**79**

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**Souvislost mezi principem nejmenší akce a termodynamickou podmínkou stability**

Maršík, František; Trávníček, Zdeněk; Antošová, Zuzana

2023 - English
The extended principle is formulated for a material point (M.P.) X, which has nonzero mass, temperature, and trajectory x(X,t). The Lagrangian of this variation principle is equal to the kinetic energy from which, the internal energy of the material point (which depends on the entropy) and the additional energy caused by the frictional force are subtracted. The relation between the inertial force and the entropy gradient is found and the gravitational force is completely replaced by the entropy gradient. Thanks to the mentioned properties of the total enthalpy, the Thermodynamic criterion of stability of the state of M.P., is formulated.
Keywords:
*principle of the least action; thermodynamic stability condition; annular swirl flow*
Fulltext is available at external website.
Souvislost mezi principem nejmenší akce a termodynamickou podmínkou stability

The extended principle is formulated for a material point (M.P.) X, which has nonzero mass, temperature, and trajectory x(X,t). The Lagrangian of this variation principle is equal to the kinetic ...

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**Deep learning methods for the acoustic emission methods to evaluate an onset of plastic straining**

Parma, Slavomír; Kovanda, Martin; Chlada, Milan; Štefan, Jan; Kober, Jan; Feigenbaum, H. P.; Plešek, Jiří

2023 - English
Development of phenomenological plasticity models, hardening rules, and plasticity theories relies on experimental data of plastic straining. The experimental data are usually measured as the stress–strain response of the material being loaded and do not provide any clues or information about the local response of\nmaterial. In this paper, we analyze the plastic deformation of the material using the acoustic emission method and current state-of-the-art neural network models such as the InceptionTime architecture.
Keywords:
*metal plasticity; strain hardening; acoustic emission; neural networks*
Fulltext is available at external website.
Deep learning methods for the acoustic emission methods to evaluate an onset of plastic straining

Development of phenomenological plasticity models, hardening rules, and plasticity theories relies on experimental data of plastic straining. The experimental data are usually measured as the ...

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**Model order reduction for particle-laden flows: systems with rotations and discrete transport operators**

Kovárnová, A.; Isoz, Martin

2023 - English
In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction (MOR) of such systems, the shifted proper orthogonal decomposition with interpolation via artificial neural networks, is further extended by improving the handling of general transport operators. First, even with intrusive MOR approaches, the underlying numerical solvers can provide only discrete realizations of transports linked to the movement of individual particles in the system. On the other hand, our MOR methodology requires continuous transport operators. Thus, the original framework was extended by the possibility to reconstruct continuous approximations of known discrete transports via another artificial neural network. Second, the treatment of rotation-comprising transports was significantly improved.
Keywords:
*model order reduction; shifted POD; artificial neural networks; CFD-DEM; Open- FOAM*
Fulltext is available at external website.
Model order reduction for particle-laden flows: systems with rotations and discrete transport operators

In the present work, we concentrate on particle-laden flows as an example of industry-relevant transport-dominated systems. Our previously-developed framework for data-driven model order reduction ...

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**Dynamics of a cantilever beam with piezoelectric sensor: Parameter identification**

Cimrman, Robert; Kolman, Radek; Musil, Ladislav; Kotek, Vojtěch; Kylar, Jaromír

2023 - English
The piezoelectric materials are electroactive materials often applied for real-time sensing or structural health monitoring, both important research topics in dynamics. Mathematical models of such structures have to allow also for the external electrical circuits and contain several material parameters that need to be identified from experiments. We present a model of a simple experiment involving dynamics of a cantilever beam with an attached piezoelectric sensor excited by a suddenly removed weight. The external circuit can be taken into account as having either a finite or infinite resistance. We also outline the parameter identification procedure based on automatic differentiation and present the experimental and numerical results.
Keywords:
*finite element method; piezo-electricity; floating potential; dynamic simulation; parameter identification*
Fulltext is available at external website.
Dynamics of a cantilever beam with piezoelectric sensor: Parameter identification

The piezoelectric materials are electroactive materials often applied for real-time sensing or structural health monitoring, both important research topics in dynamics. Mathematical models of such ...

