2019 Programme

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Monday, December 9, 2019, 13:00, Lecture Room B  

Application of the method of localized Lagrange multipliers to the partitioned solution of large-scale structural dynamic systems: The AFETI algorithm

Prof. José González, Universidad de Sevilla, Spain  
In this talk, we will discuss about classical and new numerical techniques used for parallel/partitioned computations in structural mechanics and also multi-physics or coupled-field problems. In this field, methods based on classical Lagrange multipliers, like the two-level FETI-DP method, have been de facto the preferred parallel algorithms in solid and structural mechanics for decades. However, as we will see, classical Lagrange multipliers also present some limitations. The method of localized Lagrange multipliers (LLM) is a more general coupling technique, that introduces an explicit definition of the problem interface and brings some important advantages. Under this LLM framework, new partitioned algorithms like AFETI-C method are derived from variational principles. AFETI-C uses a combination of rigid-body modes and dominant substructural deformation modes in enforcing the interface force equilibrium equation as constraint conditions. In addition, a regularization of heterogeneities of partitioned systems is appended to AFETI-C that makes it competitive with FETI-DP. These methods, their derivation and their performance will be described, providing a full understanding of the potential of LLM in the solution of coupled problems.
Friday, December 6, 2019, 11:00, Lecture Room Klub  

Cavitation and separation during water entry and exit

Alexander Korobkin, Professor in Applied Mathematics  
First part of the presentation will explain the pressure distributions over the wetted surfaces of a parabolic contour in 2D and an elliptic paraboloid in 3D for oblique water impact. The pressures are calculated by the Wagner model of water entry with focus on zones of the wetted surface, where the hydrodynamic pressure is below the ambient pressure, and the zones, where the pressure approaches the vapour pressure. When the zones of low hydrodynamic pressure approach the contact line of the body surface, the surrounding air flows into this area separating the liquid surface from the body and leading to ventilation. Several models of ventilation and cavitation for 2D problem of oblique impact of rigid and elastic plates will be introduced. The nonlinear 2D problem of oblique impact of an elliptic cylinder onto a thin liquid layer with multiple bouncing of the cylinder from water will be presented. The second part of the presentation is about the water exit problems including the problem of an elastic disc lifted from water surface. The corresponding exit models will be applied to the 3D problem of a rigid ellipsoid gliding on water surface. Comparison of the obtained results with 3D CFD results will be shown. Our exit model of elastic bodies will be compared with the experimental results for large accelerations of the body lifting.
Wednesday, December 4, 2019, 10:00, Lecture Room B  

Properties of open thermodynamic systems as the consequence of their stability

Prof. František Maršík, DrSc., Institute of Thermomechanics, The Czech Academy of Sciences, University of West Bohemia, Faculty of Physical Education and Sport, Charles University  
The presented concept deals with production of entropy generated by the nonequilibrium processes in consequence of the mass and energy transfer. Often used concept of endoreversible thermodynamics is based on non-realistic conjecture that the entire entropy production is realized at the system boundary. In this contribution, the open system in the thermodynamically non-equilibrium state is assumed. Production of entropy is generated due to the non-equilibrium processes accompanied by the energy conversion. The non-equilibrium steady state is maintained by a negative entropy flux. The stability conditions of the state with the minimum of entropy production are used to replace the endoreversibility concept.

This theory is applied to three different open non-equilibrium systems.

i) Efficiency of thermal machines and chemical reactors.
Hydrogen fuel cell with polymer electrolyte membrane are studied in details. The transport coefficients for reactants inlet, i.e. hydrogen and air, and for the products outlet, i.e. water, are connected with the actual electric efficiency. The calculated efficiency qualitatively and quantitatively corresponds to the experimentally obtained values. The further research shall focus on the relation of the parameters characterizing the membrane and transport of reactants and products to the power output.

