Structural optimisation using the principle of virtual work

Abstract

This dissertation presents a new method for the automated optimisation of structures. The method has been developed to: (1) select sections to satisfy strength and deflection requirements using minimum material, and (2) efficiently group members. The member selection method is based on the principle of virtual work, and is called the Virtual Work Optimisation (VWO) method. It addresses multiple deflection and load case constraints simultaneously. The method determines which sections provide the highest deflection and strength resistance per unit mass. When compared to several other methods in the literature, and designs from industry, the VWO method produced savings of up to 15.1%. A parametric investigation of ungrouped, multi-storey frames is conducted using the VWO method to determine optimal mass and stiffness distributions. Unusual mass patterns have been found. Diagonal paths of increased stiffness are formed in the frames, which suggests truss behaviour. A grouping algorithm is presented which determines how efficiently to create a specified number of groups in a structure. The VWO method has been incorporated into the automated algorithm to optimise the grouped structures. Members are grouped according to their mass per unit length. In the algorithm an exhaustive search of all feasible grouping permutations is carried out, and the lightest structure selected. Results produced are up to 5.9% lighter than those obtained using ad hoc grouping configurations found in the literature and based on experience.