SET OF EQUATIONS OF AFEM AND PROPERTIES OF ADDITIONAL FINITE ELEMENTS
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Abstract
The paper considers the action of additional finite elements on the main set of linear equations when developed Additional Finite Element Method (AFEM) is used for analysis of structures with several nonlinear properties at limit states and failure models. AFEM is a variant of Finite Element Method (FEM) which adds to traditional sequence of solution of problem by FEM the units of two well-known methods of structural analysis: method of additional loads and method of ultimate equilibrium. AFEM suggests the additional finite elements and additional design diagrams for gradually transformation of the main set of equilibrium equations at the first step of loading to this set at the last one according to ideal failure model of structure.
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Ermakova, A. (2019). SET OF EQUATIONS OF AFEM AND PROPERTIES OF ADDITIONAL FINITE ELEMENTS. International Journal for Computational Civil and Structural Engineering, 15(2), 51–64. https://doi.org/10.22337/2587-9618-2019-15-2-51-64
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References
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2. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСВ, 2007 – 128 p.
3. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСB, 2012 – 114 p.
4. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСV Construction, Stockholm, Sweden, 2016 – 116 p.
5. Zienkiewicz O.C. Metod konechnix elementov v texnike (The finite element method in technique), Mir, Moscow. 1975 – 541 p.
6. Ilyushin A.A. Plasticity, Gostechisdat, Moscow, 1948, 376 p.
7. Postnov V.A. Numerical methods of design of ship structures, Shipbuilding, Leningrad, 1977, 280 p.
8. Ermakova A. Actual problems of nonlinear design of reinforced concrete structures. International Journal for Computational Civil and Structural Engineering. Moscow (IAECEI) – New York (BHP), 2009, v. 5, is. 1&2, p. 23 – 34.
9. Ermakova A. Solving Some Problems of Nonlinear Analysis of Reinforced Concrete Structures by Additional finite Element/ Concrete in the Low Carbon Era. Proceedings of the International Conference held at the University of Dundee, Scotland, UK on 9–11 July 2012. Dundee, Scotland, UK, p. 1153 – 1163
10. Ermakova A. Ideal failure models of structures for nonlinear analysis by additional finite element method. Structural mechanics and analysis of constructions. 2017. N 6, p. 46-50.
11. Ermakova A. Ideal Failure Models of Structures for Analysis by FEM and AFEM. Proceedings ICIE–2017. Volume 206, p. 9–15. (SCOPUS).
12. Ermakova A.V. The solving of the set of linear algebraic equations of additional finite element method. Concrete and reinforced concrete. 2010. N 5, p. 21-24.
13. Ermakova A.V. Two ways for realization of iterative process at additional finite element method. Structural mechanics and analysis of constructions. 2018. N 6, p. 45-52.
14. Gorodetsky A.S., Evzerov I.D. Computer models of structures. Kiev: Fact. 2007 – 394 p.
15. Karpenko N. I. Construction of Schemes of Reinforced Concrete, State Administration of Construction, Moscow, 1996 - 416 p.
16. Shugaev V.V. Engineer Methods of Non-Linear Theory of Limit Equilibrium of the Shells, Gotika, Moscow, 2001 - 368 p.
17. Computer-aided of reinforced concrete structural elements. Oatul A.A., Karyakin A.A., Kutin U.F. Collected lectures. Part 4 edited by Prof. OATUL A. A., Chelyabinsk Polytechnic Institute, Chelyabinsk, 1980 - 67 p.
18. SN 63.13330.2012. Concrete and Reinforced Concrete Structures. Actual version SN and C 52-01-2003.
19. Ermakova A. Additional Finite Elements and Additional Loads for Analysis of Systems with Several Nonlinear Properties. Proceedings ICIE–2016. Volume 150, p. 1817–1823. (SCOPUS)
20. Ermakova A.V. Correlation between additional finite element method and other numerical methods of the structural analysis. Structural mechanics and analysis of constructions. 2012. N 5, p. 28-33.
21. Ermakova A.V. Additional finite element method for nonlinear analysis of reinforced concrete structures at limit states. M.: Publishing house ASV, 2017.- 60 p.
СПИСОК ЛИТЕРАТУРЫ
1. Гвоздев А.А. Расчет несущей способности конструкций по методу предельного равновесия. Вып. 1,Сущность метода и его обоснование. М: Госстройиздат, 1949 – 280 с.
2. Ермакова А.В. Метод дополнительных конечных элементов для расчета железобетонных конструкций по предельным состояниям. М.,АСВ, 2007–128 с.
3. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСB, 2012 – 114 p.
4. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСV Construction, Stockholm, Sweden, 2016 – 116 p.
5. Зенкевич О.К. Метод конечных элементов в технике.– М.: Мир, 1975.– 541с.
6. Ильюшин А.А. Пластичность. М.: Гостехиздат, 1948 – 376 с.
