Structural Mechanics of Engineering Constructions and BuildingsStructural Mechanics of Engineering Constructions and BuildingsСтроительная механика инженерных конструкций и сооружений1815-52352587-8700Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)4456110.22363/1815-5235-2025-21-1-26-36IJMKCQAnalytical and numerical methods of analysis of structuresАналитические и численные методы расчета конструкцийResearch ArticleFracture of Wedge-Shaped Body Under CompressionРазрушение тел клиновидной формы при сжатииhttps://orcid.org/0000-0002-1794-867X3392-3788StupishinLeonid Yu.СтупишинЛеонид Юлианович

Doctor of Technical Sciences, Professor of the Department of Structural and Theoretical Mechanics, Institute of Industrial and Civil Engineering

доктор технических наук, профессор кафедры строительной и теоретической механики, Институт промышленного и гражданского строительства

lusgsh@ya.ruhttps://orcid.org/0000-0002-8003-42991953-1697NikitinKonstantin E.НикитинКонстантин Евгеньевич

Candidate of Technical Sciences, Associate Professor of the Department of Structural and Theoretical Mechanics, Institute of Industrial and Civil Engineering

кандидат технических наук, доцент кафедры строительной и теоретической механики, Институт промышленного и гражданского строительства

niksbox@yandex.ruhttps://orcid.org/0000-0003-1679-86979277-7549MasalovAlexander V.МасаловАлександр Васильевич

Candidate of Technical Sciences, Associate Professor of the Department of Industrial and Civil Engineering, Faculty of Construction and Architecture

кандидат технических наук, доцент кафедры промышленного и гражданского строительства, факультет строительства и архитектуры

masalow.al@yandex.ruMoscow State University of Civil Engineering (National Research University)Национальный исследовательский Московский государственный строительный университетSouthwest State UniversityЮго-Западный государственный университет25042025211263611062025Copyright ©; 2025, Stupishin L.Y., Nikitin K.E., Masalov A.V.Copyright ©; 2025, Ступишин Л.Ю., Никитин К.Е., Масалов А.В.2025Stupishin L.Y., Nikitin K.E., Masalov A.V.Ступишин Л.Ю., Никитин К.Е., Масалов А.В.https://creativecommons.org/licenses/by-nc/4.0https://journals.rudn.ru/structural-mechanics/article/view/44561

The aim is to study the fracture process of a wedge-shaped body during compression. A large number of researchers have turned to the classical solution of the elasticity theory problem of the loaded wedge-shaped body, but the problem of a supported wedge of a finite shape still has no analytical solution. The authors conducted a study of the failure mechanism of such bodies by both computational and experimental methods. To carry out the numerical analysis, the implementation of the progressive limit state method at critical levels of strain energy in the form of the force method was used, in combination with the method of approximation of continuum by an equivalent truss. The equivalent truss model of the wedge used here clearly demonstrates the process of removing structural members due to them reaching limit states. The technique of progressive limit states, based on the consecutive identification of “weak links” in the structure, in which the limit state occurs first, made it possible to construct fracture models of the considered body. The results of the performed analysis are presented in the form of fracture models of wedge-shaped bodies. The failure mechanism of wedge-shaped bodies was also investigated by experimental methods. Wedge-shaped gypsum specimens were compressed at the tip of the wedge and brought to fracture. The differences between the obtained fracture patterns and the classical results known from the theory of elasticity obtained for infinite wedge-shaped bodies are shown. A comparison of experimental and numerical results is performed, and a conclusion is made about the real fracture patterns of wedge-shaped bodies with a supported part.

Цель - исследование процесса разрушения тела клиновидной формы при сжатии. К решению классической задачи теории упругости о нагружении тела клиновидной формы возвращалось большое количество исследователей, однако задача об опертом клине конечной формы аналитического решения не имеет до сих пор. Авторами проведено исследование процесса разрушения таких тел как расчетными, так и экспериментальным методами. Для проведения численного анализа была использована реализация метода прогрессирующего предельного состояния на критических уровнях энергии деформации в форме метода сил, в сочетании с методом стержневой аппроксимации континуума. Использованная здесь плоская стержневая модель клина наглядно демонстрирует процесс удаления связей конструкции вследствие наступления в них предельного состояния. Методика прогрессирующего предельного состояния, основанная на последовательном выявлении «слабых» связей в конструкции, в которых в первую очередь наступает предельное состояние, позволила построить схемы разрушения рассматриваемого тела. Представлены результаты выполненного анализа, в виде схем разрушения тел клиновидной формы. Характер разрушения тел клиновидной формы так же исследовался экспериментальными методами. Образцы из гипса клиновидной формы были подвергнуты сжатию в вершине клина, и доведены до разрушения. Показаны отличия получаемых форм разрушения от классических результатов, известных из теории упругости, полученных для бесконечных клиновидных тел. Выполнено сравнение экспериментальных и численных результатов, и сделано заключение о реальных формах разрушения клиновидных тел с опорной частью.

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