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On one mathematical model of creep in superalloys

Jiří Vala — 1998

Applications of Mathematics

In a new micromechanical approach to the prediction of creep flow in composites with perfect matrix/particle interfaces, based on the nonlinear Maxwell viscoelastic model, taking into account a finite number of discrete slip systems in the matrix, has been suggested; high-temperature creep in such composites is conditioned by the dynamic recovery of the dislocation structure due to slip/climb motion of dislocations along the matrix/particle interfaces. In this article the proper formulation of the...

On a system of equations of evolution with a non-symmetrical parabolic part occuring in the analysis of moisture and heat transfer in porous media

Jiří Vala — 2002

Applications of Mathematics

Most non-trivial existence and convergence results for systems of partial differential equations of evolution exclude or avoid the case of a non-symmetrical parabolic part. Therefore such systems, generated by the physical analysis of the processes of transfer of heat and moisture in porous media, cannot be analyzed easily using the standard results on the convergence of Rothe sequences (e.g. those of W. Jäger and J. Kačur). In this paper the general variational formulation of the corresponding...

The method of Rothe and two-scale convergence in nonlinear problems

Jiří Vala — 2003

Applications of Mathematics

Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.

Numerical approaches to the modelling of quasi-brittle crack propagation

Jiří Vala — 2023

Archivum Mathematicum

Computational analysis of quasi-brittle fracture in cement-based and similar composites, supplied by various types of rod, fibre, etc. reinforcement, is crucial for the prediction of their load bearing ability and durability, but rather difficult because of the risk of initiation of zones of microscopic defects, followed by formation and propagation of a large number of macroscopic cracks. A reasonable and complete deterministic description of relevant physical processes is rarely available. Thus,...

Optimization approaches to some problems of building design

Jiří ValaPetra Jarošová — 2018

Applications of Mathematics

Advanced building design is a rather new interdisciplinary research branch, combining knowledge from physics, engineering, art and social science; its support from both theoretical and computational mathematics is needed. This paper shows an example of such collaboration, introducing a model problem of optimal heating in a low-energy house. Since all particular function values, needed for optimization are obtained as numerical solutions of an initial and boundary value problem for a sparse system...

Non-local damage modelling of quasi-brittle composites

Jiří ValaVladislav Kozák — 2021

Applications of Mathematics

Most building materials can be characterized as quasi-brittle composites with a cementitious matrix, reinforced by some stiffening particles or elements. Their massive exploitation motivates the development of numerical modelling and simulation of behaviour of such material class under mechanical, thermal, etc. loads, including the evaluation of the risk of initiation and development of micro- and macro-fracture. This paper demonstrates the possibility of certain deterministic prediction, applying...

On the computational identification of temperature-variable characteristics of heat transfer

Vala, Jiří — 2013

Applications of Mathematics 2013

The mathematical analysis of a heat equation and its solutions is a standard part of most textbook of applied mathematics and computational mechanics. However, serious problems from engineering practice do not respect formal simplifications of such analysis, namely at high temperatures, for phase-change materials, etc. This paper, motivated by the material design and testing of a high-temperature thermal accumulator, as a substantial part of the Czech-Swedish project of an original equipment for...

Computational design optimization of low-energy buildings

Vala, Jiří — 2017

Proceedings of Equadiff 14

European directives and related national technical standards force the substantial reduction of energy consumption of all types of buildings. This can be done thanks to the massive insulation and the improvement of quality of building enclosures, using the simple evaluation assuming the one-dimensional stationary heat conduction. However, recent applications of advanced materials, structures and technologies force the proper physical, mathematical and computational analysis coming from the thermodynamic...

Computational approaches to some inverse problems from engineering practice

Vala, Jiří — 2015

Programs and Algorithms of Numerical Mathematics

Development of engineering structures and technologies frequently works with advanced materials, whose properties, because of their complicated microstructure, cannot be predicted from experience, unlike traditional materials. The quality of computational modelling of relevant physical processes, based mostly on the principles of classical thermomechanics, is conditioned by the reliability of constitutive relations, coming from simplified experiments. The paper demonstrates some possibilities of...

Modelling of heat and moisture propagation in building structures

Vala, Jiří — 2004

Programs and Algorithms of Numerical Mathematics

The thermal technical analysis is an important part of the design of building constructions. Especially for dwelling structures valid Czech(oslovak) and European standards formulate criteria of maximal thermal stability and minimal energy consumption that have to be verified by credible calculations. The propagation of heat through a building construction, consisting typically of several porous layers, is conditioned by the amount of moisture in such construction; simultaneously it is affected by...

Modelling of multicomponent diffusive phase transformation in solids

Vala, Jiří — 2008

Programs and Algorithms of Numerical Mathematics

Physical analysis of phase transformation of materials consisting from several (both substitutional and interstitial) components, coming from the Onsager extremal thermodynamic principle, leads, from the mathematical point of view, to a system of partial differential equations of evolution type, including certain integral term, with substantial differences in particular phases ( α , γ ) and in moving interface of finite thickness ( β ), in whose center the ideal liquid material behaviour can be detected....

On some composite schemes of time integration in structural dynamics

Vala, Jiří — 2019

Programs and Algorithms of Numerical Mathematics

Numerical simulations of time-dependent behaviour of advances structures need the analysis of systems of partial differential equations of hyperbolic type, whose semi-discretization, using the Fourier multiplicative decomposition together with the finite element or similar techniques, leads to large sparse systems of ordinary differential equations. Effective and robust methods for numerical evaluation of their solutions in particular time steps are required; thus still new computational schemes...

Numerical aspects of the identification of thermal characteristics using the hot-wire method

Vala, Jiří — 2013

Programs and Algorithms of Numerical Mathematics

The hot-wire method, based on the recording of the temperature development in time in a testing sample, supplied by a probe with its own thermal source, is useful to evaluate the thermal conductivity of materials under extremal loads, in particular in refractory brickworks. The formulae in the technical standards come from the analytical solution of the non-stationary equation of heat conduction in cylindric (finally only polar) coordinates for a simplified formulation of boundary conditions, neglecting...

Computational modelling of thermal consumption of buildings with controlled interior temperature

Vala, Jiří — 2017

Programs and Algorithms of Numerical Mathematics

New materials, structures and technologies used in civil engineering impeach traditional evaluations of the annual thermal consumption of buildings, based on the quasi-stationary estimate of the thermal resistance of the building envelope, or some operational parts of such building with the guaranteed temperature. The complete proper physical analysis, applying the principles of thermodynamics and appropriate constitutive relations for particular material layers and air in rooms, is not realistic...

Numerical solution of the Kiessl model

Josef DalíkJosef DaněčekJiří Vala — 2000

Applications of Mathematics

The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...

Identification of basic thermal technical characteristics of building materials

Stanislav ŠťastníkJiří ValaHana Kmínová — 2007

Kybernetika

Modelling of building heat transfer needs two basic material characteristics: heat conduction factor and thermal capacity. Under some simplifications these two factors can be determined from a rather simple equipment, generating heat from one of two aluminium plates into the material sample and recording temperature on the contacts between the sample and the plates. However, the numerical evaluation of both characteristics leads to a non-trivial optimization problem. This article suggests an efficient...

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