Simultaneous Topology, Shape and Sizing Optimisation of Skeletal Structures Using Multiobjective Evolutionary Algorithms

Abstract

A framework or skeletal structure is one of the most used structures in engineering applications. Using such a structure is said to be advantageous since they are simple and inexpensive to construct. It can be employed in many engineering purposes e.g. transmission towers, wind turbine towers, communication towers, civil engineering structures, and mechanical parts. In the past, the design of such a structure was usually carried out in such a way that the conceptual design stage was somewhat ignored and the initial shape of a structure had been formed by an experienced engineering designer. The classical civil engineering design approach is then applied in the preliminary and detailed design stages. Recently topology optimisation, an efficient tool for structural conceptual design, has been studied and used in a wide range of engineering applications. Considerable research work on the conceptual design of truss and frame structures by means of topology optimisation has been conducted in the last two decades (e.g. Hajela & Lee,1995; Ohsaki, 1995; Zhou, 1996; Yunkang & Xin, 1998; Hasancebi & Erbatur, 2002; Kawamura et al., 2002; Stolpe & Svanberg, 2003; Ohsaki & Katoh, 2005; Achtziger & Stolpe, 2007; Svanberg & Werme, 2007; Hagishita & Ohsaki, 2009). By the use of such design technology, the optimised layout of a skeletal structure can be accomplished. Having a structural layout from this design process, the shape and sizing design processes are then implemented. Nevertheless, a more efficient design approach can be achieved if a design problem is posed to have topological, shape, and sizing design variables at the same time. Much research work has been conducted towards combining and performing topology, shape, and sizing optimisation at the same optimisation run (e.g. Wang et al., 2004; Zhou et al., 2004; Tang et al., 2005; Shea & Smith, 2006; Achtziger, 2007; Martinez et al., 2007; Chan & Wong, 2008; Noiluplao & Bureerat, 2008; Zhu et al., 2008). The optimum design problem of the simultaneous topology/shape/sizing optimisation is usually structural weight minimisation subject to stress and other safety constraints. The optimisers employed can be a derivative-based method (Martinez et al., 2007), an evolutionary algorithm (Tang et al., 2005; Shea & Smith, 2006; Noiluplao & Bureerat, 2008), and a hybrid method (Chan & Wong, 2008). From the literature, most if not all of the optimisation problems are formulated to have one objective function, whereas in a O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg