Introducing Design Space-Independence in Beam Cross-Section Optimization

Abstract

The cross-sectional topology optimization of a slender load carrying member such as a beam typically begins with the choice of design space which is generally either a square or a rectangle. However, when subjected to bending and torsional loads, such design space may often lead to biased topologies as the material distribution is directed towards the boundaries. As it may be difficult to avoid square/rectangular design space, this work introduces a constraint which may help in decreasing the dependency on the shape of the design space. The constraint is on polar first moment of area and is different from the traditional weight constraint in a way that it simultaneously constrains the weight and enclosed volume. The outcomes from the new scheme are compared with those obtained through conventional compliance- and weight- based topology optimization formulation.