Study On Some Problems Of Topology Optimization

Topology optimization is now a most challenging topic in the field of structural optimization. Topology optimization aims at finding the optimal distribution of materials in a prescribed design domain and the optimal way of component connection in a discrete structure. It is a valuable tool for designers since it can provide novel conceptual designs. Although a lot of achievment have been made in topology optimization, there are still some problems need further explorations. In this thesis, the topics about strong singularity phenomena and unified sizing, shape and topology optimization are discussed.In the first part of this thesis, we discussed the strong singularity phenomena in structural topology optimization. We pointed out the main distinctions between strong singularity problems in topology optimization and those which only have weak singularities. We illustrate the intrinsic features of strong singularity phenomenon through concrete examples and suggested the possible ways to solve this kind of problem.In the second part of this thesis, we discuss the numerical methods for unified sizing, shape and topology optimization. In our problem formulation, both topology description function (TDF) and the thickness function are used as design variables. In this way, size, shape and topology information are all included in the optimization model. The optimization problem is solved by mathematical programming approach with the used of sensitivity information. Numerical examples illustrate the effectiveness of the proposed approach.