kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2025-22-1-197-210kaz29-1745Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESОПТИМИЗАЦИЯ ГЕОМЕТРИИ ФАСАДА ЗДАНИЯ ДЛЯ РАЦИОНАЛЬНОГО ИСПОЛЬЗОВАНИЯ ЭНЕРГИИOPTIMIZATION OF BUILDING FACADE GEOMETRY FOR RATIONAL USE OF ENERGYhttps://orcid.org/0000-0003-0579-4180АлпарС. Д.AlparS. D.

 PhD, ассоциированный профессор 

 г. Алматы 

 PhD, Associate Professor 

 Almaty 

s.alpar@iitu.edu.kzhttps://orcid.org/0000-0001-7980-8245ТокмухамедоваФ. К.TokmukhamedovaF. K.

 магистр, ассистент-профессор 

 г. Алматы 

 MSc, Assistant Professor 

 Almaty 

f.tokmukhamedova@iitu.edu.kzhttps://orcid.org/0009-0005-3004-2724ДильдабаеваА. А.DildabayevaA. A.

 магистрант 

 г. Алматы 

 Master student 

 Almaty 

adildabayeva@iitu.edu.kzМеждународный университет информационных технологийКазахстанInternational Information Technology UniversityKazakhstan202525032025221197210Copyright © Алпар С.Д., Токмухамедова Ф.К., Дильдабаева А.А., 20252025Алпар С.Д., Токмухамедова Ф.К., Дильдабаева А.А.Alpar S.D., Tokmukhamedova F.K., Dildabayeva A.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/1745

Современные исследования подчеркивают необходимость углубленного анализа как численных, так и экспериментальных подходов к оптимизации форм фасада здания с целью повышения их энергоэффективности. Актуальность дальнейших исследований объясняется сложностью численных методов, связанных с оптимизацией формы, направленных на данную задачу. Настоящая статья стремится устранить существующие пробелы в данной области посредством создания и анализа подходящей модели. Для этого предлагается использовать двумерную модель стационарной теплопроводности, которая описывает процессы теплопередачи в фасадах зданий различной конфигурации. На внешней границе вводится граничное условие Неймана (второго рода), учитывающее воздействие падающего коротковолнового солнечного излучения. Расчет последнего включает факторы, такие как освещенность и затенение поверхности стены, которые обусловлены окружающей городской средой. Для численного решения задачи с сохранением точности применяется метод граничных элементов (МГЭ), включающий дискретизацию границы исследуемой области на отдельные элементы. В ходе исследования определяются две ключевые задачи оптимизации: улучшение теплопередачи и обеспечение тепловой изоляции. Оптимальные формы фасада проектируются с соблюдением ограничения на объем используемого материала, который не должен превышать объем, необходимый для плоского эталонного фасада. Полученные результаты демонстрируют улучшение энергоэффективности на 13% летом и 100% зимой по сравнению с вариантом плоской стеновой конструкции.

Modern research emphasizes the need for an in-depth analysis of both numerical and experimental approaches to optimizing the shapes of building envelopes in order to improve their energy efficiency. The relevance of further research is explained by the complexity of numerical methods related to shape optimization aimed at this problem. This article seeks to fill the existing gaps in this area by creating and analyzing a suitable model. For this purpose, it is proposed to use a two-dimensional model of steady-state thermal conductivity, which describes the heat transfer processes in building facades of various configurations. At the outer boundary, the Neuman boundary condition (of the second kind) is introduced, considering the effect of incident short-wave solar radiation. Calculation of the latter includes factors such as illumination and shading of the wall surface, which are due to the surrounding urban environment. To numerically solve the problem while maintaining good precision, the boundary element method (BEM) is used, including discretization of the boundary of the study area into individual elements. During the study, two key optimization problems are defined: improving heat transfer and ensuring thermal insulation. Optimal façade shapes are designed with the constraint of the volume of material used not exceeding the volume required for a flat reference facade. The results obtained demonstrate a significant improvement in energy effectiveness of 13% in summer and 100% in winter compared to the flat wall facade option.

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The authors declare that there are no conflicts of interest present.