Ústav matematiky a deskriptivní geometrie

Browse

Now showing 1 - 5 of 53

Statistical inference on the local dependence condition of extreme values in a stationary sequence
(Springer, 2025-07-28) Holešovský, Jan; Fusek, Michal
The extremal index is an important characteristic measuring dependence of extreme values in a stationary series. Several new estimators that are mostly based on interexceedance times within the Peaks-over-Threshold model have been recently published. Nevertheless, in many cases these estimators rely on suitable choice of auxiliary parameters and/or are derived under assumptions that are related to validity of the local dependence condition $D^{(k)}(u_n)$. Although the determination of the correct order $k$ in the $D^{(k)}(u_n)$ condition can have major effect on the extremal index estimates, there are not many reliable methods available for this task. In this paper, we present various approaches to assessing validity of the $D^{(k)}(u_n)$ condition including a graphical diagnostics and propose several statistical tests. A simulation study is carried out to determine performance of the statistical tests, particularly the type I and type II errors.
Determination of the yield of thermal mineral springs emerging into the Bečva River in the Teplice Spa
(Sciendo, 2025-01-13) Julínek, Tomáš; Říha, Jaromír; Grešl, Milan; Holešovský, Jan; Cabalka, Matouš
The mineral water in the Teplice Spa emerges into the Bečva River bed from the hypogenic karst formed by Palaeozoic limestones. Recently the focus on the hydrological and hydrogeological conditions of the mineral springs issues from the planning of the Skalička Dam whose reservoir is believed to be interconnected with the karstic formation and may influence the regime of mineral waters in the spa. One of the related particular problems is to determine the discharge of the mineral water which emerges into the Bečva River in the river reach along the Teplice Spa. The knowledge about the emerging mineral water discharge is crucial for further assessment of an impact of planned reservoir. The most challenging issue and novelty of the study was to determine a relatively small increment of the discharge in the Bečva river, when the magnitude of the error of determination was comparable to the determined discharge. Therefore, for the assessment of the discharge three methods were applied, namely measurements by the classical current meter, measurements using the Acoustic Doppler Current Profiler and evaluation of the measurements of electrical conductivity along the river reach. The analysis of obtained results and comparison of the obtained methods indicate the emerging discharge between 250 and 500 l/s with realistic value about 350 l/s. The study shows quite good agreement of results determined by individual methods which justifies the methodology used and is good guidance for similar studies.
The generalized Kelvin chain-based model for an orthotropic viscoelastic material
(SPRINGER, 2024-03-01) Trcala, Miroslav; Suchomelová, Pavlína; Bošanský, Michal; Hokeš, Filip; Němec, Ivan
We propose a constitutive material model to describe the rheological (viscoelastic) mechanical response of timber. The viscoelastic model is based on the generalized Kelvin chain applied to the orthotropic material and is compared to the simple approach given by standards. The contribution of this study consists of the algorithmization of the viscoelastic material model of the material applied to the orthotropic constitutive law and implementation into the FEM solver. In the next step, the fitting of the input parameters of the Kelvin chain is described, and at least a material model benchmark and comparison to the approach given by standards were done. The standardized approach is based on the reduction of the material rigidity at the end of the loading period using a creep coefficient, whereas the loading history state variables are not considered when establishing the result for a specific time step. The paper presents the benefits of the rheological model. It also demonstrates the fitting algorithm based on particle swarm optimization and the least squares method, which are essential for the use of the generalized Kelvin chain model. The material model based on the orthotropic generalized Kelvin chain was implemented into the FEM solver for the shell elements. This material model was validated on the presented benchmark tasks, and the influence of the time step size on the accuracy of model results was analyzed.
A constitutive model considering creep damage of wood
(SPRINGER, 2024-03-01) Trcala, Miroslav; Suchomelová, Pavlína; Bošanský, Michal; Němec, Ivan
The serviceability of wooden structures involves multiphysical phenomena, notably the interactions among creep, plasticity, and damage. The influence of creep on the initialization of the damage and on its growth and spread can be adjusted by an additional alpha parameter in order to take into account the coupled effect between creep and damage more properly. We integrate an orthotropic viscoelastic model, based on the generalized Kelvin chain, with an orthotropic damage model, capturing both the immediate nonlinear elastic-plastic-damage response and the time-dependent viscous response of timber. The combination of these material models is important to obtain a realistic description of wood behavior, because the timber shows an immediate nonlinear elastic-plastic-damage response, but also the time-dependent viscous response. In this paper, we algorithmize, implement, and validate the concept of 'creep damage', a phenomenon observed in wooden structures. Benchmark tests reveal two distinct patterns of damage in beech wood, immediate postload damage that evolves over time and damage that occurs and spreads during the loading period.
Damage behaviour of quasi-brittle composites: mathematical and computational aspects
(MDPI, 2025-04-11) Vala, Jiří; Tomáš, Jiří
In the present paper, an evaluation of the damage behaviour of quasi-brittle composites exposed to mechanical, thermal, and other loads is studied by means of viscoelastic and/or viscoplastic material models, applying some non-local regularisation techniques to the initiation and development of damages. The methods above are presented as a strong tool for a deeper understanding of material structures in miscellaneous engineering disciplines like civil, mechanical, and many others. Nevertheless, all of the software packages reflect certain compromises between the need for effective computational tools, with parameters obtained from inexpensive experiments, within the possibilities and the complexity of both physical and geometrical descriptions of structure deformation within processes. The article is devoted to the mathematical aspects regarding a considerably wide class of computational modelling problems, emphasising the following ones: (i) the existence and the uniqueness of solutions of engineering problems formulated in terms of the deterministic initial and boundary value problems of partial differential equations theory; (ii) the problems of convergence of computational algorithms applied to (i). Both aspects have numerous references to possible generalisations and investigations connected with open problems.

Browse

Recent Submissions