Reinforcement layout design of three-dimensional members under a state of complex stress

• Autorzy: Cui Hao , Xia Junjie , Wu Lang , Xiao Min

Identyfikatory

DOI

10.24425/ace.2023.144181

• Języki publikacji: EN

Abstrakty

EN

This paper proposes a method to optimize reinforcement layout of three-dimensional members under a state of complex stress and multiple load cases (MLCs). To simulate three-dimensional members, the spatial truss-like material model is adopted. Three families of truss-like members along orthotropic directions are embedded continuously in concrete. The optimal reinforcement layout design is obtained by optimizing the member densities and orientations. The optimal design of three-dimensional member is carried out by solving the problem of minimum volume of reinforcing bars with stress constraints. Firstly, the optimized reinforcement layout under each single load case (SLC) is obtained as per the fully stressed criterion. Second, on the basis of the previous results, an equivalent multi-case optimization is proposed by introducing the idea of stiffness envelope. Finally, according to the characteristics of the truss-like material, a closed and symmetrical surface is adopted to fit the maximum directional stiffness under all SLCs. It can be proved that the densities and orientations of truss-like members are the eigenvalues and eigenvectors of the surface coefficient matrix, respectively. Several three-dimensional members are used as examples to demonstrate the capability of the proposed method in finding the best reinforcement layout design of each reinforced concrete (RC) member and to verify its efficiency in application to real design problems.

Słowa kluczowe

EN

topology optimization; truss model; reinforcement location; multiple load cases; complex stress state

PL

optymalizacja topologii; model kratownicowy; układ zbrojenia; obciążenie; stan naprężenia złożony

• Wydawca: Komitet Inżynierii Lądowej i Wodnej PAN ; Politechnika Warszawska, Wydział Inżynierii Lądowej
• Czasopismo: Archives of Civil Engineering
• Rocznik: 2023
• Tom: Vol. 69, nr 1
• Strony: 421--436
• Opis fizyczny: Bibliogr. 22 poz., il.

Twórcy

autor

Cui Hao

• College of Civil Engineering and Architecture, Jiangxi Science and Technology Normal University, Nanchang, China

• https://orcid.org/0000-0002-8292-9555

autor

Xia Junjie

• College of Civil Engineering and Architecture, Jiangxi Science and Technology Normal University, Nanchang, China

• https://orcid.org/0000-0002-5993-6474

autor

Wu Lang

• College of Civil Engineering and Architecture, Jiangxi Science and Technology Normal University, Nanchang, China

• https://orcid.org/0000-0001-9985-6578

autor

Xiao Min

• College of Civil Engineering and Architecture, Jiangxi Science and Technology Normal University, Nanchang, China

