Recent Progress In Preliminary Design Of Mechanical Components With Topology Optimization

Since 10 years topology optimisation has been trying to bring an efficient answer to the problem of automatic choice of morphology of mechanical components. This choice is one of the main questions to be addressed during the preliminary design phase of mechanical and structural components. By topology or morphology of a mechanical or structural component one means here all the basic data that touch the layout. So topology covers for example the number and the relative positions of the wholes in the structural domains, the number and the nature of the structural members, their connectivity and the character of the connecting joints. Before having topology optimisation tool, the selection of the mechanical morphology had been let to engineers’ experience or (even worse sometimes) to their intuition. For example it was a common use in industry to take the topology of an existing product and to use it as it is for the new design. With topology optimisation the choice of morphology can now rely on rational arguments and can be made in order to fit to the product characteristics. Furthermore mathematical tools, because of the optimisation formulation of the design problem, drive the determination of the structural layout. This has two advantages. At first topology optimisation can facilitate the automation of preliminary design steps. Then it can improve substantially the performance of new mechanical products. This means that topology optimisation can propose original and innovative solutions to engineering problems. Some authors suggested that in some problems topology could lead to a gain of performance that could grow up to 50 percents. This paper reports some novel contributions to topology optimisation techniques. Two areas will be addressed. The first one is concerned with recent progress related to the perimeter method of topology optimisation. The perimeter method, which was originally introduced by Haber et al (1996) in topology optimisation, consists in bounding the perimeter of the material distribution in addition to its area. At first recent research focussed on extending the method to 3-D structures. Then other work was made to new quasi-isotropic measures of the perimeter that are nearly insensitive to the mesh. The second axis of our work has been devoted to the treatment of stress constraints. We have continued along the initial work of Duysinx and Bendsøe (1998). The new developments were made to consider stress constraints in practical (industrial) design problems. Firstly we investigated the formulation of the problem in terms of global (i.e. integrated) stress constraints instead of the local stress constraints which can be very cumbersome for practical applications. A second research was devoted to extend the classic von Mises equivalent stress criterion to other kinds of criteria. Indeed in many cases such as in structures made of a material with unequal stress limits, the von Mises criterion is unable to predict a correct topology design. In order to include the effect of different behaviours in tension and compression, we are going to show that Raghava and Ishai quadratic criteria can be used. Finally in the final stage of the paper we will discuss the position of topology optimisation in the design chain. Usual answers in accordance with the current state of the art consider this topology tool as a preliminary design tool. However our experience lead us to a more complicated answer. In a similar way to stress constraints, the ‘optimal’ topology can be dependent on all the design constraints and not only stiffness performance. These constraints can come from the structural (or functional) behaviour, but they can also be related to the manufacturing aspects. Our experience showed that perimeter constraint is quite efficient to limit the design complexity in same cases, especially for planar structures. However this perimeter constraint can lead designs that are totally impossible to manufacture especially in 3-D. For example, perimeter constraint never prevents included wholes that would be impossible to carve out with some fabrication techniques. Thus we come to the conclusion that new progress in topology optimisation should be oriented towards a simultaneous approach of the design problem including most of the functional requirements as well as of the manufacturing restrictions