Improving finite element implementation in topology optimisation

Structural optimisation has the potential of producing substantial design improvements and cost reductions when applied to whole structures or structural components. Of the many possible directions of structural optimisation,... [ view full abstract ]

Structural optimisation has the potential of producing substantial design improvements and cost reductions when applied to whole structures or structural components. Of the many possible directions of structural optimisation, topology optimisation (TO) is the most challenging. On the other hand, TO has the most potential benefits in real-world applications as the whole structural layout and sizing are open to improvements, rather than member sizes only. With the development of new methods and availability of more powerful computers, TO progressed rapidly during the last 25 years. The initial difficulties encountered at the early stage of development are mostly resolved now. Many methods are currently available to carry out TO. Although there are many differences between different TO methods, they share one common aspect in the need to carry out structural analysis repeatedly. This part of TO is the most time consuming element and any improvement can produce significant efficiency improvements. Typically, finite element (FE) method is used to carry out that part of TO. FE is currently the most widely used general structural analysis method. However, its implementation in TO can be made more efficient. In this research, this task was achieved by improving the way in which the element stiffness matrix was related to TO. The particular properties of the four noded rectangular element, typically used in TO, were exploited to this end. Also, the way global stiffness matrix was handled during the repeated solution process. Different examples were solved to demonstrate the efficiency improvements. Results were compared with previously published ones and shown to be of similar accuracy.