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## The effect of finite element type on the results of superplastic forming simulation

Superplastic Forming is an industrial process to produce thin-walled products of complex shape. At the same time this process allows one to obtain the products with close to uniform thickness distribution. The process exploits the abilities of some polycrystalline materials to large elongations before failure. The best formability can be achieved only under very specific conditions of temperature and strain rate. In order to calculate the pressure regime to sustain target strain rate in critical arias it is necessary to use finite element simulation. The pressure regime calculation lasts for a day’s especially while 3 dimensional elements are use. To reduce the time of calculation it is possible to use elements from membrane theory. The main idea of this approach is to use planar elements instead of tetrahedronal for 3D tasks or 2 nodes elements instead of triangular ones for axisymmetric tasks. This reduction doesn’t take in account share stress accruing into material. The main aim of this paper is to study the effect of elements type on the accuracy of thickness distribution prognosis.

Computer simulations are fast growing approach for doing research in sciences. It is auxiliary to experimental and analytical research. The main goal of the conference is in the development of methods and algorithms which take into account trends in the hardware development, and which may help to intensive research. Conference should play role of the venue were senior scientists and students may have opportunity to speak each other and exchange ideas and views on the developments in the area of high-performance computing in most sciences.

The exploration of icy satellites such as Saturn’s moon Enceladus or Jupiter’s moons Europa and Ganymede is one of the popular branches in modern space research. Each icy body has its own feature: water ice presence on Enceladus, cryo-vulcanism on Ganymede, Europa’s smooth shell. Also conditions on these moons allow speculation about possible life, considering these moons from an astrobiological point of view.

Research in the last decade shows that there should be a deep ocean (the estimated thickness varies up to 100km) under the icy sheet of Europa. The estimated thickness of the ice on Ganymede varies up to 800km. To study this possible ocean and to look for life’s traces, it is necessary to penetrate the icy sheet. This means that special equipment should be designed. On the Earth, similar kinds of probes have been used successfully to study glaciers. Use of such probes enables extrapolation from terrestrial to extraterrestrial application.

There are several ways to penetrate through the ice. The authors consider these possibilities and explain why, in the case of exploration of icy moons, a melting probe is preferred.

Other unsolved problems are in the areas of analyzing how the probe will move in low gravity and low atmospheric pressure; whether the hole formed in the ice will be closed when the probe penetrates far enough or not; what is the influence of the probe’s characteristics on the melting process; and what would be the order of magnitude of the penetration velocity. This study explores the technique based on elasto-plastic theory and so-called “solid water” theory to estimate the melting velocity and to study the melting process. Based on this technique, the authors considered several cases of melting probe motion, estimated the velocity of the melting probe, studied and discussed the influence of different factors, and propose an easy way to optimize the parameters of the probe.

Nowadays planetary bodies' studies are of the great interest. First of all, such space objects are the icy moons of the giant planets like Jupiter and Saturn. Of particular interest is the relatively smooth Europa's surface that is covered by a bands system, valleys, and ridges. To study the planetary icy body in future space missions, one of the problems to solve is the problem of design of a special device, capable to penetrate through the ice, as well as the choice of the landing site of this probe. To select possible landing site analysis of the Europa's surface relief formation is studied. This analysis showed that the compression, extending, shearing, and bending can influence on some arbitrarily separated section of Europe's icy surface. The computer simulation with finite element method (FEM) was performed to see, what types of defects could arise from such effects. Also the problem of melting probe movement through the ice is considered: how the probe will move in low gravity and low atmospheric pressure; whether the hole formed in the ice will be closed when the probe penetrates far enough or not; what is the influence of the probe's characteristics on the melting process; what would be the order of magnitude of the penetration velocity. This study explores the technique based on elasto-plastic theory and so-called “solid water” theory to estimate the melting velocity and to study the melting process. Based on this technique, several cases of melting probe motion are considered, the velocity of the melting probe is estimated, the influence of different factors are studied and discussed, and an easy way to optimize the parameters of the probe is proposed.

The results concern roll pass design for rolling a round bar of a 20mm diameter from a 55mm diameter input. Concerning materials, this roll pass design must cover a wide range of steels, from low-carbon micro-alloyed steels to stainless steels. The roll pass design proposal takes into consideration lower plasticity of certain steels. The comparison was enabled by suggesting two roll pass designs. The classical oval-round roll pass design, where the maximum extension coefficient is set to 1.55 in oval and 1.22 in round grooves. The second roll pass design uses a combination of smooth part of the roll (curves) and round roll passes. Distribution of the extension coefficient in individual passes is similar to that of oval-round series. The paper also compares values of energy-force parameters calculated analytically using the method of finite elements. If we compare the distribution of temperature, stress and size of the grain, it is proved that the oval-round roll pass designs are the best as far as the balanced distribution of the above-mentioned values is concerned. The roll pas design combining smooth part of the roll with a round part does not achieve such balance. However, its advantage lies in far lower requirement for the needed length of the working part of the roll. Five passes are carried out on the smooth part of the roll, which considerably cuts down the required length of the roll body. Therefore it is this variant that will be used in the laboratory of wire rolling created within the project RMSTC.

