Topology optimization is a powerful structural design method that determines the optimal configuration by distributing materials efficiently within a given design domain while satisfying specified load, performance, and volume constraints. Unlike size and shape optimization, topology optimization is independent of the initial design, offering a broader design space. This paper provides a systematic review of topology optimization methods, covering two theoretical frameworks: linear elasticity and nonlinear theory. Specifically, the review focuses on sensitivity analysis, optimization criteria, and topology solution smoothing within the context of linear elasticity. In the context of nonlinear theory, the review primarily addresses nonlinear phenomena arising from stress constraints, geometric, material, and contact nonlinearities. The paper concludes by summarizing the current state of the field, identifying limitations in existing methods, and suggesting directions for future research.

Compared with scaled-model testing, full-scale destructive testing is more reliable since the test has no size effect and can truly record the mechanical performance of the structure. However, due to the high cost, only very few full-scale destructive tests have been conducted on the flexural behavior of prestressed concrete (PC) box girders with girders removed from decommissioned bridges. Moreover, related destructive testing on the flexural behavior of a new precast box girder has been rarely reported. To investigate the flexural behavior and optimize the design, destructive testing of a 30-meter full-scale simply supported prestressed box girder was conducted at the construction site. It is illustrated that the failure mode of the tested girder was fracture of the prestressing tendon, and the corresponding maximum compressive strain in the top flange was only 1456 $\mu \epsilon$ , which is far less than the ultimate compressive strain (3300 $\mu \epsilon$ ). Therefore, the concrete in the top flange was not fully utilized. A nonlinear analysis procedure was performed using the finite strip method (FSM). The validity of the analysis was demonstrated by comparing the analytical results with those of the full-scale test in the field and a scaled model test in a laboratory. Using the developed numerical method, parametric analyses of the ratio of reinforcement were carried out. The prestressing tendon of the tested girder was increased from four strands to six strands in each duct. After the optimization of the prestressed reinforcement, the girder was ductile and the bearing capacity could be increased by 44.3%.

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To study the design method of openings on the web of an I-beam, three I-beams with different circular holes were designed using the traditional truss mechanism, and the circular holes were reinforced by ring stirrups. A shear test was performed to study the failure modes of the I-beams and efficiency of the ring stirrups. A new method for establishing the truss mechanism was proposed, which used the windowed evolutionary structural optimization method to calculate the topology optimization solution of the I-beam. From the topology optimization results, the strut-and-tie model (STM) was established, which revealed the stress mechanism of the I-beam. Via the STM, the optimal shape and location for the opening of the I-beam under shear load states were presented. The quantity of reinforcing bars, porosity and ultimate load of the I-beam designed by the STM were, respectively, 0.67, 5.5 and 1.2 times those of the experimental model.

To investigate the impact of the filament winding angle of glass-fiber reinforced plastic (GFRP) on the seismic behavior of GFRP tube ultra-high performance concrete (UHPC) composite columns, this study designs two types of GFRP tube UHPC composite columns. Quasi-static tests are conducted on the specimens subjected to horizontal reciprocating load and axial force, and the skeleton curve characteristics of the structure are analyzed. Furthermore, a finite element analysis model of the composite column is established to explore the effects of the diameter-thickness ratio, circumferential elastic modulus of confined tubes, and tensile strength of concrete on the seismic performance of the composite column. The analysis includes a review of the skeleton curve, energy dissipation capacity, and stiffness degradation of the structure under different designs. The results indicate that the use of GFRP tubes effectively enhances the seismic performance of UHPC columns. The failure mode, peak load, and peak displacement of the composite columns are improved. The finite element analysis results are in good agreement with the experimental results, validating the effectiveness of the analysis model. Extended analysis reveals that the bearing capacity of the specimen increases while the energy dissipation capacity decreases with a decrease in the diameter-thickness ratio and an increase in the circumferential elastic modulus. Although the tensile strength of concrete has some influence on the seismic performance of the specimen, its effect is relatively small. Through regression analysis, a formula for shear capacity suitable for GFRP tube UHPC composite columns is proposed. This formula provides a theoretical reference for the design and engineering practice of GFRP tube UHPC composite columns.