ii) Energetic limitations of population growth.
Entropy production is characterized by general form of chemical reaction based on the mass action law. This law is usable for description of dynamics of population biology, e.g. cells, species. Moreover, this law can be even used to study dynamics of ecological systems. The reproduction process is spontaneous process with increase of entropy. The entropy increase is compensated by the negative entropy flux from the Sun. From the thermodynamic point of view, the sex reproduction is more advantageous as the cellular division because of it is reached by the lower Gibbs free enthalpy. This is probably the reason why sex reproduction is evolutionarily more advantageous.

iii) Dynamics of ecological system with migration.
Influence of reproduction and migration dynamics is evident on example of two competitive ecological systems (in general two auto catalytic reactions) of type predator and prey. The migration decreases the frequency of dynamical state of system. Due the migration this dynamical state can change to the stationary state, when time period is high enough. In principle, it is a diffusion reaction system in which a stationary spatial change of concentrations can occur. An example may be the presence of colored stripes on the body of some animals, such as cats, some fish, hornets, and the like.

Friday, November 15, 2019, 10:00, Lecture Room B  

Model reduction for the FEM of solids applied to the Rayleigh-Ritz computation of the free vibration spectrum

Prof. Petr Krysl, University of California, San Diego
Modal expansion is a workhorse used in many engineering analysis algorithms. One example is the coupled boundary element-finite element computation of the backscattering target strength of underwater elastic objects. To obtain the modal basis, a free-vibration (generalized eigenvalue) problem needs to be solved. This tends to be expensive when there are many basis vectors to compute. In the above mentioned backscattering example it could be many hundreds or thousands. Excellent algorithms exist to solve the free-vibration problem, and most use some form of the Rayleigh-Ritz (RR) procedure. The key to an efficient RR application is a low-cost transformation into a reduced basis. In this work we show how a cheap a priori transformation can be constructed for solid-mechanics finite element models based on the notion of coherent nodal clusters. The inexpensive RR procedure leads to not insignificant speedups of the computation of an approximate solution to the free vibration problem.
Wednesday, November 13, 2019, 13:00, Lecture Room B  

Non-coaxiality between two tensors: Application to stress rate decomposition and non-coaxial invariants

Prof. Yannis F. Dafalias, Institute of Thermomechanics of the Czech Academy of Sciences, Prague
Given a stress tensor and its rate, what are the analytical expressions of the parts of the stress-rate tensor that are (a) coaxial with the stress; (b) non-coaxial with the stress; (c) proportional with the stress; (d) non-proportional but coaxial with the stress; (e) orthogonal and coaxial with the stress and (f) orthogonal and non-coaxial with the stress? To answer the foregoing questions the coaxial and totally non-coaxial parts of a tensor in regard to another reference tensor are derived in closed analytical form based on representation theorems of tensor-valued isotropic functions. In the process a new interpretation is obtained for a singular case of representation theorems. The particular application of rotational shear is presented where analytical expressions are obtained for the parts of a stress rate tensor that induce (1) change of stress principal axes at fixed principal stress values, and (2) change of stress principal values at fixed stress principal axes such that the deviatoric stress orbit is circular on the π-plane. Additional application in mechanics are discussed such as the definition and role of invariants related to the non-coaxial and orthogonal parts.
Tuesday, November 5, 2019, 10:00, Lecture Room A  

Notes on Experimental Research on Transonic Compressor Blade Cascades

Dr. David Šimurda, Institute of Thermomechanics of the Czech Academy of Sciences, Prague
Despite ever increasing capabilities of CFD, experimental research on compressor blade cascades still plays important role in design and operation of gas turbines and other turbomachinery. This is true particularly in case of first stages of today’s large output gas turbine compressors and aircraft engine fans which operate at transonic range of relative inlet velocities. However, due to specific features of the flow past compressor cascades at transonic regimes, namely unstarted supersonic flow, experimental modelling is relatively complicated. Aim of the lecture will be to point out main difficulties connected with the cascade tests arising from the nature of compressor cascade flow and to provide ways of dealing with these problems.
Tuesday, October 22, 2019, 12:00, Lecture Room A  

