title: Ð Ð°ÑÑÐ¸ÑÐµÐ½Ð½Ð¾Ðµ ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐµÐ·Ð¾ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÑÑÑÐ¾Ð¹ÑÑÐ² Ð½Ð° ÑÑÐ¿ÐµÑÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð¹ Ð±Ð°Ð·Ðµ
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: Advanced finite element modeling of piezoelectric devices on a super-element base
Creators: name: ÐÐµÐ¼Ð¸ÑÐ¾Ð², ÐÐ»ÐµÐºÑÐ°Ð½Ð´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: 2021
Subjects: ÐºÐ¾Ð½ÐµÑÐ½Ð¾-ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¿ÑÐµÐ·Ð¾ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÑÑÑÐ¾Ð¹ÑÑÐ²Ð°
Ð¼ÐµÑÐ¾Ð´ ÑÑÐ¿ÐµÑÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð²
Ð¾Ð±ÑÐµÐºÑÐ½Ð¾-Ð¾ÑÐ¸ÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð°Ñ Ð³ÐµÐ¾Ð¼ÐµÑÑÐ¸Ñ
finite-element method
piezoelectric device
superelement method
object-oriented programming
differential geometry

description: Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÑÐºÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÐ°ÑÑÐ¸ÑÐµÐ½Ð¸Ðµ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»Ð° Ð¸Ð¼ÐµÑÑÐµÐ³Ð¾ÑÑ Ð¿ÑÐµÐ¿ÑÐ¾ÑÐµÑÑÐ¾ÑÐ° Ð´Ð»Ñ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð¿ÑÐµÐ·Ð¾ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÑÑÑÐ¾Ð¹ÑÑÐ² Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼ÐµÑÐ¾Ð´Ð° ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð·Ð°Ð´Ð°Ñ ÑÑÐ¾Ð²ÐµÑÑÐµÐ½ÑÑÐ²Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð±ÑÐ»Ð¸ ÑÑÐ¾ÑÐ¼ÑÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸: ÐºÐ¾ÑÑÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ¸ Ð¿Ð»Ð¾ÑÐºÐ¾ÑÑÐ¸ Ð¿ÑÐ¸ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ð¸ Ð½Ð¾Ð²Ð¾Ð¹ Ð³ÑÐ°Ð½Ð¸, ÑÐ°ÑÑÐ¸ÑÐµÐ½Ð¸Ðµ ÑÐ¸Ð¿Ð° Ð´Ð°Ð½Ð½ÑÑ, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼Ð¾Ð³Ð¾ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ð½Ð¸Ñ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÐºÐ¾Ð½ÑÑÐ°Ð½Ñ Ð¸ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸Ð½ÑÐµÑÑÐµÐ¹ÑÐ° Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ Ñ Ð¿ÑÐ¾ÑÐµÑÑÐ¾ÑÐ¾Ð¼ Ñ ÑÑÐµÑÐ¾Ð¼ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼Ð¾Ð³Ð¾ ÑÐ¸Ð¿Ð° Ð´Ð°Ð½Ð½ÑÑ. ÐÐ»Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð½Ð¾Ð²Ð¾Ð¹ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ¸ Ð¿Ð¾Ð²ÐµÑÑÐ½Ð¾ÑÑÐ¸ Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼, Ð¿ÑÐ¾Ð²ÐµÑÑÑÑÐ¸Ð¹ Ð³ÑÐ°Ð½Ñ Ð½Ð° Ð²Ð·Ð°Ð¸Ð¼Ð½ÑÐµ Ð¿ÐµÑÐµÑÐµÑÐµÐ½Ð¸Ñ Ð¸ Ð´Ð¾ÑÑÐ°ÑÐ¾ÑÐ½ÑÑ Ð³Ð»Ð°Ð´ÐºÐ¾ÑÑÑ. ÐÑÐ¸ Ð²Ð½ÐµÐ´ÑÐµÐ½Ð¸Ð¸ Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð¿Ð° Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ ÑÐ°Ð±Ð¾ÑÑ Ñ ÐºÐ¾Ð½ÑÑÐ°Ð½ÑÐ°Ð¼Ð¸, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐ¸Ð¼Ð¸ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð°, Ð±ÑÐ» ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ ÑÐ¾Ð±ÑÑÐ²ÐµÐ½Ð½ÑÐ¹ ÐºÐ»Ð°ÑÑ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐ½ÑÑ ÑÐ¸ÑÐµÐ», ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð±ÑÐ» Ð²Ð½ÐµÐ´ÑÐµÐ½ Ð² Ð¸Ð¼ÐµÑÑÑÑÑÑ ÐºÐ¾Ð´Ð¾Ð²ÑÑ Ð±Ð°Ð·Ñ Ñ ÑÑÐµÑÐ¾Ð¼ ÐµÐµ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹. ÐÑÐ» ÑÐ¾Ð²ÐµÑÑÐµÐ½ Ð¿ÐµÑÐµÐ½Ð¾Ñ Ð±Ð°Ð·Ñ Ð´Ð°Ð½Ð½ÑÑ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾Ð² Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¿ÑÐµÐ¶Ð½ÐµÐ³Ð¾ ÑÐ¸Ð¿Ð° Ð´Ð°Ð½Ð½ÑÑ Ð² Ð½Ð¾Ð²ÑÐ¹ ÑÐ°Ð¹Ð». ÐÐ°Ð»ÐµÐµ Ð±ÑÐ» Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½ ÑÐ¿Ð¾ÑÐ¾Ð± Ð·Ð°Ð¿Ð¸ÑÐ¸ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² ÑÐ°Ð¹Ð» Ñ ÑÑÐµÑÐ¾Ð¼ Ð½Ð¾Ð²Ð¾Ð³Ð¾ ÑÐ¸Ð¿Ð° Ð´Ð°Ð½Ð½ÑÑ. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¿Ð¾Ð»ÑÑÐ¸Ð»ÑÑ Ð¿ÑÐµÐ¿ÑÐ¾ÑÐµÑÑÐ¾Ñ Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²Ð°ÑÑÐ¸Ð¹ ÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾Ðµ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ ÑÑÑÐ¾Ð³ÑÑ Ð¿ÑÐ¾Ð²ÐµÑÐºÑ Ð´Ð°Ð½Ð½ÑÑ Ð¿ÐµÑÐµÐ´ Ð¿ÐµÑÐµÐ´Ð°ÑÐµÐ¹ Ð² Ð¿ÑÐ¾ÑÐµÑÑÐ¾Ñ.
description: In this bachelor's work, the functionality of the existing preprocessor was expanded to form models of piezoelectric devices using the finite element method. As tasks for improving the program, the following tasks were formulated: correcting the plane check when creating a new face, expanding the data type used to set material constants and forming an interface for interacting with the processor considering changes in the data type used. To implement a new surface check, an algorithm was developed that checks the face for mutual intersections and sufficient smoothness. When introducing a new data type for working with constants describing the properties of a material, a special class of complex numbers was implemented, which was introduced into the existing code base, considering its features. The materials database was migrated using the old data type to a new file. Further, the way of writing the model to the file was changed considering the new data type. The result is a preprocessor program that ensures the correct formation of the model and strict verification of the data before transferring it to the processor.