Email this article 
Using Solid Superelements for Nonlinear Analysis of Slab-and-Beam Structures in the PRINS Software
- Authors: Agapov V.P.1, Markovich A.S.1,2
-
Affiliations:
- RUDN University
- Moscow State University of Civil Engineering (National Research University)
- Issue: Vol 21, No 4 (2025)
- Pages: 283-293
- Section: Analytical and numerical methods of analysis of structures
- URL: https://journals.rcsi.science/1815-5235/article/view/349857
- DOI: https://doi.org/10.22363/1815-5235-2025-21-4-283-293
- EDN: https://elibrary.ru/CEBUAP
- ID: 349857
Cite item
Full Text
Abstract
The article presents a methodology for nonlinear static analysis of slab-and-beam structures using finite elements constructed using the three-dimensional theory of elasticity and plasticity. Multilayer plate/shell elements and solid beam elements (superelements) are used to analyze structures made of heterogeneous materials, including reinforced concrete. In most currently used software products, beam finite elements are constructed either on the basis of the classical theory of strength of materials or on the basis of the three-dimensional elasticity theory. When using the three-dimensional theory, restrictions are introduced on the shape and size of cross-sections, and all characteristics are reduced to points lying in the end sections of the beams along their axes. Both of these approaches make it difficult to simultaneously take into account physical and geometric nonlinearity, therefore the development of alternative methods for nonlinear static analysis of structures is relevant. To avoid this drawback, a superelement for modeling reinforced concrete columns and beams as part of combined slab-and-beam systems is proposed in this article. To date, there are no alternatives of the proposed superelement for analyzing reinforced concrete structures in known commercial finite element products. The developed methodology is adapted to the PRINS software. An example of calculating the load-bearing capacity of a two-story frame using this software is given. The PRINS software can be used by engineers of design and scientific organizations to solve engineering problems related to the analysis of reinforced concrete structures.
About the authors
Vladimir P. Agapov
RUDN University
Email: agapovpb@mail.ru
ORCID iD: 0000-0002-1749-5797
SPIN-code: 2422-0104
Doctor of Technical Sciences, Associate Professor of the Department of Construction Technology and Structural Materials, Academy of Engineering
6 Miklukho-Maklaya St, Moscow, 117198, Russian FederationAlexey S. Markovich
RUDN University; Moscow State University of Civil Engineering (National Research University)
Author for correspondence.
Email: markovich-as@rudn.ru
ORCID iD: 0000-0003-3967-2114
SPIN-code: 9203-1434
Doctor of Technical Sciences, Associate Professor of the Department of Construction Technology and Structural Materials, Academy of Engineering, RUDN University; Professor of the Department of Metal and Timber Structures, National Research Moscow State University of Civil Engineering
6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation; 26 Yaroslavl Highway, Moscow, 129337, Russian FederationReferences
- Bathe K.J., Wilson E.L. Numerical methods in finite element analysis. N.J.: Prentice-Hall; 1976. ISBN 0136271901, 9780136271901
- Zienkiewicz O.C., Taylor R.L. The Finite Element for Solid and Structural Mechanics. Sixth edition. McGraw-Hill; 2005. http://doi.org/10.1016/B978-075066431-8/50186-7
- Crisfield M.A. Non-linear finite element analysis of solids and structures. John Wiley & Sons, 2012. ISBN 1118376013, 9781118376010
- Oden J.T. Finite elements in nonlinear continua. New York: McGraw, Hill Book Company; 1972. Available from: https://archive.org/details/finiteelementsof0000oden/page/n3/mode/2up (accessed: 12.01.2025)
- Kupfer H., Hilsdorf H., Rusch H. Behavior of Concrete under Biaxial Stresses. ACI Journal Proceedings. 1969;66(8):656–666. http://doi.org/10.14359/7388
- Launay P., Gachon H. Strain and Ultimate Strength of Concrete under Triaxial Stress. ACI Spec. Publ. 1972;34:269–282. Available from: http://www.lib.ncsu.edu/resolver/1840.20/29024 (accessed: 05.03.2025)
- Mills L.L., Zimmerman R.M. Compressive strength of plain concrete under multiaxial loading conditions. ACI Journal. October 1970;67(10):802–807. http://doi.org/10.14359/7310
- Korsun V.I., Nedorezov A.V., Makarenko S.Yu. Comparative analysis of the strength criteria for concrete. Modern Industrial and Civil Construction. 2014;10(1):65–78. (In Russ.) EDN: THXXCZ
- Hansen T.C. Triaxial test with concrete and cement paste: Report No. 319. Lyngby: Technical University of Denmark, 1995. ISBN 87-7740-156-5
- Agapov V.P., Vasiliev A.V. Modeling of rectangular columns with volumetric finite elements using super-element technology. Structural Mechanics of Engineering Constructions and Buildings. 2012;(4):48–54. (In Russ.) EDN: PFPUUT
- Agapov V.P. Finite element method in statics, dynamics and stability of structures. Moscow: ASV Publ.; 2004. (In Russ.) ISBN 5-93093-303-0 EDN: QMECWX
- Agapov V.P., Markovich A.S. The family of multilayered finite elements for the analysis of plates and shells of variable thickness: La familia de elementos finitos multicapa para el análisis de placas y cascos de espesor variable. South Florida Journal of Development. 2021;2(4):5034–5048. https://doi.org/10.46932/sfjdv2n4-007
- Agapov V.P., Markovich A.S. Calculation of Massive Reinforced Concrete Structures Including Cracks. Industrial and Civil Engineering. 2023;(7):43–49. (In Russ.) https://doi.org/10.33622/0869-7019.2023.07.43-49 EDN: LRCNLR
- Agapov V.P., Markovich A.S. Nonlinear models of concrete and reinforced concrete structures. Theory and implementation in PRINS software: monograph. Moscow: RUDN; 2023. (In Russ.) ISBN 978-5-209-11784-1
Supplementary files
