Abstract:
This research presents a design optimization process that combines the finite element (FE) method, genetic programming (GP), and optimization solvers, i.e., genetic algorithm (GA) and nonlinear programming, for double-sided fiber-reinforced polymer (FRP) patches used to repair center-cracked steel plates under tension fatigue. An optimization statement is to minimize the patch volume and reduce the stress intensity factor (SIF) range at crack tips below the fatigue threshold range. A detailed three-dimensional (3D) FE model of patch-repaired cracked plates is developed to compute SIF. A total of 864 FE models of patch-repaired cracked plates with different combinations of design parameters are then analyzed to obtain a SIF database. Based on the database, a symbolic regression via GP analysis is implemented to develop a closed-form SIF solution that helps visualize the effects of design parameters on SIF, facilitates the repair design, and is used as an inequality constraint in the optimization. Finally, optimization solvers are employed to find an optimum solution (patch length, width, and thickness) that is then checked for patch rupture and debonding failure based on some failure criteria. An example is given to illustrate the design process. The example results reveal that the optimum patch design is significantly influenced by patch modulus, meanwhile, the effect of adhesive modulus is not pronounced. Furthermore, in view of debonding failure, the maximum Tresca and interfacial stresses significantly increase when adhesive modulus increases. As both stresses are relatively insensitive to patch modulus, the use of high modulus patch and low modulus adhesive is recommended for fatigue crack repairs. For large cracks, using a thick and high elastic modulus patch is the most effective.