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**Development of autonomous experimental system to analyse yield surfaces distortion due to multiaxial ratcheting**

Svárovský, Jiří; Parma, Slavomír; Štefan, Jan; Ciocanel, C.; Feigenbaum, H. P.; Marek, René; Klepač, Vilém; Plešek, Jiří

2023 - English
Multiaxial ratcheting is a failure mode of structures characterized by the accumulation of plastic strain due to cyclic loading. Despite several models having been developed to predict multiaxial ratcheting, they often fail when validated with experimental data collected under a wide array of loading conditions. In this study, an experimental setup was developed and an autonomous testing procedure was used to experimentally analyze the evolution of the yield surface shape due to cyclic biaxial loading. Thin-walled tubular test specimens were made of 304L steel with a diameter of 40mm and underwent axial-torsional testing using the Instron 8852 system. The total axial strain was increased from 0 to 1% while the total shear strain underwent 5 cycles with the strain amplitude of 0.5% and the mean strain of 0.5%. Three yield surfaces were measured after the straining sequence was completed. Results showed strong directional distortional hardening and good agreement between the flow vectors and the normals to the yield surface, lending support to the associative flow rule.
Keywords:
*yield surface distortion; strain hardening; multiaxial ratcheting; flow rule*
Fulltext is available at external website.
Development of autonomous experimental system to analyse yield surfaces distortion due to multiaxial ratcheting

Multiaxial ratcheting is a failure mode of structures characterized by the accumulation of plastic strain due to cyclic loading. Despite several models having been developed to predict multiaxial ...

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**Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB**

Moskovka, Alexej; Frost, Miroslav; Valdman, Jan

2023 - English
Many processes in mechanics and thermodynamics can be formulated as a minimization of a particular energy functional. The finite element method can be used for an approximation of such functionals in a finite-dimensional subspace. Consequently, the numerical minimization methods (such as quasi-Newton and trust region) can be used to find a minimum of the functional. Vectorization techniques used for the evaluation of the energy together with the assembly of discrete energy gradient and Hessian sparsity are crucial for evaluation times. A particular model simulating the deformation of a Neo-Hookean solid body is solved in this contribution by minimizing the corresponding energy functional. We implement both P1 and rectangular hp-finite elements and compare their efficiency with respect to degrees of freedom and evaluation times.
Keywords:
*hp-FEM; energy functionals; numerical minimization*
Fulltext is available at external website.
Numerical minimization of energy functionals in continuum mechanics using hp-FEM in MATLAB

Many processes in mechanics and thermodynamics can be formulated as a minimization of a particular energy functional. The finite element method can be used for an approximation of such functionals in ...

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**Dynamics of a cantilever beam with piezoelectric sensor: Finite element modeling**

Cimrman, Robert; Kolman, Radek; Musil, Ladislav; Kotek, Vojtěch; Kylar, Jaromír

2023 - English
An elastodynamical model of a cantilever beam coupled with a piezoelectric sensor is introduced and its discretization using the finite element method is presented. The mathematical model includes additional terms that enforce the floating potential boundary condition for keeping a constant charge on an electrode of the sensor. The behaviour of the model is illustrated using a numerical example corresponding to an experimental setup, where vibrations of the beam and the potential on the sensor are measured.
Keywords:
*finite element method; piezo-electricity; floating potential; dynamic simulation*
Fulltext is available at external website.
Dynamics of a cantilever beam with piezoelectric sensor: Finite element modeling

An elastodynamical model of a cantilever beam coupled with a piezoelectric sensor is introduced and its discretization using the finite element method is presented. The mathematical model includes ...

