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1

On the solution of a problem of extended thermoelasticity theory (ETE) by using a complete finite element approach

Shivay O.N., Mukhopadhyay S.

Computational Methods in Science and Technology

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2019

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Vol. 25, No. 2

61--70

EN

This paper attempts to apply a complete finite element approach for the solution of problems on coupled dynamical thermoelasticity theory. Presently, we employ the extended thermoelasticity theory proposed by Lord and Shulman (1969) and consider a problem of linear thermoelasticity for the hollow disk with a thermal shock applied on its inner boundary. The thermoelastic equations have been solved using the complete finite element approach, where we have used discretization in the time domain as well as space domain and applied the Galerkin’s approach of the finite element for both time and space domain. We implement our scheme for a particular case and carry out computational work to obtain the numerical solution of the problem. Further, we compare the present results with the solutions obtained by FEM with Newmark time integration method and the solutions obtained by a trans-FEM method in which Laplace transform technique is used for the time domain. We show that, there is a perfect match in solutions of complete finite element approach with trans-finite element method and Newmark method. The efficiency of the method with respect to computation time is also compared with other two methods.

2

Coupled thermoelasticity of a functionally graded cracked layer under thermomechanical shocks

Rokhi M. M., Shariati M.

Archives of Mechanics

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2013

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Vol. 65, nr 2

71-96

EN

This paper investigates linear-elastic response of cracked functionally graded layers subjected to thermomechanical loading; classical coupled thermoelastic equations are used in the calculations. The coupled dynamical system of equations obtained from the extended finite element discretization is solved by the Newmark method in the time domain. Micromechanical models for conventional composites are used to estimate properties of functionally graded layer. The interaction integral is then employed to calculate the stress intensity factors at each time step. In addition, crack propagation phenomenon under thermomechanical shocks is investigated in this paper. We have used MATLAB software to implement the algorithm and related code of problem.

3

Fictitious Parts of the Load in Thermoelasticity

Jankowski J.

Computational Methods in Science and Technology

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2008

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Vol. 14, nr 2

EN

The three-dimensional coupled quasi-static problem of linear thermoelasticity is presented. The concept is based on a spatial extension of a region occupied by the considered body and on spatial formulation of a new fictitious load. All the outside objects are termed here fictitious ones. The solution of the initial-space value problem includes fictitious displacement-temperature components. Capacity values of approximate fictitious components are calculated from a boundary condition contracted to the finite time interval. The approximate solution to the primary thermoelastic problem is obtained by contracting in space the approximate solution to the initial-space value problem. It enables us to determine the thermoelastic flow.

4

Parallel evolutionary algorithms in shape optimization of heat radiators

Burczyński T., Długosz A., Kuś W.

Journal of Theoretical and Applied Mechanics

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2006

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Vol. 44 nr 2

351-366

EN

The paper deals with the application of Parallel Evolutionary Algorithms (PEA) and the Finite Element Method (FEM) in shape optimization of heat radiators. The fitness function is computed with the use of the coupled thermoelsticity modelled by MARC/MENTAT software. The geometry, mesh and boundary conditions are created on the basis of a script language implemented in MENTAT. In order to reduce the number of design parameters in evolutionary algorithms, the shape of the structure is modelled by Bezier curves. Numerical examples for some shape optimization are included.

PL

W pracy przedstawiono zastosowanie algorytmów ewolucyjnych oraz metody elementów skończonych (MES) w optymalizacji kształtu radiatorów. Zastosowano algorytm ewolucyjny, w którym funkcja celu wyznaczana jest w sposób równoległy, więc obliczenia przeprowadzane mogą być na wielu komputerach wieloprocesorowych. Tego typu podejście znacznie skraca czas obliczeń w porównaniu do sekwencyjnego algorytmu ewolucyjnego. Wartość funkcji celu wyznaczana jest na podstawie rozwiązania zagadnienia termosprężystości z wykorzystaniem oprogramowania MES MARC/MENTAT. Przy rozwiązywania zagadnienia bezpośredniego uwzględniany jest radiacyjny strumień ciepła. Wyznaczenie stref zacieniania, niezbędnych do jego wyznaczenia, realizowane jest również za pomocą procesora MENTAT. W celu zmniejszenia liczby zmiennych projektowych przy modelowaniu geometrii radiatora wykorzystano krzywe Beziera. Ponadto praca zawiera przykłady numeryczne optymalizacji dla różnych konfiguracji warunków brzegowych.

5

Existence of global weak solutions for coupled thermoelasticity with Barber`s heat exchange condition

Bień M.

Journal of Applied Analysis

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2003

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Vol. 9, nr 2

163-185

EN

The existence of global weak solutions for coupled thermoelasticity with the nonlinear contact boundary condition and Barber's heat exchange condition is proved via the Faedo-Galerkin, monotonic-ity and compactness methods. Some a priori bounds obtained with Gronwalls inequality in connection with the embedding and trace theorems lead to accomplishing a generalization of our previous study [5]. The heat-exchange coefficient associated with Barber's heat exchange condition is dependent only on the normal displacement. This dependence is described by a bounded Lipschitz function. Moreover, this study is some extension of works due to Andrews et al. [3] and Elliot et al. [12].