title: ÐÐ¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð²ÐµÐºÑÐ¾ÑÐ½ÑÑ Ð¸ ÑÐºÐ°Ð»ÑÑÐ½ÑÑ Ð¿Ð¾Ð»ÐµÐ¹ ÑÑÐ¿ÐµÑÑÐ»ÐµÐ¼ÐµÐ½ÑÐ½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»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: Visualization of vector and scalar fields in a superelement model
Creators: name: ÐÑÑÑÐºÐ¾Ð², ÐÐ¸ÑÐ¸Ð»Ð»
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: 2022
Subjects: Ð¾Ð±ÑÐµÐºÑÐ½Ð¾-Ð¾ÑÐ¸ÐµÐ½ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐµÑÐ¾ÑÐ½Ð°Ñ ÑÑÑÑÐºÑÑÑÐ°
Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ðµ Ð¾ÑÐ¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ðµ
Ð²ÐµÐºÑÐ¾ÑÐ½Ð¾Ðµ Ð¿Ð¾Ð»Ðµ
Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ°Ñ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ
Ð¿Ð¾ÑÑÐ¿ÑÐ¾ÑÐµÑÑÐ¾Ñ
object-oriented programming
grid structure
gradient mapping
vector field
dynamic visualization
postprocessing

description: Ð Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÐ°ÑÑÐ¸ÑÐµÐ½Ð¸Ðµ ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½ÑÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐµÐ¹ Ð¿ÑÐ¸Ð»Ð¾Ð¶ÐµÐ½Ð¸Ñ Feapiezo 4.0, ÐºÐ¾ÑÐ¾ÑÐ¾Ðµ ÑÐ¾Ð·Ð´Ð°ÐµÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð¿ÑÐµÐ·Ð¾ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÑÑÑÐ¾Ð¹ÑÑÐ² Ð¿Ð¾ Ð¼ÐµÑÐ¾Ð´Ñ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÑÐ½Ð¾Ð²Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµÐ¹ Ð² Ð¿ÑÐ¾ÐµÐºÑÐµ ÑÐ²Ð»ÑÐ»Ð¾ÑÑ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ðµ Ð´Ð¾Ð¿Ð¾Ð»Ð½Ð¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¼Ð¾Ð´ÑÐ»Ñ, ÐºÐ¾ÑÐ¾ÑÑÐ¹ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐ» Ð±Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹ Ð²Ð¸Ð·ÑÐ°Ð»Ð¸Ð·Ð¸ÑÐ¾Ð²Ð°ÑÑ ÑÐ°ÑÑÐµÑÐ½ÑÐµ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸ÐºÐ¸ Ð¾Ð±ÑÐµÐºÑÐ° Ñ ÑÐ¾ÑÐ½Ð¾ÑÑÑÑ Ð´Ð¾ Ð¿ÐµÑÐµÐ¼ÐµÑÐµÐ½Ð¸Ð¹ Ð¸ ÑÐ»ÐµÐºÑÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð¾Ð². ÐÐ¾Ð½ÐµÑÐ½ÑÐ¼ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ Ð¿ÑÐ¾Ð´ÐµÐ»Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾ÑÑÐ¿ÑÐ¾ÑÐµÑÑÐ¾Ñ, Ð¸Ð·Ð¾Ð±ÑÐ°Ð¶Ð°ÑÑÐ¸Ð¹ Ð²ÑÑÐ¾Ð´Ð½ÑÐµ Ð´Ð°Ð½Ð½ÑÐµ Ð² ÑÑÐµÑ Ð²Ð¸Ð´Ð°Ñ: Ð´ÐµÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¹, Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ¾Ð² Ð¸ Ð²ÐµÐºÑÐ¾ÑÐ¾Ð². ÐÑÐµ Ð²Ð¸Ð´Ñ Ð±Ð°Ð·Ð¸ÑÑÑÑÑÑ Ð½Ð° ÑÑÐµÐ¼Ðµ Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ð¸, Ð¿ÑÐ¸ÑÑÑÐµÐ¹ 20-ÑÐ·Ð»Ð¾Ð²ÑÐ¼ Ð¸Ð·Ð¾Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ð¼ ÐºÐ¾Ð½ÐµÑÐ½ÑÐ¼ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ°Ð¼.