title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð¸ÐºÑÐ¾ÑÑÑÑÐºÑÑÑÑ ÐºÐ¾ÑÑÐ½Ð¾Ð¹ ÑÐºÐ°Ð½Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐ¾Ð¿Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Investigation of the optimality of bone microstructure based on the method of topological optimization
Creators: name: ÐÐ±ÑÐ°Ð¼Ð¾Ð²Ð°, Ð®Ð»Ð¸Ñ
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: 2020
Subjects: Ð±Ð°Ð·Ð¸ÑÐ½Ð°Ñ ÑÑÐµÐ¹ÐºÐ°
ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ
Ð¼ÐµÑ Ð°Ð½Ð¸ÑÐµÑÐºÐ°Ñ Ð½Ð°Ð³ÑÑÐ·ÐºÐ°
Ð¿ÑÐ¾ÑÐ½Ð¾ÑÑÑ
Ð¾Ð´Ð½Ð¾Ð¾ÑÐ½Ð¾Ðµ
Ð´Ð²ÑÑ Ð¾ÑÐ½Ð¾Ðµ
ÑÑÐµÑ Ð¾ÑÐ½Ð¾Ðµ Ð½Ð°Ð³ÑÑÐ¶ÐµÐ½Ð¸Ñ
ÐºÐ¾ÑÑÐ½Ð°Ñ ÑÐºÐ°Ð½Ñ
ÐºÐ¾ÑÑÑ
basic cell
finite element model
mechanical load
strength
uniaxial
biaxial
triaxial loading
bone tissue
bone

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾ÑÑÐ¸ Ð¼Ð¸ÐºÑÐ¾ÑÑÑÑÐºÑÑÑÑ ÐºÐ¾ÑÑÐ½Ð¾Ð¹ ÑÐºÐ°Ð½Ð¸ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐ¾Ð¿Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸Â». Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð° Ð¿Ð¾Ð»ÑÑÐµÐ½Ð° ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ ÑÑÐµÐ¹ÐºÐ¸ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐ½Ð¾ÑÑÐ¸ ÐºÐ¾ÑÑÐ½Ð¾Ð¹ ÑÐºÐ°Ð½Ð¸. ÐÐ°Ð½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð±ÑÐ»Ð° Ð¿Ð¾Ð´Ð²ÐµÑÐ³Ð½ÑÑÐ° ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÐ¼ Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ð¼ Ð²Ð¸Ð´Ð°Ð¼ Ð½Ð°Ð³ÑÑÐ·Ð¾Ðº. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¼ÐµÑÐ¾Ð´Ð° ÑÐ¾Ð¿Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð±ÑÐ»Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÐµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÑÐµÐ¹ÐºÐ¸ Ð¿ÐµÑÐ¸Ð¾Ð´Ð¸ÑÐ½Ð¾ÑÑÐ¸. ÐÐ°ÑÐµÐ¼ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð±ÑÐ»Ð¸ Ð½Ð°Ð¹Ð´ÐµÐ½Ñ ÑÑÑÐµÐºÑÐ¸Ð²Ð½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¸ ÐµÐµ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½ÑÑ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð²ÑÑÑÑÐ¿Ð°ÑÑ: Ð¼Ð¾Ð´ÑÐ»Ñ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ð®Ð½Ð³Ð°, ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½Ñ ÐÑÐ°ÑÑÐ¾Ð½Ð°, Ð¼Ð¾Ð´ÑÐ»Ñ ÑÐ´Ð²Ð¸Ð³Ð°. ÐÐ¾ÑÐ»ÐµÐ´Ð½ÐµÐ¹ Ð·Ð°Ð´Ð°ÑÐ° Ð·Ð°ÐºÐ»ÑÑÐ°Ð»Ð°ÑÑ Ð² Ð½Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ð¸ Ð¿Ð¾ÑÐµÑÐ¸ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÑÑÑÐºÑÑÑÑ ÐºÐ¾ÑÑÐ½Ð¾Ð³Ð¾ Ð²ÐµÑÐµÑÑÐ²Ð°. ÐÐµÑÐ¾Ð´ ÑÐ¾Ð¿Ð¾Ð»Ð¾Ð³Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð»ÑÑ Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ðµ Tosca. Ð§Ð¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½ÑÑ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð¸ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ðµ ÐÐ­ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð¾ ÑÐ¾Ð·Ð´Ð°Ð½Ð¾ Ð² Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ðµ Ansys APDL (ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐ¹ ÑÐ·ÑÐº Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ). Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÐÐ­ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ°Ð»ÑÑ ÐºÑÐ±, ÐºÐ¾ÑÐ¾ÑÑÐ¹ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÐ» 1/8 ÑÐ°ÑÑÑ Ð¸ÑÑÐ¾Ð´Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸. ÐÐ»Ñ Ð½ÐµÐ³Ð¾ Ð¼Ñ Ð¿Ð¾Ð»ÑÑÐ¸Ð»Ð¸ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ Ð²ÑÐµÑ Ð¿Ð¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½ÑÑ Ð·Ð°Ð´Ð°Ñ, Ð¿ÐµÑÐµÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ ÑÐ°Ð½ÐµÐµ. Ð ÐºÐ¾Ð½ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð±ÑÐ»Ð¾ Ð²ÑÑÐ²Ð»ÐµÐ½Ð¾, ÑÑÐ¾ Ð·Ð°ÐºÑÑÑÑÐµ ÑÑÐµÐ½ÐºÐ¸ Ð±Ð°Ð·Ð¸ÑÐ½Ð¾Ð¹ ÑÑÐµÐ¹ÐºÐ¸ ÑÐ²Ð»ÑÑÑÑÑ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹ Ð¼Ð¸ÐºÑÐ¾ÑÑÑÑÐºÑÑÑÐ¾Ð¹ ÐºÐ¾ÑÑÐ½Ð¾Ð¹ ÑÐºÐ°Ð½Ð¸. Ð­ÑÑÐµÐºÑÐ¸Ð²Ð½ÑÐ¹ Ð¼Ð¾Ð´ÑÐ»Ñ Ð®Ð½Ð³Ð° Ð½Ðµ Ð¿ÑÐµÐ²ÑÑÐ°ÐµÑ 0.22, Ð° ÐºÐ¾ÑÑÑÐ¸ÑÐ¸ÐµÐ½Ñ ÐÑÐ°ÑÑÐ¾Ð½Ð° 0.182. ÐÑÐ²Ð¾Ð´Ð¾Ð¼ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð½Ð° ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ, ÑÐ²Ð»ÑÐµÑÑÑ ÑÐ¾ ÑÑÐ¾, ÐºÐ¾ÑÑÐ½Ð°Ñ ÑÐºÐ°Ð½Ñ Ð¾Ð±Ð»Ð°Ð´Ð°ÐµÑ Ð²ÑÑÐ¾ÐºÐ¾Ð¹ Ð¿ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ. ÐÐµ Ð¼Ð¾Ð¶Ð½Ð¾ ÑÑÐ°Ð²Ð½Ð¸ÑÑ Ñ Ð¿ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ Ð¶ÐµÐ»ÐµÐ·Ð°.
description: In this work, a finite element model of the bone periodicity cell was obtained. This model was subjected to various mechanical types of loads. Based on the topological optimization method, optimal models of the periodicity cell were constructed. Then, using a numerical solution, the effective characteristics of the model and its parameters were found. The effective parameters are: Young's modulus of elasticity, Poisson's ratio, shear modulus. The last task was to find the loss of stability of the bone substance structure. The method of topological optimization was carried out in the Tosca program. The numerical solution of the effective characteristics and the construction of the FE model was created in the Ansys APDL program (numerical programming language). As a FE model, a cube was taken, which amounted to 1/8 of the original model. For him, we received optimal solutions to all the tasks listed above. At the end of the studies, it was revealed that the closed walls of the base cell are the optimal microstructure of bone tissue. The effective Young's modulus does not exceed 0.5, and the Poisson's ratio is 0.27. The conclusion to the solution of the stability problem is that bone tissue has high strength. It can be compared with the strength of iron.