Mechanical performances of titanium biomedical implants manufactured by superplastic forming are strongly related to the process parameters: the thickness distribution along the formed sheet has a key role in the evaluation of post-forming characteristics of the prosthesis. In this work, a finite element model able to reliably predict the thickness distribution after the superplastic forming operation was developed and validated in a case study. The material model was built for the investigated titanium alloy (Ti6Al4V-ELI) upon results achieved through free inflation tests in different pressure regimes. Thus, a strain and strain rate dependent material behaviour was implemented in the numerical model. It was found that, especially for relatively low strain rates, the strain rate sensitivity index of the investigated titanium alloy significantly decreases during the deformation process. Results on the case study highlighted that the strain rate has a strong influence on the thickness profile, both on its minimum value and on the position in which such a minimum is found.

The paper presents a simple technique for the characterization of materials superplasticity by free bulging tests, which is based on inverse analysis. The main idea of this technique is a semianalytical solution of the direct problem instead of finite element simulation which allows one to reduce the calculation time significantly. Presented method use experimental time-thickness and time-dome height of the workpiece dependancies as initial experimental data. Presented method has been applied for AZ31 magnesium alloy at 520. Received properties have been veracity via simulation by finite element method. Obtained time-height relations were comparison with the data presented in the literature.

The purpose of this study is to find out the characteristics of hot forming of Ti-6Al-4V titanium alloy in order to determine the conditions of its superplastic behavior. The experiments were performed in two stages: the stepped tensile-tests series (temperature range 700 – 925 °С) and the constant strain rate tensile-test series (temperature range 775 – 925 °С). By the results of stepped tensile tests the constitutive equations which describe relationship between stress and strain rate for each temperature were constructed. On the base of obtained data, the temperature and strain-rate ranges which ensure the realization of superplasticity at forming of Ti-6Al-4V alloy as well as optimal strain rates which corresponds to the maximum value of strain rate sensitivity exponent were determined. In was shown that at low temperatures (700 – 775C) the Ti-6Al-4V alloy shows all signs of superplasticity, however at these temperatures the optimal strain rates are too slow for industrial technological procedures. The dependence between optimum strain rate and reciprocal temperature appears to be well fitted by exponential low. At the second stage of the experimental research, the tensile-tests with a constant, optimum for each temperature strain-rate were carried in order, to estimate the real initial flow stress and the character of strain hardening of the material during the deformation with optimum strain rate. In was found that flow stress values obtained by stepped tensile tests matches the values form constant-strain-rate tests with effective strain value equal to 0,2 and the strain hardening during the deformation with optimal strain rates is significant.

This study proposes a method for determination of material characteristics by inverse analysis of free bulging tests results. The blow-forming tests were carried out at the temperature of 415 °C using aluminum alloy (AMg-6) sheets of a 0.92 mm thickness. Each test was performed at constant pressure. For each fixed value of pressure, a series of experiments was carried out with different forming times to obtain evolutions of dome height H and thickness s. Two different constitutive equations were used to describe the dependence of flow stress on the effective strain rate: the Backofen power equation and the Smirnov one taking into account an s-shape of stress-strain rate curve in the logarithmic scale. The constants of these equations were obtained by least squares minimization of deviations between the experimental variations of H and s and ones predicted by a simplified engineering model formulated for this purpose. Using the Smirnov constitutive model to describe the dependence of flow stress on strain rate, unlike the classical power law, makes it possible to analyze the variation of strain rate sensitivity index m with strain rate. On the basis of the obtained data, the optimum strain rate for AMg-6 processing was estimated as one corresponding to the maximum of strain rate sensitivity index. The validity of the proposed method was examined by finite element simulation of free bulging process.

Electroencephalography (EEG) is a well-established non-invasive technique to measure the brain activity, albeit with a limited spatial resolution. Variations in electric conductivity between different tissues distort the electric fields generated by cortical sources, resulting in smeared potential measurements on the scalp. One needs to solve an ill-posed inverse problem to recover the original neural activity. In this article, we present a generic method of recovering the cortical potentials from the EEG measurement by introducing a new inverse-problem solver based on deep Convolutional Neural Networks (CNN) in paired (U-Net) and unpaired (DualGAN) configurations. The solvers were trained on synthetic EEG-ECoG pairs that were generated using a head conductivity model computed using the Finite Element Method (FEM). These solvers are the first of their kind, that provide robust translation of EEG data to the cortex surface using deep learning. Providing a fast and accurate interpretation of the tracked EEG signal, our approach promises a boost to the spatial resolution of the future EEG devices.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables