Optimization of inner and outer boundaries of beams and plates with holes

This paper presents optimized shapes of inner and outer boundaries for three specific problems: a long rectangular plate with a central hole subjected to uniaxial tension, a simply-supported slotted beam subjected to a load uniformly distributed over a small area at the centre, and a square plate with a central hole under uniaxial uniform pressure. The two-dimensional photoelastic method is used for optimization. The results indicate a significant reduction in stress concentration factor or in weight, or in both. The examples presented also include cases where the inner and outer boundary stresses are mutually dependent.