电邮这篇文章 Singularity Removal in the Elasticity Theory Solution Based on a Non-Euclidean Model of a Continuous Medium
- 作者: Guzev M.A.1, Chernysh E.V.1
-
隶属关系:
- Institute for Applied Mathematics FEB RAS
- 期: 编号 1 (2025)
- 页面: 79-89
- 栏目: Articles
- URL: https://bakhtiniada.ru/0032-8235/article/view/303573
- DOI: https://doi.org/10.31857/S0032823525010069
- EDN: https://elibrary.ru/BOAJVF
- ID: 303573
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详细
A representation for singularities of the classical elastic stress field was obtained using the Airy stress function for a plane-strained state of a continuous medium. For a non-Euclidean model of a continuous medium, the structure of the internal stress field of a planestrained state was shown to consist of a classical elastic stress field and a non-classical stress field determined through the incompatibility function of deformations. The requirement for the absence of singularities in the internal stress field allowed to compensate for the singularity in the elasticity theory solution for the zero harmonic by choosing a singularity of the non-classical stress field.
作者简介
M. Guzev
Institute for Applied Mathematics FEB RAS
编辑信件的主要联系方式.
Email: guzev@iam.dvo.ru
俄罗斯联邦, Vladivostok
E. Chernysh
Institute for Applied Mathematics FEB RAS
Email: guzev@iam.dvo.ru
俄罗斯联邦, Vladivostok
参考
- Sinclair G. B. Stress singularities in classical elasticity I: Removal, interpretation and analysis // Appl. Mech. Rev., 2004, vol. 57(4), pp. 251–297. https://doi.org/10.1115/1.1762503.
- Sinclair G. B. On ensuring structural integrity for configurations with stress singularities: A review // Fatigue & Fracture of Engng. Mater. & Struct., 2016, vol. 39(5), pp. 523–535. https://doi.org/10.1111/ffe.12425.
- Cherepanov G. P. Mechanics of Brittle Fracture. Moscow: Nauka, 1974. 640 p. (in Russian)
- Vasiliev V. V. Singular solutions in problems of mechanics and mathematical physics // Izv. RAN. MTT, 2018, no. 4, pp. 48–65. https://doi.org/10.31857/S057232990000702-2.
- Vasiliev V. V., Lurie S. A. On the solution singularity in the plane elasticity problem for a cantilever strip // Izv. RAN. MTT, 2013, no. 4, pp. 40–49.
- Vasiliev V. V., Lurie S. A. Nonlocal solutions to singular problems of mathematical physics and mechanics // JAMM, 2018, vol. 82, no. 4, pp. 459–471.
- Vasiliev V. V., Lurie S. A. Differential equations and the problem of singularity of solutions in applied mechanics and mathematics // J. Appl. Mech. & Tech. Phys., 2023, vol. 64, no. 1, pp. 98–109.
- Lazar M. Non-singular dislocation loops in gradient elasticity // Phys. Lett. A, 2012, vol. 376(21), pp. 1757–1758.
- Lazar M. The fundamentals of non-singular dislocations in the theory of gradient elasticity: Dislocation loops and straight dislocations // Int. J. of Solids & Struct., 2013, vol. 50(2), pp. 352–362. https://doi.org/10.1016/j.ijsolstr.2012.09.017.
- Lazar M., Po G. The non-singular Green tensor of Mindlin's anisotropic gradient elasticity with separable weak non-locality // Phys. Lett. A, 2015, vol. 379(24–25), pp. 1538–1543. https://doi.org/10.1016/j.physleta.2015.03.027.
- Po G., Lazar M., Admal N. C., Ghoniem N. A non-singular theory of dislocations in anisotropic crystals // Int. J. of Plasticity, 2018, vol. 103, pp. 1–22. https://doi.org/10.1016/j.ijplas.2017.10.003.
- Kioseoglou J., Konstantopoulos I., Ribarik G. et al. Nonsingular dislocation and crack fields: Implications to small volumes // Microsyst. Technol., 2009, vol. 15, pp. 117–121. https://doi.org/10.1007/s00542-008-0700-6.
- Aifantis E. C. A note on gradient elasticity and nonsingular crack fields // J. Mech. Behav. Mater., 2011, vol. 20, pp. 103–105.
- Konstantopoulos I., Aifantis E. C. Gradient elasticity applied to a crack // J. Mech. Behav. Mater., 2013, vol. 22, pp. 193–201.
- Parisis K., Konstantopoulos I., Aifantis E. C. Nonsingular solutions of GradEla models for dislocations: An extension to fractional GradEla // J. of Micromech. & Molec. Phys., 2018, vol. 3, no. 03n04, art. 1840013. https://doi.org/10.1142/s2424913018400131.
- Guzev M., Liu W., Qi C. Non-Euclidean model for description of residual stresses in planar deformations // Appl. Math. Model., 2021, vol. 90, pp. 615–623.
- Godunov S. K. Elements of Continuum Mechanics. Moscow: Nauka, 1978. 304 p. (in Russian)
- Gurtin M. E. A generalization of the Beltrami stress functions in continuum mechanics // Arch. for Rat. Mech. & Anal., 1963, vol. 13, no. 1, pp. 321–329. https://doi.org/10.1007/BSF01262700.
- Myasnikov V. P., Guzev M. A., Ushakov A. A. Structure of the self-equilibrated stress field in a continuous medium // Far Eastern Math. J., 2002, no. 2, pp. 231–241.
- Kondo K. On the geometrical and physical foundations of the theory of yielding // Proc. Jap. Nat. Congr. Appl. Mech., 1952, vol. 2, pp. 41–47.
- Bilby B. A., Bullough R., Smith E. Continuous distributions of dislocations: A new application of the methods of non-Riemannian geometry // Proc. Roy. Soc., 1955, vol. 231(1185), pp. 263–273. https://doi.org/10.1098/rspa.1955.0171.
- Novikov S. P., Taimanov I. A. Modern Geometric Structures and Fields. Moscow: MCCME, 2005. 584 p. (in Russian)
- Guzev M. A. The structure of the kinematic and force fields in the Riemannian model of a continuous medium // J. of Appl. Mech. & Tech. Phys., 2011, vol. 52, no. 5, pp. 39–48.
- Gradshteyn I. S., Ryzhik I. M. Table of Integrals, Series, and Products. Moscow: Nauka, 1971. 1108 p. (in Russian)
- Williams M. L. Stress singularities resulting from various boundary conditions in angular corners of plates in extension // J. of Appl. Mech., 1952, vol. 19, no. 4, pp. 526–528.
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