Utilization of boundary integral equations in the solution of linear viscoelasticity problems of piecewise-homogeneous bodies
DOI:
https://doi.org/10.17721/1812-5409.2024/1.18Keywords:
boundary-time integral equations, viscoelasticity, piecewise-homogeneous bodies, stress tensor, resolvent operators, matrix with inclusions, differential equations with generalized fractional derivativesAbstract
This article discusses the use of the boundary integral equations method to solve problems related to linear viscoelasticity of piecewise homogeneous bodies. The method is based on the use of complex potentials, the apparatus of generalized functions, and viscoelastic operators. For flat viscoelastic piecewise homogeneous isotropic bodies, the well-known formulation of the second fundamental problem for inhomogeneous bodies in movements is considered. Integral representations for the stress vector components were used to determine the stress state of a viscoelastic half-plane with inclusions. Discrete analogues of boundary-time and defining integral relations are constructed, taking into account the peculiarities of the stress field behavior in the vicinity of angular points and its changes over time. An efficient algorithm for the numerical implementation of the proposed methodology has been developed. For the considered examples of the epoxy matrix with metal inclusions, the problem of the stress state of the viscoelastic plane was solved depending on the geometric parameters of the inclusions and their placement in the matrix. The change in the intensity of stress distribution over time is taken into account. The results for matrices with circular and square inclusions are compared.
Pages of the article in the issue: 91 - 95
Language of the article: English
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Zatula, N. I., & Zatula, D. V. (2022). Mathematical modeling of the stressed state of a viscoelastic half-plane with inclusions. Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics (2), 42–45. doi: 10.17721/1812-5409.2022/2.5.
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