The Energy-Sampling Stabilization of Nodally Integrated Continuum Elements for Dynamic Analyses

Prof. Petr Krysl,University of California, San Diego
Nodally integrated elements exhibit spurious modes in dynamic analyses (such as in modal analysis). Previously published methods involved a heuristic stabilization factor, which may not work for a large range of problems, and a uniform amount of stabilization was used over all the finite elements in the mesh. The method proposed here makes use of energy-sampling stabilization. The stabilization factor depends on the shape of the element and appears in the definition of the properties of a stabilization material. The stabilization factor is non-uniform over the mesh, and can be computed to alleviate shear locking, which directly depends on the aspect ratios of the finite elements. The nodal stabilization factor is then computed by volumetric averaging of the element-based stabilization factors. Energy-sampling stabilized nodally integrated elements (ESNICE) tetrahedral and hexahedral are proposed. We demonstrate on examples that the proposed procedure effectively removes spurious (unphysical) modes both at lower and at higher ends of the frequency spectrum. The examples shown demonstrate the reliability of energy-sampling in stabilizing the nodally integrated finite elements in vibration problems, just sufficient to eliminate the spurious modes while imparting minimal excessive stiffness to the structure. We also show by the numerical inf-sup test that the formulation is coercive and locking-free.
Monday, October 21, 2019, 10:00, Lecture Room B  

Lessons to be learned from German Attempts to Reduce Atmospheric CO2-Emissions

Prof. Dr-Ing. Roland Span, Ruhr University Bochum, Germany
With the goal to limit the increase of the average global temperature to 1.5 to 2 K, the governments of almost all developed countries agreed to drastically reduce atmospheric CO2 emissions. Though the common political will is clearly declared, concepts how the emission of greenhouse-gas emissions can be drastically reduced are very different and seem only partly realistic and appropriate. In this context Germany has launched the “Energiewende” program. This program relies essentially on a drastic increase in renewable power-production with wind and sun being the main energy sources and on reduced energy consumption in industry, private households, and traffic. Even though the availability of both wind and sun is rather limited in Germany, the program can so far be considered a success with regard to renewable power-production. The increase in renewable power-productions exceeded the politically formulated goals. However, currently the further increase is slowed down by different political measures, because a number of (mostly non-technical) limitations became obvious, that have not been addressed properly. And the required energy savings in the different sectors could not be realizedto date. Aspects of sectorial coupling have not been considered properly and problems in the areas of mobility and heat supply were underestimated. The presentation will briefly address the observed limitations and will formulate a number of theses derived from these findings. Not all of the factors influencing the further development of renewable power-production in Germany are relevant in other countries as well, but still the derived theses may serve as a starting point for general discussions on options for energy systems with largely reduced atmospheric CO2-emissions.
Wednesday, October 2, 2019, 10:30, Lecture Room B  

High Strain-rate Experiments Using Hopkinson Bar: Application on Cellular Metals and Additively Manufactured Auxetic Structures

Ing. Tomáš Fíla, Faculty of Transportation Sciences, Czech Technical University in Prague
Cellular solids, such as metal foams, hybrid foams, 3D printed lattices or additively manufactured auxetic structures are complex lightweight cellular materials with high energy absorption capabilities and possible functionally graded material properties. Thus, mechanical behavior of the materials under the representative loading conditions (i. e., dynamic impact, blast) has to be well understood. In this study, results of several experimental campaigns covering high-strain rate testing of cellular solids using conventional Split Hopkinson Pressure Bar (SHPB) and direct impact Open Hopkinson Pressure Bar (OHPB) are presented. High-speed imaging together with custom digital image correlation (DIC) technique are introduced as vital techniques for a complex experimental analysis of the materials at high strain-rates. Examples covering the evaluation of the displacement and strain fields, different methods for evaluation of Poisson’s ratio, and the analysis of the digital image correlation reliability are shown. Comparison of the digital image correlation results with the other methods (e. g. strain-gauges), its limitations and the actual challenges in this field are discussed. Overview of the experiments conducted at low and elevated temperatures observed using high-speed thermal imaging will be provided as well.
Wednesday, October 2, 2019, 10:00, Lecture Room B  

