3D nonlinear finite element model for the volume optimization of a RC beam externally reinforced with a HFRP plate

► This paper highlights the optimization of the external reinforcement of RC beams by FRP. ► 3D nonlinear numerical model predictions compared well with measured FRP RC beam. ► Two optimization methods, called the sub-problem approximation method and the first-order method, are proposed. ► The most important optimization factor is the thickness of the FRP plate. In the present study, a numerical model is developed for the optimization of the external reinforcement of reinforced concrete beams by Hybrid Fiber Reinforced Polymer (HFRP) Plate. The model uses a finite element method adopted by ANSYS. To achieve this aim, a 3D nonlinear finite-element (FE) model is developed to study the behavior of concrete beams and plates with and without external reinforcement by FRP. Half of the full beam was used for modeling, taking advantage of the symmetry of the beam and loadings. Calibration and validation of the obtained results are compared to those given experimentally for different conditions from research. Comparisons made for load–deflection, load–strain and moment–curvature curves at mid-span show a good agreement between numerical and experimental results. The static nonlinear analysis is done to find the out ultimate capacity, formation of first crack, initiation of diagonal crack and its distance from the edges of HFRP plate. Parametric study is made to evaluate both effects of height and width of the HFRP plate on the retrofitted beam. Next, our model is used to optimize the volume of the HFRP plate which is bonded externally to the concrete beam. To obtain an optimal volume for our HFRP plate, two optimization methods, called the sub-problem approximation method and the first-order method, are proposed. For both methods, the program performs a series of analysis–evaluation–modification cycles: the design of the HFRP plate volume considered as the objective function is analyzed, the results are evaluated against specified design criteria, and the design is modified as necessary. The process is repeated until all specified design and state variables are met. The geometrical design variables are the height and width of the HFRP plate, and the state variables are the normal and shear stresses.