- PII
- 10.31857/S2686740024040037-1
- DOI
- 10.31857/S2686740024040037
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 517 / Issue number 1
- Pages
- 12-17
- Abstract
- A singular solution for the elastic stress field in the Williams problem on the equilibrium of plates with corner cutouts is considered. A scheme has been constructed for the minimal expansion of the classical elastic continuum model without taking into account the Saint-Venant compatibility conditions for deformations, which leads to a non-Euclidean continuum model. Within this model framework, the total stress field is shown to contain no singularity for all cutout angles.
- Keywords
- сингулярные поля напряжений функция напряжений Эйри асимптотический метод Вилльямса неевклидова модель
- Date of publication
- 16.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 15
References
- 1. Williams M.L. Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension // J. Applied Mechanics. 1952. V. 19 (4). P. 526–528. https://authors.library.caltech.edu/records/2zph7-ee089
- 2. Barber J.R. Wedge Problems. In Elasticity. Part of the book series: Solid Mechanics and Its Applications. V. 172. Dordrecht: Springer, 2010. P. 149–170. https://doi.org/10.1007/978-90-481-3809-8_11
- 3. Pan W., Cheng C., Wang F., Hu Z., Li J. Determination of singular and higher order non-singular stress for angularly heterogeneous material notch 292 // Engineering Fracture Mechanics. 2023. 109592. https://doi.org/10.1016/j.engfracmech.2023.109592
- 4. Sinclair G.B. Stress Singularities in Classical Elasticity—I: Removal, Interpretation and Analysis // Applied Mechanics Reviews. 2004. V. 57(4). P. 251–297. http://dx.doi.org/10.1115/1.1762503
- 5. Мясников В.П., Гузев М.А. Геометрическая модель внутренних самоуравновешенных напряжений в твердых телах // ДАН. 2001. Т. 380. № 5. С. 627-629.
- 6. Годунов С.К., Роменский Е. И. Элементы механики сплошных сред и законы сохранения. Новосибирск: Научная книга, ١٩٩٨. 280 c.
- 7. Новиков С.П., Тайманов И.А. Современные геометрические структуры и поля. М.: МЦНМО, 2005. 584 с.
- 8. Гузев М.А. Структура кинематического и силового поля в Римановой модели сплошной среды // ПМТФ. 2011. Т. 52. № 5. С. 39–48.
- 9. Градштейн И.С., Рыжик И.М. Таблицы интегралов, сумм, рядов и произведений. М.: Наука, 1971. 1108 с.
