O pewnym ustalonym zagadnieniu przestrzennym termosprężystości

A steady-state three-dimensional thermo-elastic problem The object of this paper is to determine the temperature field T and the stress components (σij) in an elastic semi-space, assuming that the temperature in the region Γ of the plane bounding the semi-space is known and equal to T0(ξ, η), the r...

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Main Author: Witold NOWACKI
Format: Article
Language:English
Published: Institute of Fundamental Technological Research 1957-08-01
Series:Engineering Transactions
Online Access:https://et.ippt.pan.pl/index.php/et/article/view/3303
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author Witold NOWACKI
author_facet Witold NOWACKI
author_sort Witold NOWACKI
collection DOAJ
description A steady-state three-dimensional thermo-elastic problem The object of this paper is to determine the temperature field T and the stress components (σij) in an elastic semi-space, assuming that the temperature in the region Γ of the plane bounding the semi-space is known and equal to T0(ξ, η), the region outside Γ being kept at T = 0. The problem is solved by means of the Green's function. The temperature field T* is determined and the stress components (σij*), in the case where T = 0 over the whole plane z = 0 except an infinitely small region dΓ where T = T0. Using integral expressions (1.1) and (1.2), T and σij are determined for any temperature distribution T0(ξ, η) inside the region Γ. In the second part of the paper, the Green's functions T* and Φ* and the Galerkin's function φ are determined, using the Fourier transformation. The Green's functions obtained for the stress (σij*) are characterized by the fact that the three components σzz*, σzx*, and σzy* are zero. In the third part of the paper, consideration is given to the particular case of T0 = const over a rectangle whose sides are 2a and 2b, and that of T0 = const over an infinite strip of width 2a. In the latter case, only the stress σyy* differs from zero.
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spelling doaj-art-eafa08994be047efbed8ba3ccb1e6cd02025-08-20T03:49:50ZengInstitute of Fundamental Technological ResearchEngineering Transactions0867-888X2450-80711957-08-0153O pewnym ustalonym zagadnieniu przestrzennym termosprężystościWitold NOWACKI0Instytut Podstawowych Problemów Techniki PANA steady-state three-dimensional thermo-elastic problem The object of this paper is to determine the temperature field T and the stress components (σij) in an elastic semi-space, assuming that the temperature in the region Γ of the plane bounding the semi-space is known and equal to T0(ξ, η), the region outside Γ being kept at T = 0. The problem is solved by means of the Green's function. The temperature field T* is determined and the stress components (σij*), in the case where T = 0 over the whole plane z = 0 except an infinitely small region dΓ where T = T0. Using integral expressions (1.1) and (1.2), T and σij are determined for any temperature distribution T0(ξ, η) inside the region Γ. In the second part of the paper, the Green's functions T* and Φ* and the Galerkin's function φ are determined, using the Fourier transformation. The Green's functions obtained for the stress (σij*) are characterized by the fact that the three components σzz*, σzx*, and σzy* are zero. In the third part of the paper, consideration is given to the particular case of T0 = const over a rectangle whose sides are 2a and 2b, and that of T0 = const over an infinite strip of width 2a. In the latter case, only the stress σyy* differs from zero. https://et.ippt.pan.pl/index.php/et/article/view/3303
spellingShingle Witold NOWACKI
O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
Engineering Transactions
title O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
title_full O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
title_fullStr O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
title_full_unstemmed O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
title_short O pewnym ustalonym zagadnieniu przestrzennym termosprężystości
title_sort o pewnym ustalonym zagadnieniu przestrzennym termosprezystosci
url https://et.ippt.pan.pl/index.php/et/article/view/3303
work_keys_str_mv AT witoldnowacki opewnymustalonymzagadnieniuprzestrzennymtermosprezystosci