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

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.