Digital image correlation: from static tests to X-ray tomography and high strain-rate loading

Prof. Ondřej Jiroušek, Faculty of Transportation Sciences, Czech Technical University in Prague
In the short lecture an overview of digital image correlation (DIC) applied to strain measurement of samples loaded in mechanical tests in general will be given. Examples of using the method in several engineering applications will be given, extension of the method that enables to use it in 3D (using time-lapse tomography) will be introduced and examples of experiments performed on a wide range of materials, ranging from trabecular bone samples, whole bone samples (vertebral bodies) to metallic foams will be presented. A special attention will be given to high-strain rate loading using Split Hopkinson Pressure Bar technique.
Pondělí 23. září 2019, 14:00, posluchárna A  
Monday, September 23, 2019, 14:00, lecture room A  

Twin mortar method: A new unbiased mesh tying formulation

Ing. Ján Kopačka, Ph.D., Institute of Thermomechanics, Czech Academy of Sciences
This work was motivated by the author's six-month stay in the Aerospace Mechanics Research Center of the University of Colorado Boulder. The author joined the Multi-Physics Design Optimization group focusing on the level-set eXtended Finite Element Method (XFEM) topology optimization. The main aim was to revise existing interface formulations and come up with a new one that would be robust and stable enough to be used with the level-set XFEM. The mesh tying is an important issue encountered in the finite element analysis of complex structures. It enables to join the adjacent dissimilarly meshed parts or their regions. This problem is even more pronounced in the case of isogeometric analysis that is a modern spatial discretization technique which instead of Lagrange shape functions utilizes NURBS basis functions. Conventional mesh tying methods are based on the master-slave concept that leads to a biased algorithm. Consequently, results are influenced by the selection of the master and the slave interface. Inspired by the two-pass dual formulations, we come up with a new formulation which inherits all appealing properties of the mortar method. Namely, it preserves optimal convergence rates and is variationally consistent. At the same time, the newly proposed mesh tying formulation is unbiased, i.e. the formulation is independent on the selection of the master and slave side. As a result, it substantially simplifies the definition of mesh tying interface and has a great potential for the solution of the self-contact problems.
Monday, September 23, 2019, 13:00, lecture room A  

Recent Advances in Wave Propagation and Large-Step Transient Analysis Procedures

Prof. K. C. Park, Ann & H.J. Smead Aerospace Engineering Sciences, University of Colorado, Boulder, Colorado, USA
In recent years, there have been several notable advances both in wave propagation and explicit transient structural dynamic analysis procedures. These include: (1) accurate wavefront tracking algorithms that can handle material heterogeneities; (2) accurate explicit algorithm employing improved non-diagonal inverse mass matrices; (3) large-step explicit integration of low and medium-frequency response analysis by filtering out mesh frequencies, among others. These advances offer structural dynamicists several options in wave propagation and transient analysis for capturing the predominant physics of the problems at hand, with drastically increased computational efficiency and robustness. In this talk, we will go over some salient features of these advances, and offer potential topics for further research..
Wednesday, September 18, 2019, 10:00, lecture room B  

Film-based shear stress sensor

Ing. Zuzana Broučková, Ph.D., Institute of Thermomechanics, Czech Academy of Sciences
The talk will summarize the six-month stay of the author at the School of Mechanical, Aerospace and Civil Engineering of the University of Manchester, UK. The stay was focused on the research and development of the novel experimental technique for evaluation of the shear stresses on the wall washed by the fluid flow. This technique is based on attachment of a sensor made out of elastic material on a surface/wall (film-based shear-stress sensor). Subsequently, the shear stress is evaluated from the deformation of the sensor under loading (both instantaneous and time-average shear stresses). The advantage of this method is its possibility to measure very low shear stresses, i.e. to use it in flows with very low velocities. Moreover, it is also possible to use it e.g. in water-channels and on curved surfaces, where many other commonly used methods are unable to work.
Wednesday, August 9, 2019, 10:00, lecture room B  

