title: ÐÐ»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð´ÐµÑÐµÐ²ÑÐ½Ð½Ð¾Ð³Ð¾ ÐºÐ°ÑÐºÐ°ÑÐ° Ð¼Ð½Ð¾Ð³Ð¾ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð·Ð´Ð°Ð½Ð¸Ñ
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: Algorithm for solving the optimization problem for a wooden frame of a multifunctional building
Creators: name: Ð¡ÑÐµÑÐµÐ½ÐºÐ¾, ÐÐ°ÑÑ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´ÐµÑÐµÐ²ÑÐ½Ð½ÑÐ¹ ÐºÐ°ÑÐºÐ°Ñ
ÐºÐ»ÐµÐµÐ´Ð¾ÑÐ°ÑÐ°Ñ Ð°ÑÐºÐ°
ÐºÐ»ÐµÐµÑÐ°Ð½ÐµÑÐ½Ð°Ñ ÑÐ°Ð¼Ð°
Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ðµ Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾ÐµÐ¼ÐºÐ¾ÑÑÑ
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
matlab
wooden frame
glued wood arch
glued plywood frame
optimal design
material consumption
nonlinear programming

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¸ ÑÐµÑÐµÐ½Ð¸Ñ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð´Ð»Ñ Ð´ÐµÑÐµÐ²ÑÐ½Ð½Ð¾Ð³Ð¾ ÐºÐ°ÑÐºÐ°ÑÐ° Ð·Ð´Ð°Ð½Ð¸Ñ, Ð²ÑÐ±ÑÐ°Ð½Ð½Ð¾Ð³Ð¾ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸ ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ°ÑÑÐµÑÐ¾Ð².
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·ÑÑÐµÐ½Ð¸Ðµ Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð½ÑÑ Ð¿ÑÐ¾ÐµÐºÑÐ¾Ð² Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ Ð´ÐµÑÐµÐ²ÑÐ½Ð½ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹ Ð² ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð½ÐµÑÑÑÐ¸Ñ Ð´Ð»Ñ Ð¾Ð±ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÑ Ð¼Ð½Ð¾Ð³Ð¾ÑÑÐ½ÐºÑÐ¸Ð¾Ð½Ð°Ð»ÑÐ½ÑÑ Ð·Ð´Ð°Ð½Ð¸Ð¹. ÐÑÐ±Ð¾Ñ Ð¸ÑÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ;
2. ÐÑÐ±Ð¾Ñ, Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð¸Ð·ÑÑÐµÐ½Ð¸Ñ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ, Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ¾Ð² ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð²Ð½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð·Ð´Ð°Ð½Ð¸Ñ Ñ Ð¸ÑÑÐ¾Ð´Ð½ÑÐ¼Ð¸ Ð´Ð°Ð½Ð½ÑÐ¼Ð¸, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð² Ð·Ð°Ð´Ð°ÑÐµ 1; 
3. ÐÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ðµ ÑÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐ°ÑÑÐµÑÐ¾Ð² Ð¸ Ð¿Ð¾Ð´Ð±Ð¾ÑÐ° ÑÐµÑÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ¾Ð² ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð²Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ, Ð²ÑÐ±ÑÐ°Ð½Ð½ÑÑ Ð² Ð·Ð°Ð´Ð°ÑÐµ 2. Ð¡ÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð¿Ð¾ ÐºÑÐ¸ÑÐµÑÐ¸Ñ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾ÐµÐ¼ÐºÐ¾ÑÑÐ¸;
4. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¸ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐ¼ ÑÐ¿Ð¾ÑÐ¾Ð±Ð¾Ð¼ Ð´Ð»Ñ Ð²Ð°ÑÐ¸Ð°Ð½ÑÐ° Ñ Ð½Ð°Ð¸Ð¼ÐµÐ½ÑÑÐµÐ¹ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð»Ð¾ÐµÐ¼ÐºÐ¾ÑÑÑÑ, Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð·Ð°Ð´Ð°ÑÐµÐ¹ 3. ÐÐ¾Ð¸ÑÐº ÑÐ°ÐºÐ¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹, Ð¿ÑÐ¸ ÐºÐ¾ÑÐ¾ÑÑÑ Ð¼Ð°ÑÑÐ° Ð²ÑÐµÑ Ð´ÐµÑÐµÐ²ÑÐ½Ð½ÑÑ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹ Ð·Ð´Ð°Ð½Ð¸Ñ Ð±ÑÐ´ÐµÑ Ð¼Ð¸Ð½Ð¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð¹. 
Ð¡ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ°ÑÑÐµÑÑ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¿Ð¾ Ð°ÐºÑÑÐ°Ð»ÑÐ½ÑÐ¼ ÑÐµÐ´Ð°ÐºÑÐ¸ÑÐ¼ Ð½Ð¾ÑÐ¼Ð°ÑÐ¸Ð²Ð½ÑÑ Ð´Ð¾ÐºÑÐ¼ÐµÐ½ÑÐ¾Ð² Ñ ÑÑÐµÑÐ¾Ð¼ ÑÐµÐºÐ¾Ð¼ÐµÐ½Ð´Ð°ÑÐ¸Ð¹, Ð´Ð°Ð½Ð½ÑÑ Ð² ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¾Ð¹ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÐµ, Ð¸ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÐÐ ÐÐÐ Ð-Ð¡ÐÐÐ  2013 r3 Ð¸ ANSYS Workbench 2019 R1. Ð Ð°ÑÑÐµÑÑ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð´Ð»Ñ ÐºÐ»ÐµÐµÐ´Ð¾ÑÐ°ÑÐ¾Ð¹ ÑÑÐµÑÑÐ°ÑÐ½Ð¸ÑÐ½Ð¾Ð¹ Ð°ÑÐºÐ¸ ÑÐ»Ð»Ð¸Ð¿ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¾ÑÐµÑÑÐ°Ð½Ð¸Ñ Ð¸ ÑÐ¿Ð»Ð¾ÑÐ½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ Ð¸ ÐºÐ»ÐµÐµÑÐ°Ð½ÐµÑÐ½Ð¾Ð¹ ÑÐ°Ð¼Ñ c Ð³Ð½ÑÑÐ¾ÐºÐ»ÐµÐµÐ½ÑÐ¼Ð¸ Ð´ÐµÑÐ°Ð»ÑÐ¼Ð¸ Ð¸ Ð¿ÐµÑÐµÐ¼ÐµÐ½Ð½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. ÐÐ°ÑÐµÑÐ¸Ð°Ð»Ð¾ÐµÐ¼ÐºÐ¾ÑÑÑ Ð°ÑÐºÐ¸ Ð¿Ð¾ÑÑÐ¸ Ð² 1.5 ÑÐ°Ð·Ð° Ð¼ÐµÐ½ÑÑÐµ, ÑÐµÐ¼ ÑÐ°Ð¼Ñ Ð¿ÑÐ¸ Ð½ÐµÐ·Ð½Ð°ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð¹ ÑÐ°Ð·Ð½Ð¸ÑÐµ Ð¿Ð¾Ð»ÐµÐ·Ð½Ð¾Ð³Ð¾ Ð¾Ð±ÑÐµÐ¼Ð°. 
ÐÐ»Ñ ÐºÐ»ÐµÐµÐ´Ð¾ÑÐ°ÑÐ¾Ð¹ Ð°ÑÐºÐ¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¸ ÑÐµÑÐµÐ½Ð° Ð·Ð°Ð´Ð°ÑÐ° Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð² Matlab R2019b. ÐÐ¾Ð»ÑÑÐµÐ½Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½Ð¾Ð³Ð¾ ÑÐ°Ð³Ð° Ð°ÑÐ¾Ðº Ð¸ ÑÐ°Ð·Ð¼ÐµÑÐ¾Ð² ÑÐµÑÐµÐ½Ð¸Ñ. ÐÐ¾Ð´Ð¾Ð±Ð½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ Ð¸ Ð´Ð»Ñ Ð´ÑÑÐ³Ð¸Ñ ÑÑÐµÐ¼ Ð¸ ÐºÐ¾Ð½ÑÑÑÑÐºÑÐ¸Ð¹, ÐºÑÐ¾Ð¼Ðµ ÑÐ¾Ð³Ð¾, Ð¾Ð½ Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½ Ð¿ÐµÑÐ²Ð¾Ð½Ð°ÑÐ°Ð»ÑÐ½Ð¾ ÐºÐ°Ðº ÑÐµÑÐ½Ð¸ÐºÐ¾-ÑÐºÐ¾Ð½Ð¾Ð¼Ð¸ÑÐµÑÐºÐ¾Ðµ Ð¾Ð±Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²ÑÐ±Ð¾ÑÐ° ÑÐ°Ð³Ð° Ð½Ð° ÑÑÐ°Ð´Ð¸Ð¸ ÐºÐ¾Ð½ÑÐµÐ¿ÑÑÐ°Ð»ÑÐ½Ð¾Ð³Ð¾ Ð¿ÑÐ¾ÐµÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸Ð»Ð¸ Ð¿ÐµÑÐµÐ´ ÐºÐ¾Ð½ÑÑÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ·Ð»Ð¾Ð² Ð¿Ð¾ÑÐ»Ðµ Ð²ÑÐ±Ð¾ÑÐ° Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ ÑÐµÑÐµÐ½Ð¸Ñ.
description: The work is devoted to the development of the algorithm and the solution of the optimization problem for the wooden frame of the building, which is selected using qualitative analysis and static calculations.
The research set the following goals:
1. The study and analysis of completed projects using wooden structures as load-bearing. Selection of input data for the research;
2. Selection, based on a study of the literature, options for constructive solutions for the building with the source data obtained in task 1;
3. Performing static calculations and selecting cross sections for design options selected in task 2. Comparison of results by the criterion of material consumption;
4. The development of the algorithm and the solution of the nonlinear programming problem in an automated way for the option with the least material consumption, defined by task 3.
Static calculations were carried out according to the current versions of regulatory documents, taking into account the recommendations given in the technical literature, and using the LIRA-SAPR 2013 r3 and ANSYS Workbench 2019 R1. The calculations were carried out for a three-joints glued wood arch of an elliptical shape and a solid cross section and a glued plywood frame with bent glued parts and a variable section. The material consumption of the arch is almost 1.5 times less than the frames with a slight difference in usable volume.
For the glued wood arch an algorithm was developed and the problem of nonlinear programming in Matlab R2019b was solved. The values of the optimal step of the arches and cross section sizes are obtained. A similar algorithm can be implemented for other schemes and designs, in addition, it can be performed initially as a feasibility study for choosing a step at the conceptual design stage or before constructing nodes after choosing a specific solution.