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**Calibrated finite volume method-based simulation framework for laser shock peening**

Isoz, Martin; Gruber, Pavel; Schmidt, Jaroslav; Kubíčková, Lucie; Štefan, Jan; Kaufman, Jan; Brajer, Jan; Gabriel, Dušan

2023 - English
Modern and highly competitive industry seeks components with high strength and fatigue resistance. Both of these properties may be improved by peening of the component surface and the standard peening processes, such as the shot peening, are widely used in both automotive and aerospace industries. The laser shock\npeening (LSP), i.e. hardening of the material surface by a laser-induced shock wave, is a modern alternative to the standard peening. Concurrently, the industrial applications of LSP are promoted by recently emerged affordable high power-density lasers. However, the nascent LSP applications are still mostly a trial-and-error\nprocesses based on an extensive experimental testing. Consequently, we focused on a highly application-driven development of a framework for LSP modeling, and the internal workings and results of which are the focus of the present contribution.
Keywords:
*laser shock peening; modeling; finite volume method; OpenFOAM*
Fulltext is available at external website.
Calibrated finite volume method-based simulation framework for laser shock peening

Modern and highly competitive industry seeks components with high strength and fatigue resistance. Both of these properties may be improved by peening of the component surface and the standard peening ...

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**Mixing characteristics of a magnetically driven Rushton turbine in an unbaffled stirred tank reactor**

Idžakovičová, Kristýna; Haidl, Jan; Gebouský, Ondřej; Isoz, Martin

2023 - English
The standard and well-researched stirred vessel configuration comprises a tank equipped with one or more impellers positioned in the vessel’s axis and multiple wall-mounted baffles preventing the central vortex creation. However, particular industries, such as biotechnology, have an increased need for a sterile environment that often results in the usage of atypical stirred vessel configurations. An example of a commonly equipped atypical stirred vessel is an unbaffled stirred tank with an eccentric magnetically driven impeller. However, there is only a little knowledge about the mixing characteristics of such designs. In this work, we list experimental results for both the standard and atypical stirred vessel configurations. Furthermore, we present a CFD model of the atypical configuration. The model is used to calculate its mixing characteristics that are subsequently compared against our experimental results. It is shown that for the liquid height (H) to the vessel diameter (T) ratio H/T ≲ 1.2, the characteristics of both the standard and atypical designs coincide. For higher liquid heights (i) the characteristics of the atypical design decrease dramatically, and (ii) the characteristics estimates based on approaches developed for the standard configuration become unreliable.
Keywords:
*stirred vessel; eccentric impeller; unbaffled tank; CFD; OpenFOAM; experiment*
Fulltext is available at external website.
Mixing characteristics of a magnetically driven Rushton turbine in an unbaffled stirred tank reactor

The standard and well-researched stirred vessel configuration comprises a tank equipped with one or more impellers positioned in the vessel’s axis and multiple wall-mounted baffles preventing the ...

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**Direct construction of reciprocal mass matrix and higher order fininite element method**

Cimrman, Robert; Kolman, Radek; González, J. A.; Park, K. C.

2023 - English
When solving dynamical problems of computational mechanics, such as contact-impact problems or cases involving complex structures under fast loading conditions, explicit time-stepping algorithms are usually preferred over implicit ones. The explicit schemes are normally combined with the lumped (diagonal) mass matrix so that the calculations are efficient and moreover dispersion errors in wave propagation are partially eliminated. As an alternative to lumping with advantageous properties, the reciprocal mass matrix is an inverse mass matrix that has the same sparsity structure as the original consistent mass matrix, preserves the total mass, captures well the desired frequency spectrum and leads thus to efficient and accurate calculations. In the contribution we comment on the usability of the reciprocal mass matrix in connection with higher order FEM.
Keywords:
*higher-order finite element method; reciprocal mass matrix; transient problems; explicit time integration; lumping process*
Fulltext is available at external website.
Direct construction of reciprocal mass matrix and higher order fininite element method

When solving dynamical problems of computational mechanics, such as contact-impact problems or cases involving complex structures under fast loading conditions, explicit time-stepping algorithms are ...

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