The Martensitic Transformation in In-Tl Alloys Revisited

Prof. Trevor R. Finlayson, University of Melbourne, Australia
The traditional view for the martensitic transformation in In-xat%Tl alloys, for 15.5 ≤ x ≤ 30.5 was via a double shear such as: (101)[10-1]; (011)[01-1], on the basis of optical microscopy observations and measurements of the (c11 - c12)/2 elastic constant. These early results, together with a calculation of the phonon dispersion relations based on a model pseudopotential and the measured elastic constants as input parameters, suggested that the transformation was driven by the softening of low-ζ [ζζ0][ζ-ζ0] phonons, which provided the motivation for a measurement of the phonon dispersion relations using neutron, inelastic scattering. This now historical background for the transformation in In-Tl alloys will be reviewed.
However, the suggested low-ζ [ζζ0][ζ-ζ0] phonon softening has never been observed experimentally, despite phonon measurements to as low as ζ = 0.02 rlu on the [ζζ0][ζ-ζ0] branch. An alternative model for the formation of coherent nuclei and growth along conjugate {111} planes was once proposed by Geisler. This model is consistent with some electron diffuse scattering data as well as yielding identical x-ray pole figure results as those for the double-shear mechanism. Appropriate nuclei could be generated by <111><11-2> atomic displacements.
To test such an idea, we have measured the [ζζζ]T phonon branch for a good quality In-Tl crystal in a recent experiment using the cold triple-axis instrument, SIKA, at the Australian OPAL Research Reactor. The initial results have shown that the zone-boundary, [ζζζ]T phonon softens with decreasing temperature, which may provide the dynamical behaviour consistent with the Geisler model for the transformation. Further experiments are planned to investigate this softening and the consequential microstructural behaviour.

Associate Professor Trevor Finlayson has been an Honorary Principal Fellow at the University of Melbourne since February, 2007, following an academic career at Monash University where he had been engaged to introduce and teach Materials Science as an undergraduate discipline during the early 1970s. His research has covered a range of projects in the field of condensed matter physics/materials science, including aspects of superconductivity, magnetism, ferro- and piezo-electricity, phase transformations and the direct measurement of stresses in materials using diffraction techniques. His current projects involve studies on martensitic alloys and magnesia-partially-stabilized zirconia, using neutron scattering.

Wednesday, July 31, 2019, 10:00, lecture room B  

Control of Grid-side Converters under Grid Imbalance

Prof. Yongsug Suh, Ph.D., Chonbuk National University, Jeonju, Korea
The growing penetration of renewable energy sources into the present power grid requires that renewable energy sources provide the similar electrical characteristics as those of classical thermal power plants. In order to meet this requirement, active front-end converters; grid-side converters of renewable energy sources have been evolving to offer various control features to properly regulate the active and reactive output power. Recently, grid codes about LVRT and operation under unbalanced grid become very strict. In general, unbalanced current is caused by unbalanced grid conditions, and it leads to unbalanced voltage at PCC (Point of Common Coupling). These unbalanced voltage conditions generate a significant ripple and distortion of dc-link and ac input current of grid-side converters which eventually undermine various control features of grid side converter. This seminar covers the latest requirements on the gridside converter of renewable energy sources particularly under grid imbalance. The impact of grid imbalance on the operation of grid-side converters is analyzed based on the positive and negative sequential component theory of unbalanced electrical network. The various control techniques to properly compensate for the generation of harmonics are introduced. These control techniques are aimed to enhance the grid-friendly electrical characteristics of renewable energy sources. As a result, these control techniques are expected to play a positive role in growing penetration of renewable energy sources into the present power grid.
Wednesday, June 12, 2019, 10:00, lecture room B  

