Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

doi:10.1007/s11709-023-0963-0

Front. Struct. Civ. Eng.

2023, Vol. 17

Issue (5) : 669-685 https://doi.org/10.1007/s11709-023-0963-0

RESEARCH ARTICLE

Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

Anbang CHEN¹, Xiaoshan LIN¹, Zi-Long ZHAO², Yi Min XIE¹(

)

¹. Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne 3001, Australia
². Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China

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Abstract

Owing to advancement in advanced manufacturing technology, the reinforcement design of concrete structures has become an important topic in structural engineering. Based on bi-directional evolutionary structural optimization (BESO), a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete (SRC) structures. This approach combines a minimum compliance objective function with a hybrid truss-continuum model. Furthermore, a modified bi-directional evolutionary structural optimization (M-BESO) method is proposed to control the level of tensile stress in concrete. To fully utilize the tensile strength of steel and the compressive strength of concrete, the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete. To demonstrate the effectiveness of the proposed procedures, reinforcement layout optimizations of a simply supported beam, a corbel, and a wall with a window are conducted. Clear steel trajectories of SRC structures can be obtained using both methods. The area of critical tensile stress in concrete yielded by the M-BESO is more than 40% lower than that yielded by the uniform design and BESO. Hence, the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

Keywords bi-directional evolutionary structural optimization steel-reinforced concrete concrete stress reinforcement method hybrid model

Corresponding Author(s): Yi Min XIE

Just Accepted Date: 02 March 2023 Online First Date: 12 June 2023 Issue Date: 14 July 2023

Cite this article:

Anbang CHEN,Xiaoshan LIN,Zi-Long ZHAO, et al. Layout optimization of steel reinforcement in concrete structure using a truss-continuum model[J]. Front. Struct. Civ. Eng., 2023, 17(5): 669-685.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-023-0963-0
https://academic.hep.com.cn/fsce/EN/Y2023/V17/I5/669

Fig.1 2D truss element model for steel reinforcement in concrete: (a) orthogonal-diagonal steel bar model with four types of truss elements; (b) truss element-i with orientation θ; (c) steel-reinforced concrete structure with steel trusses embedded in concrete matrix.

Fig.2 Filter regions of two types of truss members: (a) type I and (b) type III.

Fig.3 Stress state calculation of host concrete around truss element.

Fig.4 Flowchart of BESO and M-BESO methods.

Fig.5 Simply supported beam: (a) structure; (b) uniform trusses; (c) optimized steel truss layout obtained via BESO; (d) optimized steel truss layout obtained via M-BESO. (In the color bar, the positive and negative values denote tensile and compressive stresses, respectively.)

Fig.6 Reinforcements of simply supported beam: (a) linear elastic rebars and (b) damage-based embedded rebars from Amir and Sigmund [54] (Reprinted from Structural and Multidisciplinary Optimization, 47(2), Amir O, Sigmund O, Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization, 157–174, Copyright 2013, with permission from Springer.), (c) Yang et al. [57] (Reprinted from Structural and Multidisciplinary Optimization, 67(1), Yang Z, Zhou K, Qiao S, Topology optimization of reinforced concrete structure using composite truss-like model, 79–85, Copyright 2018, with permission from Techno.), and (d) Cui et al. [59] (Reprinted from Latin American Journal of Solids and Structures, 17(4), Cui H, Zhou K, Yang Z, Reinforcement layout design of RC structures under multiple load cases using truss-like material model, 17, Copyright 2020, with permission from MARCíLIO ALVES LAJSS.).

Fig.7 Evolutions of the objective function (C(0) = 1112.4 N·m) and risk ratio (R_{FPS > 2}(0) = 16.1%) for simply supported beam: (a) BESO and (b) M-BESO results. Dashed line represents the volume fraction constraint.

Tab.1 Compliance and R_{FPS > 2} for simply supported beams with different truss layouts

Fig.8 FPS contours of simply supported beam: (a) structure with uniform steel reinforcement; (b) BESO results; (c) M-BESO results.

Fig.9 Corbel numerical examples: (a) structure; (b) uniform trusses; (c) optimized steel truss layout obtained via BESO; (d) optimized steel truss layout obtained via M-BESO method.

Fig.10 Corbel examples: (a) STM from topology optimization by Liang et al. [20] (Authorized reprint from ACI Materials Journal, 97(2), 2000, Liang Q Q, Xie Y M, Steven G P, Topology optimization of strut and-tie models in reinforced concrete structures using an evolutionary procedure.); (b) reinforcement layout by Cui et al. [59] (Reprinted from Latin American Journal of Solids and Structures, 17(4), Cui H, Zhou K, Yang Z, Reinforcement layout design of RC structures under multiple load cases using truss-like material model, 17, Copyright 2020, with permission from MARCíLIO ALVES LAJSS.); (c) optimized layout; (d) damage in optimized structure by Amir [68] (Reprinted from Computers & Structures, 114, Amir O, A topology optimization procedure for reinforced concrete structures, 46–58, Copyright 2013, with permission from Elsevier.).

Tab.2 Compliance and R_{FPS > 2} for corbels with different truss layouts

Fig.11 Evolutions of compliance and R_{FPS > 2} for the corbels: (a) BESO; (b) M-BESO results.

Fig.12 FPS contours of the corbels: (a) uniform steel truss; (b) BESO results; (c) M-BESO results.

Fig.13 Wall with a window: (a) structure; (b) uniform trusses; (c) optimized steel truss layout obtained via BESO; (d) optimized steel truss layout obtained via M-BESO.

Fig.14 Wall with a window: (a) STM from Liang et al. [20] (Authorized reprint from ACI Materials Journal, 97(2), 2000, Liang Q Q, Xie Y M, Steven G P, Topology optimization of strut and-tie models in reinforced concrete structures using an evolutionary procedure.); (b) steel layout from Yang et al. [57] (Reprinted from Structural and Multidisciplinary Optimization, 67(1), Yang Z, Zhou K, Qiao S, Topology optimization of reinforced concrete structure using composite truss-like model, 79–85, Copyright 2018, with permission from Techno.); (c) damage-based topology optimization from Amir and Sigmund [54] (Reprinted from Structural and Multidisciplinary Optimization, 47(2), Amir O, Sigmund O, Reinforcement layout design for concrete structures based on continuum damage and truss topology optimization, 157–174, Copyright 2013, with permission from Springer.); (d) STM-based reinforcement detailing from Silveira et al. [49] (Reprinted from Structures, 41, Silveira M V, Bitencourt L A, Das S, A performance-based optimization framework applied to a classical STM-designed deep beam, 488–500, Copyright 2022, with permission from Elsevier.).

Fig.15 Evolution of compliance and R_{FPS > 2} for wall with a window: (a) BESO; (b) M-BESO results.

Tab.3 Compliance and R_{FPS > 2} for wall with different truss layouts

Fig.16 FPS contours of wall with a window: (a) uniform steel structure; (b) BESO results; (c) M-BESO results.

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