7. Постнов В.А. Численные методы расчета судовых конструкций. – Л., Судостроение, 1977 – 280 с.
8 Ermakova A. Actual problems of nonlinear design of reinforced concrete structures. International Journal for Computational Civil and Structural Engineering. Moscow (IAECEI)– New York (BHP), 2009, v. 5, is. 1&2, p. 23 – 34.
9. Ermakova A. Solving Some Problems of Nonlinear Analysis of Reinforced Concrete Structures by Additional finite Element/ Concrete in the Low Carbon Era. Proceedings of the International Conference held at the University of Dundee, Scotland, UK on 9–11 July 2012. Dundee, Scotland, UK, p. 1153 – 1163.
10. Ермакова А.В. Идеальные модели разрушения конструкций для нелинейного расчета методом дополнительных конечных элементов. Строительная механика и расчет сооружений. 2017. № 6, c. 46 – 50.
11. Ermakova A. Ideal Failure Models of Structures for Analysis by FEM and AFEM. Proceedings ICIE–2017. Volume 206, p. 9–15. (SCOPUS).
12. Ермакова А.В. Решение системы линейных алгебраических уравнений метода дополнительных конечных элементов. Бетон и железобетон. 2010, № 5, с. 21 – 24.
13. Ермакова А.В. Два способа построения итерационного процесса метода дополнительных конечных элементов. Строительная механика и расчет сооружений. 2018. № 6, c. 45 – 52.
14. Городецкий А.С., Евзеров И.Д. Компьютерные модели конструкций. Киев: Факт, 2007 – 394 с.
15. Карпенко Н.И. Общие модели механики железобетона. М., Стройиздат, 1996 – 416 с.
16. Шугаев В.В. Инженерные методы в нелинейной теории предельного равновесия оболочек. – М.: Готика, 2001 – 368 с.
17. Расчет и проектирование элементов железобетонных конструкций на основе применения ЭВМ. Оатул А.А., Карякин А.А., Кутин Ю.Ф. Конспект лекций, Ч.4. Под ред. Оатула А.А. – Челябинск: ЧПИ, 1980 – 67с.
18. СП 63.13330.2012. Бетонные и железобетонные конструкции. Актуализированная редакция СНиП 52-01-2003.
19. Ermakova A. Additional Finite Elements and Additional Loads for Analysis of Systems with Several Nonlinear Properties. Proceedings ICIE–2016. Volume 150, p. 1817–1823. (SCOPUS)
20. Ермакова А.В. Взаимосвязь метода дополнительных конечных элементов и других численных методов расчета конструкций. Строительная механика и расчет сооружений. 2012. № 5, с. 28 – 33.
21. Ермакова А.В. Метод дополнительных конечных элементов для нелинейного расчета железобетонных конструкций по предельным состояниям. Текст лекций – М: Изд-во АСВ, 2017. – 64 c.
2. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСВ, 2007 – 128 p.
3. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСB, 2012 – 114 p.
4. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСV Construction, Stockholm, Sweden, 2016 – 116 p.
5. Zienkiewicz O.C. Metod konechnix elementov v texnike (The finite element method in technique), Mir, Moscow. 1975 – 541 p.
6. Ilyushin A.A. Plasticity, Gostechisdat, Moscow, 1948, 376 p.
7. Postnov V.A. Numerical methods of design of ship structures, Shipbuilding, Leningrad, 1977, 280 p.
8. Ermakova A. Actual problems of nonlinear design of reinforced concrete structures. International Journal for Computational Civil and Structural Engineering. Moscow (IAECEI) – New York (BHP), 2009, v. 5, is. 1&2, p. 23 – 34.
9. Ermakova A. Solving Some Problems of Nonlinear Analysis of Reinforced Concrete Structures by Additional finite Element/ Concrete in the Low Carbon Era. Proceedings of the International Conference held at the University of Dundee, Scotland, UK on 9–11 July 2012. Dundee, Scotland, UK, p. 1153 – 1163
10. Ermakova A. Ideal failure models of structures for nonlinear analysis by additional finite element method. Structural mechanics and analysis of constructions. 2017. N 6, p. 46-50.
11. Ermakova A. Ideal Failure Models of Structures for Analysis by FEM and AFEM. Proceedings ICIE–2017. Volume 206, p. 9–15. (SCOPUS).
12. Ermakova A.V. The solving of the set of linear algebraic equations of additional finite element method. Concrete and reinforced concrete. 2010. N 5, p. 21-24.
13. Ermakova A.V. Two ways for realization of iterative process at additional finite element method. Structural mechanics and analysis of constructions. 2018. N 6, p. 45-52.
14. Gorodetsky A.S., Evzerov I.D. Computer models of structures. Kiev: Fact. 2007 – 394 p.
15. Karpenko N. I. Construction of Schemes of Reinforced Concrete, State Administration of Construction, Moscow, 1996 - 416 p.
