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Volume 15
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10.3390/buildings15050664
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Article

Generation of Optimal FRP Layout for Strengthening Damaged Structures with a Local Displacement Constraint

by
Ping Yuan
1,
Yafu Cai
2,
Guodong Wang
2,
Xuhui Zhang
3 and
Lizhao Dai
2,*
1
School of Civil Engineering, Changsha University, Changsha 410022, China
2
School of Civil Engineering, Changsha University of Science & Technology, Changsha 410114, China
3
College of Civil Engineering, Xiangtan University, Xiangtan 411105, China
*
Author to whom correspondence should be addressed.
Buildings 2025, 15(5), 664; https://doi.org/10.3390/buildings15050664
Submission received: 21 January 2025 / Revised: 13 February 2025 / Accepted: 19 February 2025 / Published: 20 February 2025
(This article belongs to the Special Issue Structural Safety Evaluation and Health Monitoring)
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Abstract

Structural deflection is a critical factor used for evaluating the effectiveness of reinforcement. This study proposes a method for generating FRP layouts with a local displacement constraint to strengthen damaged structures. A local displacement constraint strategy is developed using the Lagrange multiplier method, integrating the constraint into the objective function and transforming the problem into an unconstrained optimization framework. The design sensitivity formula for strengthening damaged structures is derived based on this displacement-constrained strategy. Additionally, an automatic adjustment strategy of the Lagrange multiplier is given based on the bisection method. Finally, the effectiveness and applicability of the proposed method are illustrated through case studies on damaged RC beams, slabs, and arches. The FRP configurations under various constraints are discussed and compared with the results generated by the BESO method. Results demonstrate that the proposed method can effectively generate FRP configurations for damaged RC structures.
Keywords: local displacement constraint; damaged RC structures; Lagrange multiplier method; FRP configuration; automatic adjustment strategy local displacement constraint; damaged RC structures; Lagrange multiplier method; FRP configuration; automatic adjustment strategy

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MDPI and ACS Style

Yuan, P.; Cai, Y.; Wang, G.; Zhang, X.; Dai, L. Generation of Optimal FRP Layout for Strengthening Damaged Structures with a Local Displacement Constraint. Buildings 2025, 15, 664. https://doi.org/10.3390/buildings15050664

AMA Style

Yuan P, Cai Y, Wang G, Zhang X, Dai L. Generation of Optimal FRP Layout for Strengthening Damaged Structures with a Local Displacement Constraint. Buildings. 2025; 15(5):664. https://doi.org/10.3390/buildings15050664

Chicago/Turabian Style

Yuan, Ping, Yafu Cai, Guodong Wang, Xuhui Zhang, and Lizhao Dai. 2025. "Generation of Optimal FRP Layout for Strengthening Damaged Structures with a Local Displacement Constraint" Buildings 15, no. 5: 664. https://doi.org/10.3390/buildings15050664

APA Style

Yuan, P., Cai, Y., Wang, G., Zhang, X., & Dai, L. (2025). Generation of Optimal FRP Layout for Strengthening Damaged Structures with a Local Displacement Constraint. Buildings, 15(5), 664. https://doi.org/10.3390/buildings15050664

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