Numerical and Experimental Shape Optimal Design of a Hole in a Tall Beam

Abstract

Shape optimal design is a structural optimization process in which the boundary shapes of structures are optimized to meet a set of requirements. This is in contrast with early strategies which dealt mostly with the so-called sizing variables such as cross-section, length and width, rather than with the shape of boundaries. This thesis deals with the optimization of the shape of an interior discontinuity (hole) in a two-dimensional strucure, namely a tall beam. The objective is to find hole shapes with approximately uniform boundary stress to reduce the weight of the beam without increasing the maximum tensile stress originally present in the beam. Two approaches are used: 1. A numerical approach using finite element analysis, non-linear programming and interactive graphics.2. An experimental approach using photoelasticity. The hole shapes obtained from the two approaches match quite well. A CAD approach is also presented to simulate the photoelastic method. The methods described in the thesis can be used for a wide variety of two-dimensional structural problems, including reduction of weight, minimization of stress concentration and other design objectives.