Stress waves and people in the Institute of Thermomechanics

Prof. Miloslav Okrouhlík, Institute of Thermomechanics of the Czech Academy of Sciences, Prague
The lecture will cover the following topics:
- Historical overview
- Analytical approach to stress wave propagation
- Dispersion
- Musing about threshold
- Computational
- Experimental
- Continuum limits
- Case studies
- Shell – experiment vs. FE analysis
- Rock drilling – how much of impact energy is lost in the rock
- How to make torsional waves out of axial ones
- Impacted rod with spiral slots – FE vs. experiment
- Cheep wisdom (or triviality) at the end
Monday, June 10, 2019, 13:00, lecture room B  

Shock wave propagation in complex media: an experimental contribution to dynamic behavior of materials at very high strain rates

Prof. Michel Arrigoni, ENSTA Bretagne, Brest, France
High added value technologies, as well as critical infrastructures in service, are more and more subjected to severe loadings. In order to increase their survivability in harsh environment, structures and materials have to be characterized under dynamic conditions such as crash test, ballistic impact and blast loading. During these extreme events, it is not always easy to implement sensors able to catch the evolution of physical parameters. The presented work exposes an experimental contribution to the characterization of shock wave effects and propagation in materials and on structures. Cases of study are split into two categories: soft impacts and hard impacts. This includes the use of instruments developed for this intention, such as shock pressure gauges and laser Doppler velocimeters and non-destructive techniques for damage assessment.
Wednesday, April 3 2019, 10:00, lecture room B  

A parallel multilevel domain decomposition solver and its application to adaptive finite element method

Dr. Jakub Šístek, Institute of Mathematics of the CAS
In the first part of the talk, a brief overview of the development of nonoverlapping domain decomposition methods will be given. The focus will be on the iterative substructuring methods using primal unknowns. The Balancing Domain Decomposition based on Constraints (BDDC) by C. Dohrmann will be used for describing these concepts. Next, two extensions of the original BDDC method will be discussed. The first is an adaptive generation of the coarse space to enhance its robustness, e.g. for finite element problems with variable coefficients. The second is an extension of the method to multiple levels, an approach to improving scalability of the method for parallel computations. Our open-source implementation of this Adaptive Multilevel BDDC method, the BDDCML library, will be presented.
In the second part of the talk, we will discuss combination of this solver with the finite element method using an adaptive mesh refinement (AMR). AMR is challenging in the context of distributed memory parallel FEM in general. The treatment of hanging nodes will be also described. Of particular interest is the effect of disconnected subdomains, a typical output of the employed mesh partitioning based on space-filling curves.
The talk will be concluded with numerical results for benchmark Poisson and linear elasticity problems.
Thursday, March 21, 2019, 10:00, lecture room B  

Decomposition of waves, stresses and forces in rotating disks

Prof. Izhak Bucher, Mechanical Engineering, Technion, Haifa, Israel
The present talk will focus on rotating disk dynamics by introducing a novel signal-processing method geared towards capturing the dynamics of such systems. The method exploits multiple sensors and is thus capable of handling spatially complex transient dynamics. Rotating disks identification methods rely on special features of rotating elements, e.g. cyclic-symmetry, gyroscopic effects, directional whirling and circumferentially traveling deformations, all have a physical meaning and are exploited in the proposed approach.
The ‘eyes’ of ‘Smart Rotating Machines’ are the sensors and the accompanied, real-time signal processing methods play the role of a ‘brain’ in the assessment of measured data. Indeed ‘smart’ also means combining advanced sensing capabilities with an electronic brain which is aware of the underlying physics laws to which the model obeys. At the moment, it seems that the pendulum leans heavily towards numerical modeling. Finite Element models are the basis for analysis and design, while testing and measurements provide only limited verification means for some of the model parameters due to poor deployment and simplistic signal processing procedures. The new method narrows the gap between models and experiment and it illustrates what can be gained when they are added.
The presentation will highlight the advantages of model-based signal processing over past and presently used methods and will try to point to a path leading from older methods and techniques towards present, state-of-the-art methods and further into the future where smart machines will have ‘eyes’ and ‘brains’.
Specifically, the presentation will describe spatial, temporal and directional decomposition of rotating machine vibrations during rapid rotational accelerations. Real time signal processing methods that exploit Hilbert transform based decompositions; directional order-tracking and time-frequency maps will be demonstrated via simulations and experiments. The spatial and temporal decomposition method enables a Smart-Machine to assess true stress and strain on parts rotating relative to an array of sensors and thus help to enhance safety.
One additional topic will be briefly shown if time allows: active detection of imbalance for high-speed modes, using slow rotation data.
Thursday, March 21, 2019, 11:00, lecture room B  

