Quasi-Square Hole with Optimum Shape in an Infinite Plate Subjected to In-Plane Loading. Optimization of Inner and Outer Boundaries of Beams and Plates with Holes.

摘要

This paper (Report no. 58) deals with the optimization of the shape of the corners and sides of a square hole, located in a large plate and subjected to in-plane loads, with the object of minimizing stress concentrations. Appreciable disagreement has been found between the results obtained previously by other investigators. In this paper new tests have been conducted and discrepancies have been corrected. Using an optimization technique, the authors have developed a quasi square shape which introduces a stress concentration of only 2.54 in a uniaxial field, the comparable value for the circular hole being 3. The efficiency factor of the proposed optimum shape is 0.90 whereas the efficiency factor of the best shape developed previously was 0.71. The shape also is developed that minimizes the stress concentration in the case of biaxial loading when the ratio of biaxiality is 1:-1. This paper (Report no. 59) 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.