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| Perturbation method for solving tensile and compressive deformation of circular rod with axisymmetric rough surface |
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Abstract Due to factors such as processing techniques, daily abrasion, and atmospheric corrosion, the surfaces of components typically exhibit a certain level of surface roughness. This paper primarily investigated the tensile and compressive deformation behavior of circular rods with axisymmetric random rough surfaces. First, a digital reconstruction of the rough circular rod model was conducted, where the rough surface was jointly characterized by two statistical parameters: the root mean square height and the correlation length. Then, the dimensionless governing differential equation for the tensile and compressive cases of the rough circular rod was derived through the infinitesimal element method. Subsequently, in combination with the perturbation method and the fast Fourier transform, the governing equation was solved, obtaining the perturbation solution for the tensile and compressive deformation of the rough circular rod. The validity of the perturbation solution was verified by comparison with the analytical solution and the finite element solution. Finally, in order to explore the influence of the statistical parameters of rough surfaces on tensile and compressive deformation, the contributions of the first-order and second-order perturbation solutions to the results were systematically compared, and an empirical formula for the perturbation amplitude was established. The influence of perturbation on the results gradually increases with the increase of the root mean square height and the correlation length; the proportion of the second-order perturbation solution in the perturbation grows with the increase of the root mean square height, while it is not affected by the correlation length. This work not only expands the research scope of traditional problems in mechanics of materials related to tensile and compressive, but also provides an example of the application of mathematical and physical methods in mechanical practice. Moreover, this study offers a theoretical basis for optimizing the manufacturing processes of components and quantitatively assessing the impact of surface defects on the mechanical properties of components.
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Received: 05 September 2024
Published: 23 April 2025
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2025, Vol. 46 
