title: Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð¿Ð»Ð¾ÑÐºÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð­ÑÐµÐ»Ð±Ð¸ Ð´Ð»Ñ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¸ Ð¿Ð¾Ð»Ð¸Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Comparison of the plane Eshelby problem for cylindrical and polygonal inclusions
Creators: name: Ð§Ð¶Ñ ÐÐ¸Ð½ÑÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: ÐÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ñ ÑÐµÑÐ¼Ð¸ÑÐµÑÐºÐ°Ñ
Ð§Ð¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ
Ð·Ð°Ð´Ð°ÑÐ° Ð­ÑÐµÐ»Ð±Ð¸
ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐµ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸
Ð¿Ð¾Ð»Ð¸Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ðµ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ðµ
ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ

description: ÐÐ°Ð´Ð°ÑÐ° Ð­ÑÐµÐ»Ð±Ð¸ ÑÐ¾ÑÑÐ¾Ð¸Ñ Ð² Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ð¸ Ð¿Ð¾Ð»ÐµÐ¹ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð¸ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¹ Ð¸Ð½Ð¸ÑÐ¸Ð¸ÑÑÐµÐ¼ÑÑ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸ÐµÐ¼ Ñ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½Ð¾Ð¹ Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸ÐµÐ¹ Ð² Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾-ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ ÑÑÐµÐ´Ðµ. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ, Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐÐ­-Ð¿Ð°ÐºÐµÑÐ° ANSYS Ð±ÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð´Ð²ÑÑÐ¼ÐµÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð´Ð»Ñ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¸ Ð¿Ð¾Ð»Ð¸Ð³Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹, Ð° Ð¸Ð¼ÐµÐ½Ð½Ð¾: 1. ÐÑÐ¿Ð¾Ð»Ð½ÐµÐ½ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÑÐ°ÑÑÐµÑ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð° Ð²ÐµÑÐ¸ÑÐ¸ÐºÐ°ÑÐ¸Ñ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÑÐµÑÐµÐ½Ð¸Ñ. 2. ÐÑÐ¿Ð¾Ð»Ð½ÐµÐ½ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÑÐ°ÑÑÐµÑ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½ÑÑ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹ (ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°Ð»Ð¸ÑÑ ÑÐµÑÑÑÐµÑÑÐ³Ð¾Ð»ÑÐ½ÑÐµ Ð¸ ÑÐµÑÑÐ¸ÑÐ³Ð¾Ð»ÑÐ½ÑÐµ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ) Ð² Ð´Ð²ÑÐ¼ÐµÑÐ½Ð¾Ð¹ Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾Ð¹ Ð¾Ð±Ð»Ð°ÑÑÐ¸. 3. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½ÑÑ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½ÑÑ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹ Ð² ÑÐ°Ð·Ð½ÑÑ Ð½Ð°Ð¿ÑÐ°Ð²Ð»ÐµÐ½Ð¸ÑÑ Ð¸ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹.
description: The Eshelby problem consists in determining the strain field of an infinite linearly elastic homogeneous medium due to a uniform eigenstrain prescribed over a subdomain, called inclusion, of the medium. In this paper, based on the ANSYS platform and focusing on two-dimensional (2D) case, we studied the cylindrical inclusion and polygonal inclusions where the main contents include: 1. We have done a numerical calculation of the finite element model of a cylindrical inclusion in a two-dimensional infinite domain and verified it with the analytical solution to prove the correctness of the model. 2. Then, we have done a numerical calculation of the finite element model of a polygonal inclusion (quadrilateral and hexagonal inclusions in this article) in a two-dimensional infinite domain. 3. Comparing the results of the finite element stress analysis for polygonal inclusions in different directions and cylindrical inclusion. Estimations of the relative difference in the stresses.