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Determination of the initial stress tensor from deformation of underground opening-theoretical background and applications
Malík, Josef; Kolcun, Alexej
2023 - English
In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the excavation process. This methods is based on the solution of eighteen auxiliary problems in the theory of elasticity with force boundary conditions. The optimal location of the pairs of points on the wall of underground work is studied. The pairs must be located so that the condition number of a certain matrix has the minimal value, which guarantees a reliable estimation of initial stress tensor.
Keywords:
initial stress tensor; first boundary value problem of the theory of elasticity; condition number of matrices
Fulltext is available at external website.
Determination of the initial stress tensor from deformation of underground opening-theoretical background and applications
In this paper a method for the detection of initial stress tensor is proposed. The method is based on measuring distances between some pairs of points located on the wall of underground opening in the ...
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 ...
Hidden symmetry in turbulence and analytic study of shell models
Caggio, Matteo
2023 - English
This short communication concerns symmetries in developed turbulence and analytic study of shell models. However scale-invariance is broken due to the intermittency phenomenon, is possible to established a hidden self-similarity in turbulent flows. Using a shell model, the author in [18] (see also [19]) addressed the problem deriving a scaling symmetry for the inviscid equations. Here, first we discuss the analysis presented in [18], then, from the mathematical perspective, we propose an analytic study for the shell model with the presence of the viscous terms. This brief paper should be understood as an introductory note to this new scaling symmetry with implications for mathematical analysis [5].
Keywords:
turbulence; scale-invariance symmetry; intermittency; shell-models
Available in digital repository of the ASCR
Hidden symmetry in turbulence and analytic study of shell models
This short communication concerns symmetries in developed turbulence and analytic study of shell models. However scale-invariance is broken due to the intermittency phenomenon, is possible to ...
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 ...
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 ...
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 ...
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
Béreš, Michal
2023 - English
In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG system of equations is kept in the compressed tensor form and its solution is a very challenging task. Here, we present the reduced basis (RB) method as a solver which looks for a low-rank representation of the solution. The construction of the RB consists of iterative expanding of the basis using Monte Carlo sampling. We discuss the setting of the sampling procedure and an efficient solution of multiple similar systems emerging during the sampling procedure using deflation. We conclude with a demonstration of the use of SG solution for forward uncertainty quantification.
Keywords:
stochastic Galerkin method; reduced basis method; Monte Carlo method; deflated conjugate gradient method
Fulltext is available at external website.
Reduced basis solver for stochastic Galerkin formulation of Darcy flow with uncertain material parameters
In this contribution, we present a solution to the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with uncertain material coefficients in the separable form. The SG ...
Numerical realization of the Bayesian inversion accelerated using surrogate models
Bérešová, Simona
2023 - English
The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte Carlo (MCMC) methods accelerated with surrogate models. A surrogate model is understood as an approximation of the forward model which should be computationally much cheaper. The target distribution is not fully replaced by its approximation. Therefore, samples from the exact posterior distribution are provided. In addition, non-intrusive surrogate models can be updated during the sampling process resulting in an adaptive MCMC method. The use of the surrogate models significantly reduces the number of evaluations of the forward model needed for a reliable description of the posterior distribution. Described sampling procedures are implemented in the form of a Python package.
Keywords:
Bayesian inversion; delayed-acceptance Metropolis-Hastings; Markov chain Monte Carlo; surrogate model
Fulltext is available at external website.
Numerical realization of the Bayesian inversion accelerated using surrogate models
The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown ...
Dynamics of a cantilever beam with piezoelectric sensor: Experimental study
Kolman, Radek; Kylar, Jaromír; Kotek, Vojtěch; Cimrman, Robert; Musil, Ladislav
2023 - English
Online and real-time sensing and monitoring of the health state of complex structures, such as air-craft and critical parts of power stations, is an essential part of the research in dynamics. Several types of sensors are used for sensing dynamic responses and monitoring response changes during the operation of critical parts of complex systems. The piezoelectric (PZ) materials belong to one group of electroactive materials, which transform mechanical deformation into an electrical response. For example, PZ ceramics or PVDF foils are employed for online sensing of the time history of mechanical deformation. Experimentally obtained response of a cantilever beam structure with a glued PZ sensor is the case of interest in this contribution. During the transient problem of the beam loaded by suddenly interrupted load due to the weight of a mass at the end of the beam, the time history of normal velocity at a point on the beam surface has been measured by a laser vibrometer and parallely, the output voltage on the PZ sensor has been measured by an electric device. The experimental data in the case of the first eigen-frequency is in good agreement with the value given by the formulae from the theoretical modeling of free vibration of a linear beam.
Keywords:
dynamics of beam-like structure; piezo-electric material; sensing of dynamic response; structural Health Monitoring; laser vibrometer measurement
Fulltext is available at external website.
Dynamics of a cantilever beam with piezoelectric sensor: Experimental study
Online and real-time sensing and monitoring of the health state of complex structures, such as air-craft and critical parts of power stations, is an essential part of the research in dynamics. Several ...
On a stepladder model walking (with and without a decorator)
Polach, P.; Prokýšek, R.; Papáček, Štěpán
2023 - English
This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the real-time movement of the laboratory walking robot, designed and built at the Department of Control Theory of the Institute of Information Theory and Automation of the Czech Academy of Sciences [1, 6, 7]. Underactuated biped robots with an upper body form a subclass of legged robots, see, e.g., [4] for a review on the control of underactuated mechanical systems and [2] for a study of an asymptotically stable walking for biped robots. It is obvious that in general, the walking control of underactuated walking robots is a more challenging problem than walking control of fully actuated walking robots. As follows, we examine the well-known mechanical system of the stepladder model with and without a decorator, whose role is substituted by an external inertial force according to the D’Alembert principle. It is well known, that stepladder walking is possible due to the periodic movement (pendulating) of an operator – decorator1 The rigorous dynamical analysis of stable cyclic walking of a class of stepladder models is presented in the next section.
Keywords:
Underactuated biped robot models; Control algorithms; Legged robots
Fulltext is available at external website.
On a stepladder model walking (with and without a decorator)
This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the ...
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