Optimal design of the fiber-reinforcement to strengthen existing structures

An original approach is proposed to define the optimal design of any unidirectional fiber–reinforcement to improve the structural performance of existing structural elements. A problem of topology optimization is formulated, simultaneously searching for the regions to be strengthened and the optimal local fiber orientation. The maximum equivalent stress in the underlying material is minimized, for a given amount of reinforcement. The Tsai–Wu strength criterion is employed, to take into account the different strength properties of the material in tension and compression and the possible material anisotropy. Tensile stresses along the fiber direction are not allowed in the reinforcement. The resulting multi–constrained min–max problem is solved by mathematical programming. A numerical example is presented to discuss the features of the achieved optimal layouts, along with their possible application to the preliminary design of any fiber reinforcement.