• https://orcid.org/0000-0001-8078-6119

Bibliografia

• [1] O. Sigmund and K. Maute, “Topology optimization approaches”, Structural and Multidisciplinary Optimization, vol. 48, no. 6, pp. 1031-1055, 2013, DOI: 10.1007/s00158-013-0978-6.
• [2] G. Dzierżanowski and K. Hetmański, “Optimal design of archgrids: the second-order cone programming perspective”, Archives of Civil Engineering, vol. 67, no. 4, pp. 469-486, 2021, DOI: 10.24425/ace.2021.138512.
• [3] X. Guo, W. Zhang, and W. Zhong, “Doing topology optimization explicitly and geometrically-new moving morphable components based framework”, Journal of Applied Mechanics, vol. 81, no. 8, art. no. 081009, 2014, DOI: 10.1115/1.4027609.
• [4] V.N. Hoang and G.W. Jang, “Topology optimization using moving morphable bars for versatile thickness control”, Computer Methods in Applied Mechanics and Engineering, vol. 317, pp. 153-173, 2017, DOI: 10.1016/j.cma.2016.12.004.
• [5] Q.Q. Liang, Y.M. Xie, and G.P. Steven, “Topology optimization of strut-and-tie models in reinforced concrete structures using an evolutionary procedure”, ACI Structural Journal, vol. 97, no. 2, pp. 322-331, 2000.
• [6] Q.Q. Liang, Y.M. Xie, and G.P. Steven, “Generating optimal strut-and-tie models in prestressed concrete beams by performance-based optimization”, ACI Structural Journal, vol. 98, no. 2, pp. 226-232, 2001.
• [7] H.G. Kwak and S.H. Noh, “Determination of strut-and-tie models using evolutionary structural optimization”, Engineering Structures, vol. 28, no. 10, pp. 1440-1449, 2006, DOI: 10.1016/j.engstruct.2006.01.013.
• [8] R.M. Lanes, M. Greco, and M.B.B.F. Guerra, “Strut-and-tie models for linear and nonlinear behavior of concrete based on topological evolutionary structure optimization (ESO) ”, Revista IBRACON de Estruturas e Materiais, vol. 12, no. 1, pp. 87-100, 2019, DOI: 10.1590/S1983-41952019000100008.
• [9] L.J. Leu, C.W. Huang, C.S. Chen, et al., “Strut-and-tie design methodology for three-dimensional reinforced concrete structures”, Journal of Structural Engineering, vol. 132, no. 6, pp. 929-938, 2006, DOI: 10.1061/(ASCE)0733-9445(2006)132:6(929).
• [10] V. Shobeiri and B. Ahmadi-Nedushan, “Bi-directional evolutionary structural optimization for strut-and-tie modelling of three-dimensional structural concrete”, Engineering Optimization, vol. 49, no. 12, pp. 2055-2078, 2017, DOI: 10.1080/0305215X.2017.1292382.
• [11] V. Shobeiri, “Determination of strut-and-tie models for structural concrete under dynamic loads”, Canadian Journal of Civil Engineering, vol. 46, no. 12, pp. 1090-1102, 2019, DOI: 10.1139/cjce-2018-0780.
• [12] M. Bruggi, “Generating strut-and-tie patterns for reinforced concrete structures using topology optimization”, Computers & Structures, vol. 87, no. 23-24, pp. 1483-1495, 2009, DOI: 10.1016/j.compstruc.2009.06.003.
• [13] Y. Xia, M. Langelaar, and M.A.N. Hendriks, “A critical evaluation of topology optimization results for strutand-tie modeling of reinforced concrete”, Computer-Aided Civil and Infrastructure Engineering, vol. 35, no. 8, pp. 850-869, 2020, DOI: 10.1111/mice.12537.
• [14] W. Qiao and G. Chen, “Generation of strut-and-tie models in concrete structures by topology optimization based on moving morphable components”, Engineering Optimization, vol. 53, no. 7, pp. 1251-1272, 2021, DOI: 10.1080/0305215X.2020.1781843.
• [15] M. Victoria, O.M. Querin, and P. Martí, “Generation of strut-and-tie models by topology design using different material properties in tension and compression”, Structural and Multidisciplinary Optimization, vol. 44, no. 2, pp. 247-258, 2011, DOI: 10.1007/s00158-011-0633-z.
• [16] Z. Du, W. Zhang, Y. Zhang, et al., “Structural topology optimization involving bi-modulus materials with asymmetric properties in tension and compression”, Computational Mechanics, vol. 63, no. 2, pp. 335-363, 2019, DOI: 10.1007/s00466-018-1597-2.
• [17] O. Amir and O. Sigmund, “Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization”, Structural and Multidisciplinary Optimization, vol. 47, no. 2, pp. 157-174, 2013, DOI: 10.1007/s00158-012-0817-1.
• [18] Y. Luo and Z. Kang, “Layout design of reinforced concrete structures using two-material topology optimization with Drucker-Prager yield constraints”, Structural and Multidisciplinary Optimization, vol. 47, no. 1, pp. 95-110, 2013, DOI: 10.1007/s00158-012-0809-1.
• [19] Z. Yang, K. Zhou, and S. Qiao, “Topology optimization of reinforced concrete structure using composite truss-like model”, Structural Engineering and Mechanics, vol. 67, no. 1, pp. 79-85, 2018, DOI: 10.12989/sem.2018.67.1.079.
• [20] H. Cui, L. Xie, M. Xiao, et al., “Conceptual design of reinforced concrete structures using truss-like topology optimization”, Archives of Civil Engineering, vol. 68, no. 3, pp. 523-537, 2022, DOI: 10.24425/ace.2022.141900.
• [21] K. Zhou and X. Li, “Topology optimization of truss-like continua with three families of members model under stress constraints”, Structural and Multidisciplinary Optimization, vol. 43, no. 4, pp. 487-493, 2011, DOI: 10.1007/s00158-010-0584-9.
• [22] H. Cui and K. Zhou, “Topology Optimization of Truss-Like Structure with Stress Constraints Under Multiple-Load Cases”, Acta Mechanica Solida Sinica, vol. 33, no. 2, pp. 226-238, 2019, DOI: 10.1007/s10338-019-00125-3.