Axisymmetric poroelasticity problem for a multilayered cylinder

Natalya Vaysfeld; Zinaida Zhuravlova

doi:10.17721/1812-5409.2025/2.11

Authors

Natalya Vaysfeld King's College London, London, United Kingdom
Zinaida Zhuravlova Odesa I. I. Mechnikov National University, Odesa, Ukraine https://orcid.org/0000-0002-3271-8864

DOI:

https://doi.org/10.17721/1812-5409.2025/2.11

Keywords:

axisymmetric problem, poroelasticity, multilayered cylinder, integral Fourier transform, matrix differential calculation, recurrent correspondences

Abstract

Poroelastic materials are the object of close attention of researchers due to their wide representation both in the natural environment (geological formations, biological tissues) and in technical applications (engineering structures, filtration systems). Among them, cylindrical structures are of particular importance, often characterised by radial layering and heterogeneity. The study of the stress-strain state of such objects is of significant practical importance for calculating their strength, stability, and efficient operation. Despite the considerable amount of scientific work, most of it is based on numerical modelling. At the same time, it is analytical methods that allow us to gain a deeper understanding of physical laws, identify limit regimes, and verify numerical approaches.

In this paper, we consider an analytical solution of an axisymmetric problem for a finite-length poroelastic cylinder with a radially layered structure. A load is applied to the cylindrical surface, which can be either a mechanical or a pressure load. The top and bottom edges of the cylinder are in smooth contact and are impermeable. Perfect mechanical contact is maintained between the layers. The application of the Fourier integral transform method allows us to reduce the original problem to a one-dimensional vector boundary value problem, the general solution of which is found using the matrix differential calculation. The method of recurrence relations is used to find the unknown constants of each layer of the cylinder. As a result, an exact solution was derived, which allows us to study the distribution of normal stress and pore pressure depending on the applied load, geometric characteristics, and physical and mechanical properties of the layers. The obtained results are important for the further development of the analytical mechanics of poroelastic media.

Pages of the article in the issue: 87 - 90

Language of the article: English

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