Design of FRP laminates using evolutionary algorithms

Abstract

To address growing demand on fibre reinforced polymer (FRP) strengthening systems for reinforced concrete (RC) structures, some code proposals or recommendations have been published in different countries or continents. This work is focused on designing flexural and shear reinforcements, according to the specifications of FIB Bulletin 14 and EC-2. For the flexural strengthening of RC beams with externally bonded FRP soffit plates, different failure modes are reported in literature. In the case of flexural strengthening, failure can happen when exceeding the tensile strength of the FRP soffit plate or the compressive strength of the concrete, but most frequently, plate interfacial debonding or concrete cover separation are reported. Also in the case of shear strengthening, interfacial debonding of the FRP sheets or strips is more frequently reported than rupture of the composite material. Interfacial debonding failure occurs in a brittle manner, which is unacceptable from the point of view of structural safety. Consequently, many research works have focused on this important issue through both experimental and theoretical investigations and the existing design recommendations warn against this kind of brittle failure mode. This work is aimed at obtaining an optimum design for the flexural and shear FRP strengthening system of simply supported RC beams, subjected to the limitations and recommendations specified in FIB Bulletin 14. For that purpose, evolutionary optimization has been used. The formulation of the present optimization problem is minimizing the cost of the repairing or retrofitting (which is the objective function), subject to a series of design constraints specified in FIB Bulletin 14. The cost depends not only on the volume of FRP material used in the FRP reinforcement, but on the surface preparation work needed and the amount of adhesive required, as well. Some of the variables are of a discrete nature, and the search space of solutions for the optimization problem is controlled by the commercial standards available. Two databases or brochures have been prepared with the specifications of a manufacturer of FRP reinforcements for concrete structures. Other variables are the length of the FRP soffit plate for flexural strengthening and the number of U-jacketed sheets used for shear strengthening. An optimum design algorithm for flexural and shear strengthening of RC beams strengthened with FRP is presented. The proposed procedure minimizes the material cost associated to this kind of strengthening while satisfying the serviceability and strength requirements of the code proposal from European Community. A methodology for implementing commercial standard solutions is described, as well. As research on this reinforcing technique progresses and revisions of the existing guidelines appear, the introduction of new design constraints is simple and automatic since neither explicit variable functions nor gradient information are required by the optimization algorithm itself. With a simple example, an idea of the complex interaction between the design variables and constraints is given, yet the GA proves to be simple, systemic and automatic.