16. Shugaev V.V. Engineer Methods of Non-Linear Theory of Limit Equilibrium of the Shells, Gotika, Moscow, 2001 - 368 p.
17. Computer-aided of reinforced concrete structural elements. Oatul A.A., Karyakin A.A., Kutin U.F. Collected lectures. Part 4 edited by Prof. OATUL A. A., Chelyabinsk Polytechnic Institute, Chelyabinsk, 1980 - 67 p.
18. SN 63.13330.2012. Concrete and Reinforced Concrete Structures. Actual version SN and C 52-01-2003.
19. Ermakova A. Additional Finite Elements and Additional Loads for Analysis of Systems with Several Nonlinear Properties. Proceedings ICIE–2016. Volume 150, p. 1817–1823. (SCOPUS)
20. Ermakova A.V. Correlation between additional finite element method and other numerical methods of the structural analysis. Structural mechanics and analysis of constructions. 2012. N 5, p. 28-33.
21. Ermakova A.V. Additional finite element method for nonlinear analysis of reinforced concrete structures at limit states. M.: Publishing house ASV, 2017.- 60 p.
СПИСОК ЛИТЕРАТУРЫ
1. Гвоздев А.А. Расчет несущей способности конструкций по методу предельного равновесия. Вып. 1,Сущность метода и его обоснование. М: Госстройиздат, 1949 – 280 с.
2. Ермакова А.В. Метод дополнительных конечных элементов для расчета железобетонных конструкций по предельным состояниям. М.,АСВ, 2007–128 с.
3. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСB, 2012 – 114 p.
4. Ermakova A.V. Additional finite element method for analysis of reinforced concrete structures at limit states. М., АСV Construction, Stockholm, Sweden, 2016 – 116 p.
5. Зенкевич О.К. Метод конечных элементов в технике.– М.: Мир, 1975.– 541с.
6. Ильюшин А.А. Пластичность. М.: Гостехиздат, 1948 – 376 с.
7. Постнов В.А. Численные методы расчета судовых конструкций. – Л., Судостроение, 1977 – 280 с.
8 Ermakova A. Actual problems of nonlinear design of reinforced concrete structures. International Journal for Computational Civil and Structural Engineering. Moscow (IAECEI)– New York (BHP), 2009, v. 5, is. 1&2, p. 23 – 34.
9. Ermakova A. Solving Some Problems of Nonlinear Analysis of Reinforced Concrete Structures by Additional finite Element/ Concrete in the Low Carbon Era. Proceedings of the International Conference held at the University of Dundee, Scotland, UK on 9–11 July 2012. Dundee, Scotland, UK, p. 1153 – 1163.
10. Ермакова А.В. Идеальные модели разрушения конструкций для нелинейного расчета методом дополнительных конечных элементов. Строительная механика и расчет сооружений. 2017. № 6, c. 46 – 50.
11. Ermakova A. Ideal Failure Models of Structures for Analysis by FEM and AFEM. Proceedings ICIE–2017. Volume 206, p. 9–15. (SCOPUS).
12. Ермакова А.В. Решение системы линейных алгебраических уравнений метода дополнительных конечных элементов. Бетон и железобетон. 2010, № 5, с. 21 – 24.
13. Ермакова А.В. Два способа построения итерационного процесса метода дополнительных конечных элементов. Строительная механика и расчет сооружений. 2018. № 6, c. 45 – 52.
14. Городецкий А.С., Евзеров И.Д. Компьютерные модели конструкций. Киев: Факт, 2007 – 394 с.
15. Карпенко Н.И. Общие модели механики железобетона. М., Стройиздат, 1996 – 416 с.
16. Шугаев В.В. Инженерные методы в нелинейной теории предельного равновесия оболочек. – М.: Готика, 2001 – 368 с.
17. Расчет и проектирование элементов железобетонных конструкций на основе применения ЭВМ. Оатул А.А., Карякин А.А., Кутин Ю.Ф. Конспект лекций, Ч.4. Под ред. Оатула А.А. – Челябинск: ЧПИ, 1980 – 67с.
18. СП 63.13330.2012. Бетонные и железобетонные конструкции. Актуализированная редакция СНиП 52-01-2003.
19. Ermakova A. Additional Finite Elements and Additional Loads for Analysis of Systems with Several Nonlinear Properties. Proceedings ICIE–2016. Volume 150, p. 1817–1823. (SCOPUS)
20. Ермакова А.В. Взаимосвязь метода дополнительных конечных элементов и других численных методов расчета конструкций. Строительная механика и расчет сооружений. 2012. № 5, с. 28 – 33.
21. Ермакова А.В. Метод дополнительных конечных элементов для нелинейного расчета железобетонных конструкций по предельным состояниям. Текст лекций – М: Изд-во АСВ, 2017. – 64 c.