Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder
An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled...
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| Format: | Article |
| Language: | English |
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University of Tehran Press
2013-12-01
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| Series: | Civil Engineering Infrastructures Journal |
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| Online Access: | https://ceij.ut.ac.ir/article_40489_ba3890ac0ca4f37b332b7c85d6009ac0.pdf |
| _version_ | 1811344022719954944 |
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| author | Morteza Eskandari-Ghadi Mohammad Rahimian Amin Mahmoodi Azizollah Ardeshir-Behrestaghi |
| author_facet | Morteza Eskandari-Ghadi Mohammad Rahimian Amin Mahmoodi Azizollah Ardeshir-Behrestaghi |
| author_sort | Morteza Eskandari-Ghadi |
| collection | DOAJ |
| description | An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements. |
| first_indexed | 2024-04-13T19:40:19Z |
| format | Article |
| id | doaj.art-b24849190a294f52b0d755807ef74096 |
| institution | Directory Open Access Journal |
| issn | 2322-2093 2423-6691 |
| language | English |
| last_indexed | 2024-04-13T19:40:19Z |
| publishDate | 2013-12-01 |
| publisher | University of Tehran Press |
| record_format | Article |
| series | Civil Engineering Infrastructures Journal |
| spelling | doaj.art-b24849190a294f52b0d755807ef740962022-12-22T02:32:55ZengUniversity of Tehran PressCivil Engineering Infrastructures Journal2322-20932423-66912013-12-0146210712310.7508/ceij.2013.02.00140489Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a CylinderMorteza Eskandari-Ghadi0Mohammad Rahimian1Amin Mahmoodi2Azizollah Ardeshir-Behrestaghi3University of Tehran, Collage of Engineering, Dept. of Engineering ScienceCollage of Civil Eng., Faculty of Engineering, University of Tehran, Tehran, Iran.Collage of Civil Eng., Faculty of Engineering, University of Tehran, Tehran, Iran.PhD candidate, Faculty of Civil Eng., Babol Noshirvani University of Technology, Babol, Iran,An infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. The two-dimensional coupled thermoelastodynamic PDEs are specified based on equations of motion and energy equation, which are uncoupled using Nowacki potential functions. The Laplace integral transform and Bessel-Fourier series are used to derive the solution for the potential functions, and then the displacements-, stresses- and temperature-potential relationships are used to determine the displacements, stresses and temperature fields. It is shown that the formulation presented here are identically collapsed on the solution existed in the literature for simpler case of axissymetric configuration. A numerical procedure is needed to evaluate the displacements, stresses and temperature at any point and any time. The numerical inversion method proposed by Durbin is applied to evaluate the inverse Laplace transforms of different functions involved in this paper. For numerical inversion, there exist many difficulties such as singular points in the integrand functions, infinite limit of the integral and the time step of integration. With a very precise attention, the desired functions have been numerically evaluated and shown that the boundary conditions have been satisfied very accurately. The numerical evaluations are graphically shown to make engineering sense for the problem involved in this paper for different case of boundary conditions. The results show the wave velocity and the time lack of receiving stress waves. The effect of temperature boundary conditions are shown to be somehow oscillatory, which is used in designing of such an elements.https://ceij.ut.ac.ir/article_40489_ba3890ac0ca4f37b332b7c85d6009ac0.pdfbessel-fourier seriescoupled thermoelasticitylaplace transformnumerical inversionpotential functionsseries expansionsingular points |
| spellingShingle | Morteza Eskandari-Ghadi Mohammad Rahimian Amin Mahmoodi Azizollah Ardeshir-Behrestaghi Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder Civil Engineering Infrastructures Journal bessel-fourier series coupled thermoelasticity laplace transform numerical inversion potential functions series expansion singular points |
| title | Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder |
| title_full | Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder |
| title_fullStr | Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder |
| title_full_unstemmed | Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder |
| title_short | Analytical Solution for Two-Dimensional Coupled Thermoelastodynamics in a Cylinder |
| title_sort | analytical solution for two dimensional coupled thermoelastodynamics in a cylinder |
| topic | bessel-fourier series coupled thermoelasticity laplace transform numerical inversion potential functions series expansion singular points |
| url | https://ceij.ut.ac.ir/article_40489_ba3890ac0ca4f37b332b7c85d6009ac0.pdf |
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