The role of topology and shape in structural design

When we design mechanical components, it is important to make the best use of material by choosing appropriate shape and material connectivity of the object being designed. Designers often make this choice intuitively. Given that human intuition can miss out on interesting design options that are mechanically efficient, this approach is never satisfactory in situations that are demanding in terms of the designs being light and strong (as in the aerospace industry). This proposal is an attempt to efficiently search optimal shapes and connectivity in an automated way.Complex mechanical objects require several geometrical parameters to describe this shape. Engineers have traditionally searched designs by altering the parameters and assessing the mechanical performance of the resulting designs by calculating stresses or deflections when the structure is loaded by given forces. Since complex designs require a large number of these geometrical parameters, the search is very time consuming; and given finite resources of the computer, it may be restrictive. Often the information that a designer is interested in is the change in the mechanical performance (the change in stress, for example) when the shape is altered in a relatively simpler way (such as by stretching in a particular direction or deforming in a specified way). The proposed research will make use of such shape changes to search efficient designs. Several mathematical descriptions will be used to describe shape changes. The nearness of shape will be compared with the nearness of mechanical response when similar shaped (but not identical) objects are stressed. This correlation will be used to find efficient designs while avoiding unaffordable amount of calculations.Studies on the role of connectivity (technically, topology) of solid material in a mechanical object will be carried out. The information about the change in connectivity and its relationship with the performance of a design will be used for finding optimal designs. Finally, the relative importance of connectivity and shape on mechanical efficiency of designs will be explored. The relative importance of shape and connectivity may depend on the stage of design. We will make use of this understanding to search efficient mechanical designs. Design search is primarily a theoretical and computation discipline because building and testing a large number of designs is impractical and economically infeasible. Therefore, the approach to be taken in the proposed research will be to build computer models and make quantitative assessments about the performance of each design. The novelty in the proposed research lies in the way design search will be carried out. The main elements of this are: (i) a novel approach to shape change description, (ii) use of shape sensitivity in the design search, (iii) understanding of the sensitivity of mechanical performance to alterations in connectivity, (iv) simultaneous optimisation of shape and connectivity, and (v) understanding of their relative roles in design.