Optimization of Reinforcement for a Class of Openings in Plate Structures

A numerical/analytical procedure has been developed which yields the optimum amount of reinforcement for a given hole shape in a large elastic plate under prescribed boundary stresses. This procedure is based on determining the usual two complex potentials which describe the entire stress field, constructing the strain energy density function in terms of the unknown amount of reinforcement, integrating this function around the opening boundary, and finally minimizing this integral with respect to the reinforcement. The method is first developed for a general hole shape and then demonstrated in some detail for a circular and a square-like opening.