Least Strain Energy in Nonlinear Problems of Bar Nonuniform Deformation
https://doi.org/10.31675/1607-1859-2024-26-6-214-223
EDN: WIGGXY
Abstract
Optimization of building structures is one of the priority engineering tasks. Its relevance is determined by the expansion of the variety of internal structures of nonuniform structural elements, as well as the need to construct refined mathematical models considering nonlinear deformation factors.
Purpose: The aim is to the integral criterion for the least strain energy in relation to a nonuniform, nonlinearly deformed bar. The design diagram of the Timoshenko bar has a symmetrical structure and contains structural elements (layers) made of homogeneous nonlinear elastic materials.
Methodology: The material deformation is described by a polynomial approximation of an arbitrary order. Nonlinear dependencies are obtained for internal forces as functions of generalized strain of the axial line. Their coefficients are rigidity characteristics of higher orders.
Research findings: The suggested dependences used for strain energy components, are derived depending on deformation, curvature and average shear. Their use makes it possible to simplify formulation of optimization problems solved using the energy criterion with regard to physical non-linearity and nonuniformity of bars.
About the Author
A. V. Mishchenko
Novosibirsk State University of Architecture and Civil Engineering;
Order of Zhukov Novosibirsk Higher Military Command School
Russian Federation
Russian Federation
Andrey V. Mishchenko, DSc, A/Professor;
113, Leningradskaya Str., 630008, Novosibirsk
49, Ivanov Str., 630117, Novosibirsk
References
1. Teters G.A. Multi-Objective Optimal Design of Composite Structures. A Review. Mekhanika kompozitnykh materialov. 1996; 32 (3): 363–376. (In Russian)
2. Tamrazyan A.G., Alekseytsev A.V. Modern Methods for Optimizing Structural Solutions for Load-Bearing Systems of Buildings. Vestnik MGSU. 2020; 15 (1): 12–30. DOI: 10.22227/1997-0935.2020.1.12-30 (In Russian)
3. Yuryev A.G. Natural Factor for Optimizing Structure Topology. Vestnik Belgorodskogo gosudarstvennogo tekhnologicheskogo universiteta im. V.G. Shukhova. 2013 (5): 46–48. (In Russian)
4. Mondrus V.L., Stupishin L.Yu. Implementation of Criterion of Critical Energy Levels in Problems of Structural Mechanics for Systems with Lumped Parameters. In: Coll. Papers RAACS “Fundamental, exploratory and applied research of the RAASN on scientific support for the development of architecture, urban planning and the construction industry of the Russian Federation in 2021”. Moscow, 2022. Pp. 269–281. (In Russian)
5. Stupishin L.Yu. Critical Levels of Internal Potential Energy of Deformation of Solid Deformable Bodies. Moscow, 2022. 387 p. DOI: 10.47581/2022/Stupushin.01 (In Russian)
6. Vasilkov G.V. Evolutionary Problems of Structural Mechanics. Synergetic Paradigm. – Rostovon-Don: InfoService, 2003. 178 p. (In Russian)
7. Zinkova V.A. Optimization of Metal Truss Topology. Vestnik Belgorodskogo gosudarstvennogo tekhnologicheskogo universiteta im. V.G. Shukhova. 2015; (2): 37–40. (In Russian)
8. Krotkikh A.A., Maksimov P.V. Global Minimum of Strain Energy in Developing Topological Optimization Algorithm. Matematicheskoe modelirovanie v estestvennykh naukakh. 2017; 1: 39–43. (In Russian)
9. Kryzhevich G.B., Filatov A.R. Integrated Approach to Topological and Parametric Optimization of Ships. Trudy Krylovskogo gosudarstvennogo nauchnogo tsentra. 2020; 1 (391): 95–108. (In Russian)
10. Mishchenko A.V. Optimization of Structurally Inhomogeneous Rod Structures Based on Energy. Criterion Izvestiya vysshikh uchebnykh zavedenii. Stroitel'stvo. 2021; 6 (750). 20–32. DOI: 10.32683/0536-1052-2021-750-6-20-32 (In Russian)
11. Mishchenko A.V. Calculation Model of Nonlinear Dynamic Deformation of Composite Multiphase Rods. Vestnik MGSU. 2014; (5): 35–44. DOI: 10.22227/1997-0935.2014.5.2014 (In Russian)
12. Mishchenko A.V. Formation of Nonlinear Physical Relationships in Direct and Inverse Analysis of Multiphase Rods. Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Ser.: Stroitel'stvo i arkhitektura. 2014; 14 (3): 12–16. EDN: TAAFRD (In Russian)
13. Vasiliev V.V. Structural Mechanics of Composite Materials. Moscow: Mashinostroenie, 1988. 272 p. (In Russian)
Review
For citations:
Mishchenko A.V. Least Strain Energy in Nonlinear Problems of Bar Nonuniform Deformation. Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitel'nogo universiteta. JOURNAL of Construction and Architecture. 2024;26(6):214-223. (In Russ.) https://doi.org/10.31675/1607-1859-2024-26-6-214-223. EDN: WIGGXY
Views:
93
Email this article 