Thermodynamical modeling via GENERIC: from quantum mechanics to semiconductor devices

Prof. Alexander Mielke, Weierstrass Institute for Applied Analysis and Stochastics, and Humboldt University Berlin
We discuss the thermodynamically consistent modeling of semiconductor devices from the mathematical point of view. The task lies in coupling of several physical effects that occur on different temporal or spatial scales, namely optics via the Maxwell equations, charge transport
via drift-diffusion models and quantum mechanical processes in embedded quantum dots, wires or layers.
Using the framework of GENERIC, which is an acronym for General Equations for Non-Equilibrium Reversible Irreversible Coupling, we construct suitable hybrid models that are thermodynamically consistent in the sense that for the isolated system we have energy conservation and positive entropy production. The conservative dynamics is driven by a Hamiltonian structure involving the energy, whereas the dissipative dynamics is driven by an entropic gradient system.
Wednesday, March 6, 2019, 10:00, lecture room B  

Reconstruction of past climate changes from temperature measurements in deep boreholes

Jan Šafanda, Institute of Geophysics of the CAS
One of the frequently discussed topics of today is the nature and causes of global warming observed in the last 100-150 years and the prediction of its future development. The answers to these questions are mainly sought using climatic and meteorological models based on the current (imperfect) state-of-the-art about processes in the
atmosphere, hydrosphere and lithosphere. In addition to data from observations proxy data on the climate history over longer periods of time are also used for model calibration. One of the paleoclimatic methods producing proxy data is the reconstruction of the ground surface temperature history from temperature-depth profiles measured in deep boreholes. The lecture will focus on the principles and results of this method.
Wednesday, February 13, 2019, 10:00, lecture room B  

Theoretical and implementation problems of the multi-dimensional Fokker-Planck equation analysis using the Finite Element Method

Dr. Jiří Náprstek, Institute of Theoretical and Applied Mechanics of the CAS
Fokker–Planck equation is one of the most important tools for investigation of dynamic systems under random excitation. Finite Element Method represents very effective solution possibility particularly when transition processes are investigated or more detailed solution is needed. However, a number of specific problems must be overcome. They follow predominantly from the large multi-dimensionality of the Fokker–Planck equation, shape of the definition domain and usual requirements on the nature of the solution which are out of a conventional practice of the Finite Element employment. Unlike earlier studies it is coming to light that multi-dimensional simplex elements are the most suitable to be deployed. Moreover, new original algorithms for the multi-dimensional mesh generating were developed as well as original procedure of the governing differential and algebraic systems assembling and subsequent analysis. Finally, an illustrative example is presented together with aspects typical for the problem with large multi-dimensionality.
Wednesday, January 9, 2019, 10:00, lecture room B  

Dynamical damage and phase-field fracture models

Tomáš Roubíček, Institute of Thermomechanics of the CAS
Damage is a phenomenon/concept in continuum mechanics of solid materials undergoing various degradation processes with numerous applications in engineering and in computational mechanics and (geo)physics. Combination with inertial effects may be important modelling issue to prevent various undesired effects otherwise occuring in quasistatic models. Various damage models and their variants as a phase-field fracture will be overviewed. Also, several numerical approaches will be presented, amenable to compute vibrations or waves emitted during fast damage/fracture, together with various extensions of the basic scenario, combining mass or heat transfer, or plasticity.

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