transformer have been possible. Then, a fast current-control loop ensures that the converter injects a sinusoidal current in phase with the grid voltage, while a relatively slower feedback loop regulates the converter dc-side voltage, that is, the PV array voltage, at a desired value. To simulate the converter and to design the controllers, the thesis also presents nonlinear large-signal and linearized small-signal state-space averaged models. The performance of the converter is assessed through simulation studies conducted using the aforementioned averaged models, a detailed topological model in the PLECS software environment, and a prototype. Keywords: Photovoltaic, PV, Microinverter, Dual Active Bridge, Phase-shift Modulation, High Frequency Transformer