Â Ð Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÑÐºÐ¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ» ÑÐµÑÐµÐ½ ÑÑÐ´ Ð·Ð°Ð´Ð°Ñ, ÑÐ²ÑÐ·Ð°Ð½Ð½ÑÑ Ñ Ð½Ð¾ÑÐ¼Ð°Ð»Ð¸Ð·Ð°ÑÐ¸ÐµÐ¹ Ð´Ð°Ð½Ð½ÑÑ, Ð¾ÑÐ¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸ÐµÐ¼ Ð²ÐµÐºÑÐ¾ÑÐ¾Ð² Ð² Ð¿ÑÐ¾ÑÑÑÐ°Ð½ÑÑÐ²Ðµ, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸ÐµÐ¼ ÑÐ²ÐµÑÐ¾Ð²Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÑ Ð´Ð»Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ³Ð¾ ÑÐ¾Ð·Ð´Ð°Ð½Ð¸Ñ Ð³ÑÐ°Ð´Ð¸ÐµÐ½ÑÐ½Ð¾Ð¹ ÐºÐ°ÑÑÐ¸Ð½Ñ.ÐÐ¿ÑÑÐ½ÑÐ¼ Ð¿ÑÑÐµÐ¼ Ð±ÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ ÑÐ¾ÑÐ¼ÑÐ»Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð½ÐµÐ¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¹ ÑÐµÑÐºÐ¸ Ð² ÐºÐ°Ð¶Ð´Ð¾Ð¹ Ð¿Ð¾Ð´ÑÑÑÑÐºÑÑÑÐµ ÑÐ¾ ÑÐ»Ð¾Ð¶Ð½Ð¾Ð¹ Ð°Ð´ÑÐµÑÐ°ÑÐ¸ÐµÐ¹ Ð·Ð° ÑÑÐµÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ ÑÑÐµÐ¼ ÑÑÐ°Ð½ÐµÐ½Ð¸Ñ ÑÐ°Ð±Ð¾ÑÐ¸Ñ Ð´Ð°Ð½Ð½ÑÑ. ÐÑÐ»Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð° Ð°Ð½Ð¸Ð¼Ð°ÑÐ¸Ñ Ð´Ð»Ñ Ð¾ÑÐ¾Ð±ÑÐ°Ð¶ÐµÐ½Ð¸Ñ Ð³Ð°ÑÐ¼Ð¾Ð½Ð¸ÑÐµÑÐºÐ¸Ñ ÑÐ°ÑÑÑÑÐ½ÑÑ ÑÐ°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð² ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¼ Ð²ÑÐµÐ¼ÐµÐ½Ð¸. Ð ÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ Ð¸Ð½ÑÐµÑÑÐµÐ¹Ñ, Ð² ÐºÐ¾ÑÐ¾ÑÐ¾Ð¼ Ð¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°ÑÐµÐ»Ñ Ð¼Ð¾Ð¶ÐµÑ Ð² Ð¿Ð¾Ð»Ð½Ð¾Ð¹ Ð¼ÐµÑÐµ Ð¾ÑÐµÐ½Ð¸ÑÑ ÐºÐ°ÑÐµÑÑÐ²Ð¾ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐ¸ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ.
description: In the final qualifying work, the functionality of the Feapiezo 4.0 application was expanded, which creates models of piezoelectric devices using the finite element method. The main task in the project was to create an additional software module that would allow using model construction methods to visualize the calculated characteristics of an object with accuracy to displacements and electrical potentials. The result of the work done is a postprocessor depicting the output data in three types: deformations, gradients, and vectors. All types are based on the interpolation scheme inherent in 20-node isoparametric finite elements.In the bachelor's work, several tasks related to data normalization, mapping vectors in space, determining the color value of the coordinate for the subsequent creation of a gradient picture were solved.Experimentally, formulas for constructing an inhomogeneous grid in each substructure with complex addressing were developed using optimal working data storage schemes. Animation was implemented to display harmonic design characteristics in real time. An interface is implemented in which the user can fully evaluate the quality of the model using the capabilities of the program.