title: Ð ÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÑÐ°ÑÐ¸ÐºÐ¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¡ÐD-ÑÐ¸ÑÑÐµÐ¼
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: Implementation of Graphic Statics Methods using CAD Systems
Creators: name: ÐÐ¾ÑÐ´Ð°, ÐÐ½Ð°ÑÑÐ°Ñ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: 2023
Subjects: ÐÐ°ÑÐ¸Ð½Ð½Ð°Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ°
Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÑÐ°ÑÐ¸ÐºÐ°
Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐ°ÑÑÐµÑÐ°
ÑÐ¸Ð»Ð¾Ð²Ð¾Ð¹ Ð¼Ð½Ð¾Ð³Ð¾ÑÐ³Ð¾Ð»ÑÐ½Ð¸Ðº
Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹
graphic statics
force diagram
form diagram
structural optimization

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐµÐ¹ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ°ÑÑÐµÑÐ° Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð¿Ð»Ð¾ÑÐºÐ¸Ñ ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸Ð¼ÑÑ ÑÑÑÐµÐ¶Ð½ÐµÐ²ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹ Ñ Ð¿Ð¾ÑÐ»ÐµÐ´ÑÑÑÐµÐ¹ Ð¸Ð½ÑÐµÐ³ÑÐ°ÑÐ¸ÐµÐ¹ Ð² ÑÐ°ÑÑÐµÑ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: 1. ÐÐ±Ð¾Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ Ð¾Ð±Ð»Ð°ÑÑÐ¸ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼Ð¾ÑÑÐ¸ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ°, ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÐµÐ³Ð¾ Ð¼ÐµÑÐ¾Ð´Ñ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÑÐ°ÑÐ¸ÐºÐ¸, Ð²ÑÐ±Ð¾Ñ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² ÑÐ°ÑÑÐµÑÐ°, Ð¿ÑÐ¸Ð³Ð¾Ð´Ð½ÑÑ Ð´Ð»Ñ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸, Ð¸ ÑÑÐµÐ´Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ¸. 2. Ð¡Ð¾Ð·Ð´Ð°Ð½Ð¸Ðµ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ° Ð² Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð¹ ÑÑÐµÐ´Ðµ. 3. ÐÐ°Ð»Ð¸Ð´Ð°ÑÐ¸Ñ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ° Ð¿ÑÑÐµÐ¼ Ð¿ÑÐ¾Ð²ÐµÑÐºÐ¸ ÐºÐ¾ÑÑÐµÐºÑÐ½Ð¾ÑÑÐ¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². 4. ÐÐ½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð² Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¹ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð°. ÐÑÐµÐ½ÐºÐ° ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÐ¸. Ð ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ» ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½Ñ Ð´Ð»Ñ ÑÐ°ÑÑÐµÑÐ° Ð¿Ð»Ð¾ÑÐºÐ¸Ñ ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹, ÑÐµÐ°Ð»Ð¸Ð·ÑÑÑÐ¸Ð¹ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÑÐ°ÑÐ¸ÐºÐ¸, ÑÐ¾ÑÑÐ¾ÑÑÐ¸Ð¹ Ð¸Ð· Ð´Ð²ÑÑ ÐºÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ¾Ð² â ÐÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ° Ð¿Ð¾Ð¸ÑÐºÐ° Ð¾Ð¿Ð¾ÑÐ½ÑÑ ÑÐµÐ°ÐºÑÐ¸Ð¹ Ð¸ ÐÐ¾Ð¼Ð¿Ð¾Ð½ÐµÐ½ÑÐ° Ð¿Ð¾Ð¸ÑÐºÐ° ÑÑÐ¸Ð»Ð¸Ð¹ ÑÑÐµÑÐ¶Ð½ÐµÐ²ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². Ð¢ÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ð¸ Ð²Ð°Ð»Ð¸Ð´Ð°ÑÐ¸Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ° Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¼ÐµÑÐ¾Ð´Ð° ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ»ÐµÐ¼ÐµÐ½ÑÐ¾Ð². ÐÐ¾Ð¼Ð¸Ð¼Ð¾ ÑÑÐ¾Ð³Ð¾, Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð° Ð¸Ð½ÑÐµÐ³ÑÐ°ÑÐ¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð³ÐµÐ½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð² ÑÐ¸ÐºÐ» ÑÐ°ÑÑÐµÑÐ°, ÑÐµÐ°Ð»Ð¸Ð·ÑÐµÐ¼Ð¾Ð³Ð¾ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÐ¼ Ð¸Ð½ÑÑÑÑÐ¼ÐµÐ½ÑÐ¾Ð¼, Ð¸ Ð¾ÑÐµÐ½ÐµÐ½Ð° ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸Ð¼Ð¾Ð¹ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÑÐµÑÐ¶Ð½ÐµÐ²Ð¾Ð¹ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¸. ÐÐ»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ Ð¾Ð¿Ð¸ÑÐ°Ð½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð² ÑÐ°Ð±Ð¾ÑÐµ Ð±ÑÐ»Ð¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ñ ÑÐ»ÐµÐ´ÑÑÑÐ¸Ðµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐµ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ð¸: CAD-ÑÐ¸ÑÑÐµÐ¼Ð° McNeel Rhinoceros, ÑÑÐµÐ´Ð° Ð²Ð¸Ð·ÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Grasshopper, ÑÐ·ÑÐº Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python, ÑÐ°ÑÑÐµÑÐ½ÑÐ¹ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑ SCAD Office.
description: This work is dedicated to exploring the possibilities of automating graphic statics methods using the example of two-dimensional statically determinate truss structures and integrating them into an optimization tool. The research set the following goals: 1. Defining the applicability domain of the tool implementing graphic statics methods, selecting graphic calculation methods suitable for automation, and choosing the development environment. 2. Creating the tool within the chosen environment. 3. Validating the tool by verifying the accuracy of the obtained results using the finite element method. 4. Integrating an optimization algorithm into the developed tool. Assessing its effectiveness. During the research, a tool for analyzing two-dimensional truss structures was developed, implementing automated graphic statics methods. The tool consists of two components: the Support Reactions Search Component and the Member Forces Search Component. Testing and validation of the developed tool were performed using the finite element method. Additionally, an optimization genetic algorithm was integrated into the calculation cycle of the tool, and the effectiveness of the truss structure optimization was evaluated. To achieve these results, the following information technologies were utilized in the study: McNeel Rhinoceros CAD system, Grasshopper visual programming environment, Python programming language, and the SCAD Office calculation suite.