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Dynamic of an inhomogeneous three-layer sphere under cyclic pressure.

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Title: Dynamic of an inhomogeneous three-layer sphere under cyclic pressure.
Authors: Zhang, Xi-meng1,2 (AUTHOR) zhangximeng@hrbeu.edu.cn, Qi, Hui3 (AUTHOR)
Source: Acta Mechanica. Oct2024, Vol. 235 Issue 10, p6181-6224. 44p.
Subjects: Spherical waves, Algebraic equations, Stress concentration, Euler equations, Finite element method
Abstract: In this paper, the dynamic characteristics of inhomogeneous three-layer spheres under spherical wave induced by cyclic pressure are studied. The density is assumed to have a square of inverse proportional function distribution along the radius. Firstly, on the basis of Lamb decomposition and variable separation method, the analytical expression of spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere, and the Euler equation is obtained due to inhomogeneity. Next, algebraic equations with respective boundary conditions are composed and solved by effective truncation techniques. Finally, a comparison and discussion are conducted between the model presented in this article and the homogeneous model obtained by the Legendre polynomial expansion. Obtained results enable to reveal the influence on the dynamic stress concentration factor intensity under proper conditions. The conclusions of this article are verified by comparing the analytical solutions to the ones obtained by finite element method. This paper can provide a theoretical method for the analysis of mechanical properties of inhomogeneous multilayered spherical structure under dynamic loading. [ABSTRACT FROM AUTHOR]
Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Dynamic of an inhomogeneous three-layer sphere under cyclic pressure.
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  Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Xi-meng%22">Zhang, Xi-meng</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> zhangximeng@hrbeu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Qi%2C+Hui%22">Qi, Hui</searchLink><relatesTo>3</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Acta+Mechanica%22">Acta Mechanica</searchLink>. Oct2024, Vol. 235 Issue 10, p6181-6224. 44p.
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  Data: <searchLink fieldCode="DE" term="%22Spherical+waves%22">Spherical waves</searchLink><br /><searchLink fieldCode="DE" term="%22Algebraic+equations%22">Algebraic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stress+concentration%22">Stress concentration</searchLink><br /><searchLink fieldCode="DE" term="%22Euler+equations%22">Euler equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink>
– Name: Abstract
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  Data: In this paper, the dynamic characteristics of inhomogeneous three-layer spheres under spherical wave induced by cyclic pressure are studied. The density is assumed to have a square of inverse proportional function distribution along the radius. Firstly, on the basis of Lamb decomposition and variable separation method, the analytical expression of spherical wave is conducted, which satisfies the stress equilibrium on the outer and inner surfaces of the sphere, and the Euler equation is obtained due to inhomogeneity. Next, algebraic equations with respective boundary conditions are composed and solved by effective truncation techniques. Finally, a comparison and discussion are conducted between the model presented in this article and the homogeneous model obtained by the Legendre polynomial expansion. Obtained results enable to reveal the influence on the dynamic stress concentration factor intensity under proper conditions. The conclusions of this article are verified by comparing the analytical solutions to the ones obtained by finite element method. This paper can provide a theoretical method for the analysis of mechanical properties of inhomogeneous multilayered spherical structure under dynamic loading. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00707-024-04041-7
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      – Code: eng
        Text: English
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        PageCount: 44
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        Type: general
      – SubjectFull: Algebraic equations
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      – SubjectFull: Stress concentration
        Type: general
      – SubjectFull: Euler equations
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              Text: Oct2024
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