A systems approach to shape and topology optimisation of mechanical structures

Optimisation techniques have become more and more important as the possibility of simulating complex mechanical structures has become a reality. A common tool in the layout design of structural parts is the topology optimisation method, which finds an optimum material distribution within a given geometrical design space to best meet loading conditions and constraints. Another important method is shape optimisation, which optimises weight given parametric geometric constraints. In the case of complex shaped parts or elaborate assemblies, for example automobile body structures, shape optimisation is still hard to do; mainly due to the difficulty in translating shape design parameters into meaningful analysis models. Tools like the parametric geometry package SFE CONCEPT are designed to mitigate these issues. Nevertheless, shape methods usually cannot suggest new load path configurations, while topology methods are often confined to single parts. To overcome these limitations the authors have developed a method that combines both approaches into an Integral Shape/Topology Method (IST) that is capable of finding new optimal solutions. This is achieved by an automated optimisation loop and can be applied for both thin walled structures as well as solid 3D geometries. When optimising structures by applying IST, global optimum solutions can be determined that may not be obtained with isolated shape- or topology-optimisation methods.

An integrated approach to shape and topology optimisation of mechanical structures

In mechanical engineering, simulation and optimisation methods have become indispensable. The thesis looks into a novel way to combine shape and topology optimisation approaches. The proposed method - named IST for Integrated Shape And Topology Optimisation - proves to be beneficial for many application in the automotive and aerospace industry.

Simultaneous pattern and size optimisation of rock bolts for underground excavations

Designing a rock bolt reinforcement system for underground excavation involves determining bolt pattern, spacing, and size. In this paper, a topology optimisation technique is presented and employed to simultaneously optimise these design variables. To improve rock bolt design, the proposed technique minimises a displacement based function around the opening after bolt installation. This optimisation technique is independent of the material model and can be easily applied to any material model for rock and bolts. It is also extremely flexible in that it can be applied to any mechanical analysis method. To illustrate the capabilities of this method, numerical examples with non-linear material models and discontinuities in the host rock are presented. It is shown that the complexity of systems optimised using this approach is only restricted by limitations of the method used to analyse mechanical system responses.

Simultaneous material and structural optimization by multiscale topology optimization

Acknowledgments The authors acknowledge the support from Engineering and Physical Sciences Research Council, grant number EP/M002322/1. The authors would also like to thank Numerical Analysis Group at the Rutherford Appleton Laboratory for their FORTRAN HSL packages (HSL, a collection of Fortran codes for large-scale scientific computation. See http://www.hsl.rl.ac.uk/).

Shape and size of red blood cells from the Pygoscelid penguins of Antarctica using atomic force microscopy

Antarctic biodiversity is evolutionarily complex, reflecting the extreme ambient conditions. Therefore, Antarctic organisms exhibit sophisticated adaptations in all organization levels, including organs, tissues, and cells. Since red blood cells (RBCs) travel through the vertebrates blood delivering O(2) to all tissues and organs and purging the unwanted CO(2), they represent an interesting model to investigate biological adaptations. We have used atomic force microscopy (AFM) to compare the shape and size of RBCs of the Pygoscelid penguins. A total of 18 landmarks were measured in AFM images. When analyzed individually, the parameters were not capable of discriminating the RBCs of each species. However, the simultaneous use of multiple parameters discriminated (74%) among the RBCs. In addition, the use of RBC measurements was sufficient to hierarchically cluster the species in accordance to other common and reliable phylogenetic strategies. In light of these results, the use of RBC characters could effectively benefit taxonomic inferences.

Quantitative analysis of imprint shape and its relation to mechanical properties measured by microindentation in bone

Microindentation in bone is a micromechanical testing technique routinely used to extract material properties related to bone quality. As the analysis of microindentation data is based on assumptions about the contact between sample and surface, the aim of this study was to quantify the topological variability of indentations in bone and examine its relationship with mechanical properties. Indentations were performed in dry human and ovine bone in axial and transverse directions and their topology was measured by atomic force microscopy. Statistical shape modeling of the residual imprint allowed to define a mean shape and to describe the variability in terms of 21 principal components related to imprint depth, surface curvature and roughness. The indentation profile of bone was found to be highly consistent and free of any pile up while differing mostly by depth between species and direction. A few of the topological parameters, in particular depth, showed significant but rather weak and inconsistent correlations to variations in mechanical properties. The mechanical response of bone as well as the residual imprint shape was highly consistent within each category. We could thus verify that bone is rather homogeneous in its micromechanical properties and that indentation results are not strongly influenced by small deviations from an ideally flat surface.

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.